MUSI
ML
3812
.C24
PES
A 1,270,645
ESSAY
THE
WTH
THE
SICAL
ALE
DOF
DERN
HONY
NIVERSITY OF MI
MICHIGAN
16
Andrus
1911
HL·LIB
&
R
AN ESSAY
30130
ON THE
Growth of the Musical Scale
AND OF
MODERN HARMONY
BY
ohn
J. Moore
CAPES, M.A.
LONDON: NOVELLO, EWER & Co.,
I, BERNERS STREET (W.), AND 80 & 81, QUEEN STREET (E.C.)
lusic
ML
30Z
NOVELLO, EWER AND CO.,
TYPOGRAPHICAL MUSIC AND GENERAL PRINTERS,
I, BERNERS STREET, LONDON (w.)
DEDICATION.
to
me
an
MY DEAR DR. STAINER, -I cannot deny myself the
pleasure of dedicating this little book to you,
partly in acknowledgment of the great advantage
I have derived from your very valuable suggestions,
and partly because of your warm encouragement
to publish what I have written as
important contribution towards the advancement
of true musical science. It was also through reading
your “ Theory of Harmony, founded on the Tempered
Scale,” which I had long believed to be the only
theory that could bear any really scientific investi-
gation, that I was induced to attempt a short and
systematic demonstration of the physiological truth
of the views upon which your treatise was based.
I cannot, indeed, hope that you will be able to agree
with me in every opinion or statement which I have
here put forth ; but, at the same time, I trust that you
will accept this expression of my sense of what is
due to you, both from the music-loving world in
general, and especially from myself.
Believe me,
Yours very truly,
J. M. CAPES.
PREFACE.
THE study of the origin and growth of spoken
languages, modern as well as ancient, is one of the
most striking characteristics of the literary work of
to-day. English scholars in particular have dis-
covered that the language which was once held to
have hardly had any existence as the speech of
Englishmen, before the times of Shakspeare and
Spenser, had its real birth in a remote antiquity, and
that its pedigree is as well worth examining and
recording, at least to us Englishmen, as the birth
and growth of the speech of Homer and Plato and
Sophocles.
It is, therefore, in harmony with the spirit of all
modern philology that an attempt should be made to
trace the origin and growth of musical language, as
a result of those physical laws, which have hitherto
vi
PREFACE.
been studied almost exclusively by men who were
physicists and nothing more. For the music of Bach
and Beethoven possesses as truly a physiological
history of its own as does the poetry of Milton and
Byron possess a philological history. No purely
musical history of their works can be satisfactory or
profound which is not preceded by a correct percep-
tion of those great atmospheric facts upon which all
music is actually based.
In the following pages I have made an attempt to
analyse, from the scientific as well as the musical
point of view, the origin and growth of all modern
music, as an achievement of the human intelligence
under the influence of the phenomena of sound. I
need hardly say that though, to myself, the conclu-
sions which I here lay before the reader appear to
be correct, my little work is only an attempt, an
Essay,” after all. I do not know whether or not
ine same attempt has been made before me, and I
am therefore especially liable to all those errors
which beset the path of every one who ventures into
a field of science hitherto unexplored.
PREFACE.
vii
Of the existence of the great fact upon which my
conclusions are based there can be no doubt what-
ever, though it has been hitherto little, if at all,
recognised by any of the various learned writers to
whom we owe the construction of musical grammar
and theories. Marked attention has, however, been
lately called to its existence by Professor Helmholtz,
who has discovered in its mysteries (for such they
may be called) the cause of those inexplicable varia-
tions in what musicians call the 66 quality" which
distinguishes one instrument from another. This
fact is the composite nature of every single musical
tone. In this composite nature I have endeavoured
to detect the origin of the musical scale, and the
processes by which the first steps of modulation are
suggested to the mind. I have endeavoured, further,
to show that the only settlement of the conflict
between the theories of equal and unequal tempera-
ment can be attained by a resolute reference to this
fact, that no single musical sounds exist, or ever can
exist, and that the aim of the theorist of the future
should be to reconcile the necessities of key-relation-
ship in the structure of harmony with the undeniable.
viii
PREFACE.
truths of atmospheric movement. Those movements
are among the most complicated which the whole
physical universe presents to the analytical skill of
the learned in physical science. * Possibly they are
beyond the powers of all human analysis, however
momentous is their influence on all spoken and all
musical speech.
The study of the physical origin and growth of all
melody and harmony is further a necessary qualifica-
tion for the study of music as a progressive art. In
a late address to the students of the Royal Academy
of Music, Professor Macfarren wisely urged upon his
hearers the impossibility of their understanding the
music of the present without a careful study of the
* The number of the collisions of every particle in the com-
bined gases which we call the atmosphere, occasioned by every
musical sound, is beyond all calculation. At each sound the
atmosphere is set in motion in every possible direction, both
directly and by reflection. These movements cross and thwart
one another in a degree which imagination fails to realise. We
can only feebly dream what must be the result, when we
remember that, by the latest calculations, every particle in a
mass of hydrogen, at ordinary temperature and pressure, has on
the average 17,700,000,000 collisions per second with other
particles.
PREFACE,
ix
works of the whole series of great composers from
the time when modern music was first created. And
I would venture to add, that such a study would be
rendered much more easy if Mr. Macfarren, or any
other equally learned and competent musician, would
compile and publish a selection of passages from the
writings of the great masters themselves, showing the
consecutive steps by which modulation has been
carried onwards, from the modesty and simplicity of
the sixteenth century to the freedom and boldness
(not to say audacity) of the nineteenth.
I will only add that it is with no little diffidence
that I offer this essay to the learned, as well as to
those who are beginning their study of the divine
art. Especially, perhaps, may I be thought to have
laid myself open to censure in the opinions I have
put forth as to the difference in essence between the
major and the minor modes, and of the absolutely
artificial nature of the leading" note in the diatonic
scale, however necessary may be its creation to the
existence of all true harmony as well as melody.
I can only ask those learned musicians who may be
X
PREFACE.
disposed to reject my views, to regard the theory here
advanced as a whole, and to consider whether any
other can be reconciled with the unquestionable laws
of musical sound.
J. M. CAPES.
8, Blandford Square, London, N.W.,
November 1876.
ERRATA.
Page 15, line 8 from top, for “E” read “C”
33, line 6 from bottom, for
66 half"
quarter” read
51,
- inferior
09
read
line
4
from top, for
" superior"
, 60, line 9 from bottom, for " sounded. When"
read " sounded, when"
103, line in music, for "saufte” read " sanfte
”
CONTENTS.
CHAPTER I.
PAGE
Object of present work: the simplification of
the study of musical science by recurrence
to the first laws of musical sound.--Dif-
ference between the structure of ancient and
modern versification. --Difficulties arising
from the inconsistencies of ordinary
nomenclature.- Perfect and imperfect inter-
vals.-Harmonics, with their relation to
the diatonic and chromatic scales.--Dis-
sonances and consonances, which of the
two is the more agreeable to the ear? ...
I
CHAPTER II.
Difference between music and noise.-Modern
music essentially a natural growth. Its
early stages. Music the creation of
modern times, every other art having its
origin in the classical period.-Invention
of the semitone, and of the octave as the
limit of melody.--The composite nature
of all single tones.-Symmetry of form a
necessity in the works of man; its rarity
in the works of nature
22
xii
CONTENTS.
PAGB
CHAPTER III.
The minor scale; its probable origin, and dif-
ference in essence from the major.-Con-
cordant and discordant sounds.-What
chords are most agreeable to the ear?
Perfect and imperfect intervals.-Differences
in degree of dissonance.-The common chord
the necessary basis of all modulation
52
CHAPTER IV.
Chords made up of a series of thirds.-The
necessary influences of the chords of the
dominant and of the flat seventh.–Naked
fifths ...
78
CHAPTER V.
Key-relationship in complicated harinonies
102
CHAPTER VI.
First attempts at harmonies.--Consecutive
octaves and fifths
108
CHAPTER VII.
Equal and unequal temperament. --- Claudio
Monteverde.-The diminished seventh
118
CHAPTER VIII.
The pedal point
135
CONCLUSION
...
142
:
CHAPTER I.
Object of present Work: the simplification of the study of
musical science by recurrence to the first laws of musical
sound.--Difference between the structure of ancient and
modern versification.—Difficulties arising from the incon-
sistencies of ordinary nomenclature.- Perfect and imperfect
intervals.—Harmonics, with their relation to the diatonic
and chromatic scales.—Dissonances and consonances; their
respective effects upon the ear.
.
I. My object in writing this little book is to
satisfy the desires of a large number of intelligent
persons with whose feelings I sincerely sympa-
thise. They love music, but they are conscious,
and often pathetically confess, that they do not,
as they say, "understand" it; and they are sure,
moreover, that to be “a good musician” means
something more than to be able to play difficult
music, or to sing at sight. There are hidden
mysteries, they do not doubt, in the divine art;
and it is their belief that the key to these mys-
teries is to be found by "learning harmony," as
it is termed, or, as the last generation more com-
monly called it, “thorough bass." Now and then
in some old music book they meet with long pas-
sages consisting of a bass part only, with figures
written under most of the notes, wearing a caba-
B
2
listic look, but entirely incomprehensible to their
present-day understanding.
2. Then, again, they often wish that they could
write a little music themselves, or even extempo-
rise on the pianoforte, though this last is a some-
what presumptuous aspiration, which they do not
venture publicly to avow. Tunes come into their
heads, in a sort of deformed shape, it is true, but
still really tunes; and they lament that they
cannot "put a bass to them,” for when they try
to play their bass upon the pianoforte their ears are
dissatisfied, and they know that they are making
some horrible blunders, while how to set them-
selves right is beyond their power. Nor are they
to be blamed for this, any more than people who
love poetry and learn to write English are to be
blamed for wishing to write verses of their own.
3. Or, again, they are puzzled by what they
read and hear about music and musical instru-
ments, and about the composers of different ages,
and they wish to understand what it all means,
and whether it is not a foolish trifling after all.
Just now, there are an unusual number of sub-
jects which trouble the musical world in its many
varieties, of which the chief are Gregorianism
3
and the tuning of organs. What can possibly,
they ask, be the reason of the extraordinary diffe-
rence between all modern European music and
the Gregorian plain chant ? And just the same
sort of difference, they see, is to be discerned
between modern European music and many old
Scotch and Irish airs. If they have friends who
have heard the national music of the Turks or
the Chinese or other Oriental nations, the same
unaccountable phenomenon is to be found every-
where. A Turkish lady protests that Europeans
incessantly sing out of tune; while the same
Turkish lady's own performance is absolutely
excruciating to the Western ear. Why is all
this ? the meditative amateur asks himself:
is there any reason for these differences in
the necessary constitution of man ? Was it
an inborn peculiarity of the Celtic blood which
caused so many Irish melodies to seem as if they
have neither beginning, middle, nor ending ?
Why, if one sits down to the piano, and plays
indiscriminately upon the black keys within the
compass of an octave, does the result seem
exactly like a Scotch song or dance ?
4. Further, these Oriental and other melodies,
being ancient, may they not bear some affinity to
4
the old Greek music, of which such curious things
are said by old Greek writers ? Nobody, indeed,
knows exactly what Plato and other Greeks
meant in what they wrote concerning the melodies
to which they attributed such marvellous effects;
but one thing is certainly clear. They divided
their musical scale on a system different from our
own; and they apparently used sounds less widely
separated from one another than our sounds,
which are separated by what we term a semitone.
Were, then, the Greeks wiser than we are ? As
sculptors, we are as children in their presence.
Were their ears so correctly attuned to the
highest laws of musical beauty that their “ Ly-
dian" or “ Dorian” or “ Phrygian” measures were
as much above the symphonies of Beethoven as the
marbles of the Parthenon are above the statues
which decorate the squares and streets of London ?
There is, again, a fundamental difference between
the structure of our modern music and that of
classical antiquity, arising from the change that
has taken place in our ideas of pronunciation
and of versification. All modern poetry depends
for its rhythm and musical beauty upon a fixed
and rigorous adherence to certain syllabic arrange-
ments, differing absolutely from those which were
5
invented by the Greeks and Romans, and still
further by the introduction of rhyme, a thing
unknown to the ancients. This change in the
conception as to what constitutes verse, as
distinguished from prose, was the necessary
consequence of the loss of those fixed" quantities"
in the utterance of words which were characteristic
of Greek and Roman utterance. But as the know-
ledge of even the elements of Greek and Latin is
unfortunately still confined almost entirely to
men, and is by no means universal among men
who wish to study music, it is necessary to
explain that in Greek and Latin nearly every
syllable had a fixed “ quantity” of its own,
according to which it was dwelt upon for a
greater or less length of time. We have nothing
in any modern language which exactly corre
sponds to this conception of quantity. It is
not the same thing as accent or as emphasis,
though it bears a species of similarity to both of
them. It seems, in truth, that the full significance
of the idea of “ quantity” is really unknown, even
to the most accomplished of scholars, and that no
human being exists who could recite a chorus of
Sophocles or an ode of Horace precisely as
Sophocles or Horace would themselves have
recited them.
6
The utterance of ancient Latin, and still more
of Greek, being thus at once strengthened and
enriched by a thousand delicacies unknown to
ourselves, their versification did not require that
strongly marked and measured beat without
which modern versification is almost impossible ;
and still less did it require the assistance of those
rhymed terminations without which, except in
the heroïc measure, blank verse is felt to be
scarcely versification at all. As the old Greek
poetry was thus more free in its movements than
our modern verse, so it was quite possible for
Greek music to be always of the nature of a
recitative. In fact, it was always recitative, or,
in another form, a chant; like the Gregorian
music in the Roman Catholic and Greek churches,
and like the music of all Oriental or semi-civilised
nations.
When, then, the old Roman tongue was lost
in the irruptions of the northern barbarians, and
the languages of modern Europe, especially the
Italian, the Spanish, and the French, rose by
degrees out of the ruins, the new tongues were
destitute of the refinements and rules' of antique
quantity.” The poetry of the middle ages
appeared as a versification of rigid beats, and an
7
ill-matched alliance grew up between the ancient
chant and the modern measures. And hence it is
that when music first became a really living art,
through the invention of the modern scale, the
entrance of the bar was for many years practi-
cally obstructed. Melody itself for some time bore
the marks of its origin, in the chant or recitative.
No one can study the works of Palestrina, of Orlando
di Lasso, and even of our own early madrigal
writers, without recognising this peculiarity in
the structure of their themes or subjects; and I
think that every cultivated musician will agree
with me in the opinion that the skill with which
these early masters worked out their melodies in
the shape of elaborated fugue-like harmonies
constitutes one
of their chief claims to our
admiration and to the study of their works.
At length, however, the bar triumphed, following
the leadership of modern poetry, and the develop-
ment of the resources of harmony, impossible with-
out its measured divisions of time, went on un-
hindered. The recitative still remains, and always
will remain, as the form most adapted to declama-
tion and recitation ; while the observance of those
many delicacies and modifications of time which
constitutes what we call phrasing, marks the
8
difference between the true player and the mere
mechanical performer. It is to be observed, too,
that in Beethoven's latest works, both for piano-
forte and orchestra, and in his mass in D, some
of his most exquisite melodies are less strongly
marked with the sentiment of the “bar” than are
his other writings or those of any other of the
greatest masters.
5. The question of tuning and temperament is
another matter which exercises the minds of
organists and organ-builders of a school not yet
passed away, and is destined to exercise the minds
of musical theorists for many years to come.
How bewildering are the sensations of many an
unlearned but enthusiastic musical amateur when
he or she goes into a large church or hall, and
hears the organist, or perhaps the rector, in a
rapture of delight at having accomplished, at no
little cost, the retuning of his organ upon the
“equal temperament” principle, and so having
got rid of that horrible “wolf” which, especially
on damp days, made the performance of modern
music a source of positive physical torture.
"Is it a fact," immediately asks the visitor, “that
an organ is tuned upon one plan and a pianoforte
9
upon another? And is there any truth in what is
sometimes said as to the powers of violin players
to play really correctly, while the players upon so
many other instruments are fated, by the laws of
sound, always to play wrong?”
6. The song of birds is another source of puzzle
to the lover of music. Try, what one will, it is
impossible to reproduce their exquisite melodies
upon any instrument whatever. Ingenious singers
or whistlers succeed in producing something like
a correct imitation of the song of some few birds,
though the effect is more curious than agreeable.
But to reproduce their warblings on the piano-
forte, or even the flute, is simply impossible, for
we have no sounds at our command which corre-
spond to the intervals between the notes in their
melodies. Even the two simple notes of the
cuckoo cannot be given with real accuracy. How
is this, then ? What is the reason, if there is any
reason, why there should exist this radical dis-
crepancy between the lovely carolling of the
woods and fields and the music of the concert
room? Is the song of birds founded upon the
true laws of musical beauty, while the music of
man is at best an artificial and arbitrary invention
which delights us only because of our uncultivated
ΙΟ
ignorance, just as the women's clothing invented
by the fashionable dressmaker of the hour pleases
the ordinary mind more than the most perfect
drapery that grew into form under the Greek
sculptor's chisel ? Is there truth, after all, in
Pope's biting sarcasm,
"Strange that such difference there should be
'Twixt tweedle-dum and tweedle-dee?"
7. In the following pages I propose to consider
these and similar questions, and to show the
intelligent lover of music that the rules of modern
harmony are founded on the unchangeable facts
of natural musical sound; and that their study, as
such, not only materially increases our enjoyment
of the works of the great musical composers, but
enables us, if we are disposed, to write real music
of our own, simple or elaborate, according as we
may prosecute the study of harmony, and its
development, counterpoint, in books which treat
fully on the subject in its various details. My
special aim is to show the student what are the
principles of harmony, rather than to repeat the
minute rules which are to be found in the works
of theorists, explaining, however, those few funda-
mental rules which are the immediate result of
the application of these principles to musical
composition in its simpler forms.
II
8. These principles will be most easily under-
stood if we adopt a method of study which differs
from that which is generally found in ordinary
works on the science and art of music. The sub-
ject will, I think, be made especially attractive to
the student if it is treated at once scientifically
and historically, so that he will clearly understand
all along what is the meaning of every word that
is used, and what is the reason why each assertion
is made and each rule laid down. With the
ordinary amateur, and with very many profes-
sional students also, the study of the theory of
music is often made needlessly difficult and repel-
lent because he fails to comprehend the precise
meaning of the terms that he hears employed,
and because his memory is thus overloaded with
technicalities whose value he has not thoroughly
mastered.
9. It is difficult, indeed, for advanced musicians
to understand the extent of the repulsion which
beginners feel in the study of harmony, from the
defective nature of our musical nomenclature.
That nomenclature, like the pronunciation of all
languages, and especially that of the English
language, has grown up by degrees, and the
bewilderment which our English pronunciation
I2
causes to foreigners is naturally extreme. Con-
ceive, for instance, the astonishment of a French-
man or Italian when he learns that the syllable
ough” is to be pronounced in eight different
ways, namely, as oo in “through,” as ov in
“plough,” as off in “cough,” as uff in “enough,"
as ock in “hough," as o in “dough," as au in
ought," and with a brief unspellable sort of
grunt in "thorough.”
10. Just such is the confusion of the beginner
in music when he is told to master the technicali-
ties of that strange mingling of the diatonic scale,
the chromatic scale, and the actual laws of
musical sound which constitutes the basis of our
musical nomenclature. All that he really under-
stands is this : that between any two of the
notes that are called octaves there is a surprising
likeness mingled with a real difference, and that
the farther the two octaves are removed from one
another on the pianoforte, the greater seems the
difference between them. He knows also that
the space between the two sounds of the octave
is divided on the pianoforte into twelve divisions,
and when all these divisions are taken in strict
order, the whole is called the “ chromatic scale."
If he knows a little Greek and Latin, he is aware
13
that the term " chromatic scale ” must be a com-
pound of a Greek with a Latin word, and must
mean something like a “coloured ladder," and if
he is not very dull he will see at once that this
particular scale is meant to include all the various
shades of sound between the two octaves. But
as to the meaning of the term “the diatonic
scale," his Greek and Latin leave him utterly at
fault. He is told that all music is written in the
diatonic scale, either major or minor, and with
that important information he must be satisfied.
II. When he proceeds to his study of harmony
his real confusion begins. The diatonic scale he
sees consists of seven notes-C, D, E, F, G, A, B,
and then the C again.
6
E
RA
E F G A B C
It seems quite right, therefore, that these notes
should be called the second, the third, the fourth,
the fifth, and so on, according to their distance
from the lowest C. Then begins a process which
reminds him of the sleight-of-hand tricks of a
conjuror operating upon a pack of cards. From
C to G is called a fifth, which he sees to be the
fact by the use of his eyes. But then he is
14
con-
informed that it is something far more mystical
than simply a fifth. It is not only a fifth but a
“perfect" fifth, while he is left to guess wherein
consists this "perfection," and is equally left in
the dark as to the particular note which is to be
regarded as the “imperfect” fifth, standing in
this strange relationship to its “perfect
gener. All that he sees is that there is no such
remarkable entity to be detected in the scale
itself. If sounds are counted upwards from the
lowest note of the octave, well and good; G is
the fifth from C. But if they are to be counted
upwards from the lowest note in the only other
scale in existence, that is, the chromatic, G is the
seventh.
oto
to-
to
Nevertheless, the student is ordered to call the
fifth a major or perfect fifth, and the interval
between the C and the flattened G a minor or
imperfect fifth. He is thus impressed with the
conviction that some deep relationship exists
between
and
t
15
whereas in reality the real fifth is the most con-
cordant of all unions of sounds, next to the octave,
while the union of the "imperfect" fifth is a
frightful discord.
12. Something of the same kind of confusion
arises when the word "augmented” is introduced;
as, for instance, between C and G# and between
CE and B#, which are called respectively the
augmented fifth and the augmented seventh,
whereas there is only a partial relationship between
them. As the words are frequently used, we
might just as rationally call a man our first cousin
because he lives next door to us in a row of
houses, while there is only a distant trace of
blood relationship between us.
13. A similar confusion results from the use of
the words “major” and “minor thirds” in two
different senses. A “major third” means an
interval of four semitones, a “minor third” an
interval of three. This is what the words mean
when they are applied to sounds as realities, and
used in this way they are not particularly objec-
tionable, inasmuch as “major" meaning "greater"
in Latin, and “minor” meaning "less," it is not
absolutely nonsensical to call an interval of four
16
semitones the greater and an interval of three the
less. The practical mischief lies in this, that
when used to designate two varieties of the dia-
tonic scale they convey an entirely false idea of
the real relative musical relationship of the sounds
in question, inasmuch as the origin of that rela-
tionship is essentially chromatic, depending upon
semitones and not upon the intervals of the
diatonic scale. The essence of their relationship
lies in this, that they are to one another as the
number four is to the number three, and that to
call both of them "thirds" is incorrect and untrue.
As materials for harmony they depend (as I shall
hereafter show) upon their relations to that vast
composite tone which is produced by the sounding
of any single string or tube, tuned to a low pitch,
which, though popularly regarded as a pure un-
mixed sound, is, in fact, a combination of all the
harmonics of the sound itself.
14. The assumed relationship between the
major and the minor scales is indeed one of the
most serious difficulties which beset the path
of the young musical student; a difficulty which,
if my ideas are correct, is materially increased by
his want of all knowledge of the physiological
and historical origin of the scale. If the views
17
which I am about to offer to the student are
correct, while the major diatonic scale is essen-
tially natural, the minor diatonic scale is, to a
great extent, artificial. And hence it is that
while there is but one form of the major scale,
one only being possible, there are three or four
forms of the minor scale, the flattened third being
the only peculiarity in which they all agree.
Hence, too, the extremely unsatisfactory cha-
racter of the usual signature of the minor scale,
which, in all consistency, ought to indicate that
one peculiarity in which the minor always differs
from the major, leaving all other flattening of
tones to be treated as accidental” wherever it
occurs. It is in this question, indeed, that I fear
that I must expect dissent, even from those whose
views I am bound to regard with the utmost
respect. Admitting that for the sake of con-
venience, and perhaps from the necessities of
composition, the major and the minor scales must
both of them be called scales, and usually treated
as real scales, I cannot admit that physiologically
they are scales in the same sense. I cannot
admit that the common chord of a minor scale
has the same foundation in the facts of harmonics,
and in the great overlooked fact of the composite
nature of every musical sound, in which I per-
С
18
ceive the actual origin of the major scale, and
the explanation of the mysterious growth of the
musical art from Palestrina to Beethoven.
only ask for a fair consideration of the acoustical
facts of the case.
I can
15. So, again, with the extraordinary use of the
word “perfect” in connection with the idea of
concord. Surely the idea of perfection is that of
excellence. Any work of art, like any machine
or other human invention, approaches perfection
just so far as it attains the end for which it was
devised. No one would have the folly to say that
the solar system is imperfect because the year
consists of three hundred and sixty-five days and
a quarter, and that it would have been more
perfect if the solar year had exactly coincided
with a certain number of the revolutions of the
earth on its axis, so that the year would have
been exactly three hundred and sixty-five days
long. Yet this is just the kind of dreaming
which has led to the use of the words. "perfect "
and “imperfect," as applied to certain intervals
and chords in the musical scale. Thus, the interval
ween C and Gb is called an “imperfect" fifth,
and the interval of the sixth is called "imperfect,"
whether it is a "major” or “minor” sixth.
19
16. In reality the greater or less degree of per-
fection in a chord depends solely upon the degree
of pleasure which it conveys to the mind through
the ear, and whether or not that pleasure depends
upon certain arithmetical relations between the
combined movements of the air by which those
sounds are produced is of no moment whatsoever.
It may be quite right and desirable to call certain
intervals more or less consonant or dissonant,
which is the statement of a physical fact. But
by degrees of perfection and imperfection we
mean something which more or less attains the
end of its existence. And therefore those intervals
and chords which most completely satisfy the
emotions and the intelligence are the most com-
pletely perfect, whatever the variety in the
vibrations of the air by which they are produced.*
17. It is, then, misleading to the student to
confuse the greater or lesser degrees of perfection
in chords as music, with their greater or lesser
degrees of numerical consonance as sounds. In
truth the whole progress of the musical art has
* Dr. Stainer has vigorously attacked the old superstition
about perfect and imperfect intervals in the 2nd and 3rd Chapters
of his " Theory of Harmony," and what I here say is in entire
agreement with his principle, except that I enter rather more into
details.
20
depended upon the success with which the great
masters have established the close relations of
chords and melodies as music, in the teeth of the
resistance of those who were enslaved to the
old superstitions about perfect and imperfect
arithmetical combinations. It is just like the
progress of the art of war. The advance of the
military art has been a struggle between genius
and common sense on one side, and pipe-clay,
pig-tails, and the rules of parade on the other.
18. There is one further objection to the
perpetuation of the old phraseology about per-
fection in chords, which deserves a few words of
notice. It is undeniable that men's minds are no
more exactly alike in their fondness for certain
combinations of sounds than they are exactly
alike in their faces. Minds equally sensitive to
musical beauty and truth, and equally cultivated
and unprejudiced, do certainly differ in their
preference for the works of certain composers ;
that is, in other words, for certain combinations
and sequences of chords and melodies. One
person will thus call one interval more perfect,
and another another, thus furnishing us with an
additional reason for discarding the use of the
word altogether.
21
19. One more obstacle—and that of the utmost
importance—in the student's path must be cleared
away before he can fully understand the nature of
the study on which he is entering. He has been,
in all probability, brought up in the belief that
music consists in a correct arrangement of sounds,
each of which is pure and single in itself; whereas,
in fact, there is no such a thing in nature as a
pure and single musical sound. He has also
supposed that what the mind most loves as sooth-
ing and suggestive of repose, completeness, and
intellectual and emotional harmony, is a "concord
of sweet sounds," in which there is nothing of what
is commonly understood as discord and harshness,
and in which sounds seem to melt into one another
so as to become apparently one. The reverse is
the truth. The mind loves dissonance rather than
consonance, and pure concords would be simply
repellent. The aim of musical science is to
ascertain what discords and what concords and
what successions of discords and concords are most
agreeable to the mind, and in what manner the
rigidity of rules and the individuality of liberty can
best combine to awake in the heart and head those
profound thoughts and emotions which music can
call into life with a united force and tenderness
beyond the reach of any other art of man's devising.
CHAPTER II.
Difference between music and noise.--Modern music essentially
a natural growth. Its early stages.—Music the creation of
modern times, every other art having its origin in the classical
period.--Invention of the semitone, and of the octave as the
limit of melody,—The composite nature of all single tones.-
Symmetry of form a necessity in the works of man ; its rarity
in the works of nature.
20. What, then, in the first place, is musical
sound ? The question may be thought super-
fluous, and the answer to it may seem to take the
student into a region of inquiry into which it is
needless that he should enter. Nevertheless, it
is necessary that the full meaning of this answer
should be thoroughly mastered, as upon its com-
prehension depends all understanding of the laws
of musical science. Musical sound, then, is the
effect upon the ear of the rapid movement of the
atmosphere, in pulsations equally distant from one
another in time. These pulsations or, as they
are usually termed, vibrations, are produced
primarily by the vibrations of any solid bodies
which are capable of being made to move to and
fro at equi-distant and quickly succeeding inter-
vals. Upon the greater or less rapidity of these
vibrations depends, in other words, the height or
23
the depth-the pitch-of the musical sounds thus
generated. Unless the vibrating substance sets
in motion a column which repeats its strokes
about thirty-three times in a second, no distinctly
musical sensation is communicated to the ear;
while the rapidity of the vibrations which produce
sounds very high in pitch is marvellous. The
highest C of the grand pianoforte as now manu-
factured sets in motion a column of air vibrating
more than 4,000 times in a second.
21. All sounds which are produced by the
vibrations of bodies at irregular intervals of time
are not music, but noise. They may be agreeable,
or they may be disagreeable, but they are in all
cases noise. For it would be a grievous mistake
to imagine that all sounds which we popularly
call musical are necessarily the sounds of music.
Such are those voices of men and women which
we term musical, and which produce so pleasant
a feeling in those who are susceptible of the
influences of sound.
6. Her voice was ever soft,
Gentle and low; an excellent thing in woman."
So cries Lear, in the last agony of his woe, with
the dead body of Cordelia in his arms.
24
To those who are insensible to the influence of
music, it may seem paradoxical if I say that this
sudden recollection of his daughter's lovely voice
at that awful moment, when in his madness he
fancies that she breathes again, conveys a
conception of the infinite tenderness of the
broken-hearted father's love, which fills the eye
with tears, through its exquisite truth and beauty.
Nevertheless, a voice may be thus “musical "
and yet not one strictly musical note may ever
proceed from the lips. On the other hand,
almost all effective orators distinctly sing in many
parts of their speeches. The sounds they utter
are perfectly musical sounds, and they are
separated from one another by intervals exactly
the same as those of the musical scale of a
pianoforte, bearing a striking resemblance
recitative. In some speakers this singing utter-
ance is most agreeable to hear, while in others it
is almost intolerable.
а.
22. Some musical sounds, again, wholly destitute
of the real musical nature, convey an impression to
the mind closely akin to those of actual music.
How pleasant is the gentle rustling of the myriad
leaves of the forest; and how full of suggestions
of life and activity, unmingled with pain, is the
25
flow of streams and rivers; and what a sensation
of irresistible and yet not cruel power is in the
mighty crash of the cataract! Yet this beauty of
sounds is not the beauty of strictly musical
vibration. Thus, too, with the voices of four-
footed animals. The bark of a dog is unmitigated
noise; while the mewing of a cat is often a strictly
musical sound, though it is as detestable as the
lowing of the cow, while she is waiting for the
dilatory milkmaid, is grand and solemn, and in
quality like the diapason of an organ.
23. Music, then, whether produced by the human
voice or by tubes, strings, or other instruments, is
the result of these vibrations of the atmosphere,
following each other at equi-distant intervals of
time, or, in technical language, isochronous
intervals. And the first question that calls for
solution when we attempt the study of European
music, as it has been gradually brought to its
present development, is this-How has it come
about that our musical scale and our rules of
harmony are what they are, and none other? Has
the scale a historical origin, and was its growth
the effect of the operation of certain irresistible
physical laws ? Or is it the arbitrary creation of
theorists and performers, who were no more
26
compelled by nature to build up this vast structure
of theory and achievement than a Frenchman is
compelled by the eternal laws of being to call the
covering which he puts upon his head a chapeau,
while an Englishman calls the same thing a hat ?
We are now in possession of a vast treasure of
musical masterpieces, the accumulation of more
than three centuries, totally dissimilar to anything
which the Classical and Mediæval or the Oriental
civilisations have created. Here, at least, our
modern life has accomplished its one great artistic
work, which is its own special characteristic, and
in which there is no question of rivalry with the
past, or any possibility of accusing us of mediocrity
failure or antiquarian revivalism. Have we, then,
been really wasting our energies in the creation of
a fabric which rests upon some purely arbitrary
hypothesis ? Or does there exist a profound
and subtle relationship between our music and
the physical laws of nature and the moral and
intellectual structure of our own minds?
or
24. Now there can be no doubt that the growth
of music, like the growth of spoken language, has
been the result of certain instinctive desires and
emotions, and has not been the deliberate creation
of grammarians and theorists. Men first made
27
language and then analysed it into grammar.
And in the same manner they first made music,
and afterwards analysed it into the rules which
they henceforth followed, and thus detected the
existence of the.musical scale, and finally of the
necessary rules of harmony. “If the Romans
had been compelled to spend their energies in
learning the Latin grammar," says Heinrich
Hein: in one of his witty exaggerations, “they
never would have had time to become the con-
querors of the world.” So it has been with the
long series of novelties in harmonious combinations
by which successive masters in the musical art
have developed the motetts of Palestrina into the
ninth symphony of Beethoven. Does any theorising
stickler for musical correctness imagine that each
new invention was the result of the careful study of
the theory of harmony; or that when some startling
combination of sounds rushed into the brain of
Bach or Mozart or Beethoven the inspiration was
the effect of a deliberate meditation on concords
and discords, and of painful trials as to what new
combinations might be invented without incurring
the displeasure of pedantry and dulness?
25. And so it was with the first beginnings
of vocal melody. The first singers did not
28
deliberately adopt a certain set of intervals and
call the result a scale, in accordance with which
they invented their simple tunes. Nor did they
try to fashion some elementary musical grammar,
based upon the songs of the birds, which were
as sweet in the earlier stages of civilisation as
they are at this moment. The nightingale and
the lark sang the same melodies when men were
little better than naked savages, as they now sing
to our ravished ears. But, nevertheless, when
man, emerging from his early barbarism, began
himself to sing, he found himself forced to adopt
the first elements of that very diatonic scale
which is the basis of all our modern music, little
as he knew what he was doing, and long as were
the ages that would roll away before the advance
of musical cultivation and the ingenuity of the
makers of musical instruments would reveal to
him the true meaning of those laws of sound
which he was compelled to follow.
26. His singing was controlled by the fact
that the pipe or tube from which he drew his
first attempts at musical sound would only yield
a certain limited number of tones, and that these
were the same, whatever pipe or tube he employed.
Nor is the significance of this fact affected by
29
any doubt as to whether men sang before they
blew sounds out of pipes, or whether they played
upon pipes before they attempted to sing. The
truth remains that a tube, whether of metal, horn,
or of wood, must have been the first instrument
from which man, in an early stage of incipient
civilisation, could draw more than one single
musical sound, and that as he could not change the
capabilities of the pipe, he must adapt his own
singing to the notes which he drew from his
instrument. In other words, when he invented
a tune or melody, its notes must be the same as
those which he could produce by blowing, in every
way that he could devise, into his tube or horn.
27. These sounds are what we now call the
harmonics of the lowest note which can be called
forth from any tube of wood or metal-that is,
the harmonics of the fundamental tone must con-
stitute the first elements in any succession of
tones out of which every variety of scale can be
constructed. Man, in inventing a musical scale,
had nothing to do with the intervals upon which
the songs of birds are constructed, nor upon any
theoretical and practical divisions of tones in which
he might follow them with his own voice, so long
as his song was unaccompanied by any instrument.
30
The capacities of instruments must necessarily be
the law which he must ultimately obey: in the
first place because he must otherwise sing without
any instrumental accompaniment; and, in the
second place, because his ear being accustomed to
those sounds which his instruments could produce
would speedily come to regard all other sounds as
disagreeable and unmusical. All union between
voices and instruments was impossible, except
upon the condition that the voices should attune
themselves to the instruments, and thus a certain
number of elementary sounds were irrevocably
fixed upon as the basis upon which all melody
must be framed. For melody must have begun long
before harmony, and generation after generation
must elapse and the musical aspirations of man-
kind be still satisfied with simple "tunes." And
such, in fact, has been the case. Music has been
the latest of all the arts and of all human inven-
tion in passing beyond the stage of infancy. For
tens of thousands of years men have played and
sung in simple unisons; but music, as we mean
it, that is, harmonised music, is not yet four
hundred years old.
Musical art, moreover, stands alone at the
present time in not being more or less a revival,
31
but rejoices in all the freedom and vigour of its
first mature manhood. Even painting itself is in
comparison an ancient art, for in the sixteenth and
seventeenth centuries, which gave birth to painters
whose equals the world has not yet seen, music
was only beginning to feel its way to its final
development. The period of the renaissance in art
and literature could not extend to the musical art,
because a "new birth" was impossible to that
which had never before existed, except in a semi-
barbarous and tentative condition. Strictly speak-
ing, music began with Palestrina, for his immediate
predecessors bore the same relation to him that
the predecessors of Phidias bore to that greatest of
Greek sculptors. And from the days of Palestrina
to this day the history of music has alone been
the history of one steady unbroken advance from
early youth to maturity. Taking the first half of
the present century, and surveying the whole field
of art and literature, nowhere is to be found a name
whose glory is not surpassed by that of some who
have gone before. In music only does one
stand forth whose greatness may possibly
have been equalled, but most unquestionably
has never been outshone. There has been but
one Beethoven, and his only equal was perhaps
Sebastian Bach.
32
28. These "harmonics,” however-returning to
our main subject-do not precisely supply the
tones of that diatonic scale in which all music
is now written. They are practically as follows,
though the series may be continued indefinitely
upwards, in mere theory :-
ebote
a 7
29. The last two tones in the series must,
indeed, have been quite impracticable even in the
mediæval period, when the desire for the com-
bination of sounds in harmony began to make
itself felt, and when musicians were unconsciously
preparing the way for that almost sudden out-
burst of harmonised music which was one of the
chief glories of the Renaissance. It is in the
first twelve of the series that we must seek for
the elementary sounds of the diatonic scale, all
conception of the chromatic scale being quite
undreamt of. Here, then, we have the funda-
mental note, or key-note, as it ultimately came to
be regarded, C, three times repeated, at intervals,
which came to be called octaves, when the com-
plete scale was finally formed; the note G,
ultimately the fifth in the completed scale, three
times repeated ; the note E, ultimately the third
33
once.
200
in the completed scale, twice repeated ; Bb* once,
D once, and a note which is set down as F#,
though it is not much sharper than our modern
FH, The scale thus formed is as follows,
repeating the D in the octave below :-
О.
a
30. On this scale two remarks instantly occur.
There are no semitones, for the F being only
slightly sharper than in our scale, the interval
between the F and the succeeding G is neither a
semitone nor a whole tone, and thus the notes
A, Fy, and Bh in the diatonic scale are totally
wanting. It is also clear on reflection that our con-
ception of the octave, as supplying us with the
natural limits, between which all musical phrases
must necessarily be written, is not even hinted at
in this peculiar scale. The note C, it is true, is
repeated, and so is the note G; but the Bb
preceding the upper C, as practically used, is a
whole tone below it; and the F* preceding
helf
the upper G is more than a quarter tone below
it; while it is absolutely essential to our own
feeling for the octave that it should be preceded
by a semitone.
* This harmonic BV is decidedly flatter than the true BD
in the chromatic scale.
D
34
31. Hence it is that in almost all very old
melodies our modern feeling for the octave is
wanting, while in many cases no notes occur
except those which are included in this embryonic
scale. A well-known instance is to be observed
in the Fourth Gregorian Tone for the Psalms, a
melody which strikes the modern ear as especially
shapeless and grotesque. It is this :-
#-bo
lolt boa
to a
32. How, then, in the next place, did musical
composers come at last to recognise the insuf-
ficiency of this limited scale ? How was it that
they acquired the perception of the semitone as
such ? and how were they led to substitute a Bh
for the Bb as the note leading into the octave ?
That they were impelled by some instinctive
impulse to make the new additions and altera-
tions cannot be doubted. No one could maintain
for a moment that before the twelfth
twelfth and
thirteenth centuries musicians deliberately betook
themselves to the theoretical division of the long
interval between
and
into various smaller intervals, with the view
35
of including certain of the tones produced by
their horns and pipes, and of substituting a
Bh for a Bb. They composed by what is called
the “rule of thumb," for they knew no more of
the mathematical divisions of the scale than they
knew of the electric telegraph. They simply
went on trying and trying how certain succes-
sions and combinations of tones sounded. They
put their pipes together in the form of the organ
in its simplest forms, and blew their horns and
trumpets, and sounded their stringed instruments,
the progeny of the Greek lyre, and the origin of
the modern harp and violin. And so by degrees
they felt their way to the introduction of new
sounds and combinations, and the modification of
others. They cultivated their feeling for music
as the Greeks cultivated their feeling for form and
beauty, and the final result was the modern
diatonic and chromatic scales, the fugues of Bach,
and the choral symphony of Beethoven.
33. But the interesting and practically impor-
tant question is this: How did they come to
recognise the semitone as an essential element in
all music, and the chords which we call concords
as the foundation of all harmony? The latter
half of this question I for the present postpone,
36
because it is impossible to understand the true
principles on which all harmony is based until
we have studied the steps by which the scale
itself was formed. The principles of harmony, if
my view is correct, are identical with those of
melody, and they both depend upon the operation
of the unchangeable natural laws of sound.
34. Of these laws, one of the most practically
important, as it is certainly one of the most
marvellous, regarded solely as a physical pheno-
menon, is this, as already briefly mentioned
that there is no such thing as a simple musical
sound in nature. At least, if there are such, they
may be set aside as having no bearing upon
the laws of musical composition. Fresh atten-
tion to this fact has been recently called by
the writings of Professor Helmholtz, who has
been led to draw from it certain interesting
and apparently true deductions respecting the
quality" of different instruments and voices;
though the fact itself has always been known to
everyone who has studied the sounds produced by
a pianoforte, violin, or violoncello, or who has
listened to the strange wild harmonies that some-
times float upon the ear beneath the vaulted roofs
of a great mediæval cathedral. All those sounds
37
which the ordinary listener imagines to be single
tones are, in reality, made up of a large number
of sounds different from that which we imagine to
stand alone in its solitary unity, and mingling
with it in an inexplicable sweetness and richness.
The whole, strictly speaking, is identical in theory
with what we call one mighty discord; but, as
produced by the wonderful action of nature her-
self, it leaves on the ear an impression as rich
and delightful as that of the purest theoretical
harmony.
X t
į
35. The reality of the phenomenon may be
tested by a simple experiment on a pianoforte,
more easily on a grand pianoforte than any other,
as the mechanism of the instrument is more acces-
sible. Place a finger close to the strings of one
of the lowest notes, say the lowest G, not actually
touching them, but so close that it may be pressed
upon them the moment you wish. Press down
the loud pedal, and then with a finger of the
disengaged hand strike the note G with some
force. Then immediately press down the strings
of G with the finger held in readiness, but keep
the foot still upon the pedal. The result will be
that the strings of the note G will become
instantly silent, while a delicious « concord of
38
sweet sounds" continues to flow forth from all
the other strings of the instrument, lasting for a
full half minute in duration, and dying gently into
silence. It is thus evident that the whole number
of strings, through all their variations of tone,
have been set in motion by the vibration of the
fundamental tone G.
36. But what is it that thus sets them vibrat-
ing? There is but one possible reply. Each
string is made to vibrate by being struck by a
wave of the atmosphere, moving at the precise
rate which corresponds to its own tune or tension.
A string which vibrates 512 times in a second must
have been struck by a wave which moves at the
rate of 512 times in a second. A string which
vibrates 256 times must have been struck by an
atmospheric wave which vibrates 256 times; one
which vibrates 128 times by a wave vibrating
at the same speed, and so on.
But these waves,
though many themselves, have all been set in
motion by one single string. The conclusion is
obvious. That string itself not only vibrates 512
times, but also 256, 128, 64, and 32 times, all at
the same inoment. And this is the actual fact.
The string that is struck by the hammer vibrates
in its whole length, in its half length, in the
39
third, and in the quarter, the fifth, &c., of its
whole length, at the same moment; and thus
a series of waves of air, rushing along at a great
variety of rates of speed, is set moving simul-
taneously, and so the whole series of strings in
the instrument begin sounding all together. The
same also is true of any tube of metal or wood
which is capable of producing a musical sound.
37. These sounds, thus wonderfully produced,
are the harmonics of the original fundamental
sound which calls them into being. They are
the octave, the twelfth, the fifteenth, the seven-
teenth, &c., of the fundamental note. In other
words, when we strike the bass note C-
o
on the pianoforte, what we really hear is this
chord, allowing for the slight differences of pitch
in the actual Bb and F-
并
​fo:
40
together with other sounds still higher, but grow-
ing more and more faint as they ascend in
pitch.
38. Further, it is obvious that what is true
of the vibrations of the fundamental string or
pipe is equally true of all the other strings and
tubes which are set vibrating by its composite
movements. They also vibrate with a come
posite movement of their own, and set in
motion those other strings and tubes which are
tuned so as to respond to those movements.
The result is that every string in a pianoforte,
and every pipe in an organ, produces a flood
of sounds, which, if loud, would produce a
sensation of intolerable discord, but which,
mingled by the requisite chemistry, so to say,
of the atmosphere, fill the ear with a sensation
of delight.
39. One more simple experiment with the
sounds of a pianoforte will bring out more clearly
the truth of the statement here made. Place
the foot upon the loud pedal, so as to allow a free
vibration to all the strings of the instrument;
then play as follows :
41
.
놔
​mf
다
​Ped. 5
The three C's struck in unison will fill the ear
with a composite sound in which any tolerably
good ear will detect a combination of soft tones
mingling with the loud clear sound of the C,
which is popularly supposed to be the only tone
which is sounded. While this sound continues,
through the action of the pedal, the introduction
of the By played moderately loud will produce a
sensation of distress almost amounting to physical
pain, the ear instantly feeling that it is in violent
discord with the mellifluous multitudinous concord
of sounds upon which it is dwelling. Next play
as follows, with the pedal down as before : -
f
mf
Ped. Õ
The contrast will be complete. The ear will
feel at once that the tone G is already sounding,
42
and merely assumes a somewhat more prominent
place in the mighty concord than it held when
the C's alone were struck.
40. Continue the experiment thus:-
JE
t
mf
and
mf
Ped. - -
Ped. @
nor the
and in each case the introduction of the new tone
will appear a painful intrusion. In each instance
the reason is the same. Neither the B4
F nor the A is found in the chord composed of
the harmonics of the fundamental C, while the
introduction of G (and it would be the same with
E) is felt to be sweet and concordant. The
introduction of the sound Bb, after the striking of
the C, produces a curious result. The ear is
neither pleased nor displeased, and is conscious
of a sensation of something which is neither
concord nor discord ; the reason being this, that
the note Bb, which is given as one of the
harmonics of C, is really not quite so sharp as
the Bb of the pianoforte, and the effect on the ear
is consequently vague and uncertain.
43
41. Let us now see if we can throw any light
on the introduction of the semitone, as an interval
agreeable to the cultivated ear. Let me first
remind the student that the formation of the
scale must necessarily have been the result of
innumerable attempts at enlarging the rudimental
harmonic scale. There was no reason in the
capacities of the human voice, or in the nature
of stringed instruments in their earlier or later
forms, why the interval between a tone and its
octave should not be divided into quarter tones,
or thirds of a tone, or any other of those small
subdivisions which, as far as we can judge, were
in use among the Greeks, and which are still in
use among various Eastern nations, causing their
singing to appear frightfully out of tune to our
ears. What we want to know is the nature of
that controlling force in the physical laws of
sound which compelled the European mind, as it
advanced in the practice of music, to adopt the
Bh in the place of the Bb, as the sound leading
up to and into the octave C.
42. The process I can conceive to have been
this; and though it is impossible to prove that
such was certainly the case, the process is so
natural, that it may well be accepted as the
44
probable account of one of the great facts of the
history of music. It may be taken as certain
that men came by degrees to sound at the same
moment horns which, as giving forth harmonics,
were in harmony with one another. Thus they
must have sounded what we should now call a G
horn with a Chorn. Try, then, the effect upon
the ear of the following chords on a pianoforte :
d
Ped. fő
P р
The disagreeable effect of the BH following
immediately after the chord upon C is nearly gone,
because the G in the first chord has its own effect
in creating its own harmonics, in company with
those of C; and among the harmonics of G is Bh.
Its presence is felt in the mingled sounds of the
chord, and its entrance as a positive sound in the
subsequent chord is no longer resented as an
intrusion. Besides, G is the most important of
all the harmonics of the simple C, and takes a
place next to C in generating its own sub-
harmonics, even when the Calone is sounded.
And thus it is that on analysing the chord
2
45
as
as it continues sounding, the ear detects a
peculiar piquancy in the presence of the Bh
following the note C, while the old bitter sourness
of the interval is entirely gone, neutralised by the
powerful influence of the G.
43. But it is not only to the influence of the
first harmonic G that this tolerance and ultimate
adoption of the Bh is due. The influence of the
harmonic E, which sounds in power next to the
G and the octave C, materially assists in the
creation of the new tone. Bø is the most promi-
nent of the harmonics of E, being its fifth, or
reckoning the full distance from the fundamental
note, the twelfth. And being its harmonic, it
has all along been faintly sounded, and has thus
gradually glided into the unconscious ear, which
has been thus prepared to admit its claim to a
place in the scale, both for the purpose of melody
and that of harmony, the moment either the note
E or the note B becomes a prominent sound, and
still more when they are prominent together.
44. Here, too, let me notice a most suggestive
instance of the overruling influence of the under-
tones of the harmonics in acquiescing in any
modulation founded upon their presence.
46
000
fa P
Here we have a change from the single note C to
the common chord of E, without the introduction
of any note of that chord. Yet the modulation
seems perfectly natural and agreeable, though
somewhat surprising. And why so? Simply
because the E, which is the fundamental note of
the new chord, was already present in the ear of
the listener as a harmonic of C.
45. Thus, then, the idea of the semitone, as such,
is generated. An interval immediately preceding
the key-note of the tube is made familiar to the ear,
and the voice practises it accordingly. At once,
like the construction of the arch when introduced
by the Romans into pure Greek architecture, the
whole conception of musical divisions and combi-
nations begins to be radically modified. Composers
begin to see their way to some self-consistent
division of the intervals yielded by the original
harmonics. They had already got this chord :-
oooo
Between the C and the E was an interval;
between the E and the G was another; and
47
between the G and the Bb was another, not
quite as wide as that between the C and the E;
and between the Bb and the following C was
another. Apply, then, this newly-found interval
as the divisor of all the others, and see what
will result. Instantly the whole problem is
solved. Of the mathematical subtleties of perfect
tuning the early musicians knew nothing. They
merely tried to cut up the whole octave into
semitones, and, behold! they succeeded. And
thus the chromatic scale itself sprang into life.*
The interval between the fundamental note C
and the E was found to be four semitones;
between E and G was found to be three, between
G and B4 another four; and between By and the
octave C one, making altogether the twelve semi-
tones of the chromatic scale. The notes still
wanting in the diatonic scale were at once invented;
Fy being a semitone above the already existing
E, while A was found to be practically a semi-
tone below the original harmonic Bb.
* The peculiar nature of the sharpened seventh as the note
“ leading" into the octave is shown in the care with which it has to
be handled in harmonising. It is the only note in the scale which
cannot be doubled when the common chord of the dominant passes
into the chord of the tonic. Essential as is its presence to the
construction of melody in harmony, there always remains about this
note a certain weakness resulting from its hereditary artificial origin.
48
46. Why, then, it may be asked, was the
diatonic, as distinguished from the chromatic,
scale, adopted as the basis of all future melody
and harmony ? Why do we reject the chromatic
scale, which, when complete, is as follows:-
a
Jeg
and adopt a selection of the same sounds, as the
element with which to form our musical phrases,
namely, this following, absurdly called diatonic?
o 트
​For irresistible reasons. In the first place, the
chromatic scale supplies neither beginning nor
ending, and is thus in direct contradiction to that
element in human nature which requires measured
form, balance, and limitation in all works of art,
whether music, poetry, or the fine arts. This
demand, indeed, for the introduction of exact
measured symmetry in some form or other in all
the works of man, stands in striking contrast
with the works of nature herself, who accomplishes
her triumphs of beauty by means of what, in our
hands, degenerate into unmeaning irregularities,
implying a helpless feebleness, little removed from
49
lifelessness itself. This, in truth, is the mighty
marvel of all creation, that except in the case of
crystallisation and a few kindred instances nature
knows nothing of straight lines. Except in the
planetary movements and a few other instances,
she knows nothing of strictly geometrical forms;
and, except in such wonders as the equal divi-
sion of musical strings in their compound vibra-
tions, knows nothing of literal arithmetical pro-
portions. Herein is the unapproachable miracle
of her life. The different detailed forms of each
leaf, each flower, each cloud, each mountain,
each wave of the ocean, are never strictly sym-
metrical, but in their infinite variety betoken the
inconceivable resources of her hidden vitality. The
corresponding features and forms of every human
countenance and body are never literally alike.
Everywhere is some token of the presence of that
Infinite Being which, in its essence, is incom-
prehensible to the finite intelligence, but which,
in these boundless varieties of form and colour
and movement, takes us, as it were, into a
mysterious fellowship with Himself, and permits
us to witness some few of the results of His own
Eternal Life, Glory, and Power. We, on the
other hand, are restrained within the limits of
time and rigid form and number, and it is when
E
50
we move with the largest degree of possible
freedom within these limits, by our skill and our
imaginative inventiveness, that we show that,
after all, our life is a real life, and that there is a
certain actual sense in which man may be said to
be made in the “image of God.” And thus it is,
returning to the special subject before us, that no
real progress can be made in musical invention
until we have constructed our one elementary
symmetrical form, within which, and by means of
which, all our works are to be accomplished:
Thus it is that the limitations supplied by the con
ception of the well-marked octave are as neces-
sary to the development of perfect melody as the
“sentence," ending in a full stop, is necessary in
spoken or written articulate speech. And until
the flat or minor seventh gave way to the major
seventh (as it is somewhat absurdly called), the
mere repetition of the sound of the octave, sup-
plied by the natural harmonics, left the musician
to wander aimlessly to and fro. All development
of melody by means of modulation and variation
was impossible.
47. In the second place, a distinctly prominent
position must be ensured to the chief harmonics
of the fundamental note, that is, to G and E, and
51
to the harmonic D, which is the next important
after the Bb, eliminated for the reasons I have
given. If any scale were adopted which reduced
Siperion
these harmonics to a position in no way inferior
to that of the various semitones into which the
octave may be divided, the physical laws of sound
would produce an endless amount of discord, with
an utterly irremediable amount of vagueness and
feebleness of rhythm. Melodies constructed on
any but the diatonic scale are weak and unmean-
ing, such as spoken verses would be if written
without definitely
definitely and frequently recurring
syllables of full strong sound. And so it is found in
practice. It is a token of weakness in a composer
when he is perpetually introducing semitones
into his melodies, changing from one key to
another, with a view of covering the poverty of
his melodic conceptions; just as a painter who is
uncertain or weak in his outlines labours to con-
ceal their feebleness or vagueness by an extrava-
gant use of colour. So certain it is that the
diatonic scale is not, as some suppose, a mere
arbitrary arrangement of tones, but is nothing
less than a sequence founded upon the irreversible
laws of physical sound.
CHAPTER III.
The minor scale; its probable origin and difference in essence
from the major.-Concordant and discordant sounds.-—What
chords are most agreeable to the ear? Perfect and imperfect
intervals.—Differences in degree of dissonance.—The com-
mon chord the necessary basis of all modulation.
48. Having thus pointed out to the student the
real origin of the musical scale in the primary
laws of sound, our next step is to inquire into the
origin of that modification of the diatonic scale
which is called the minor scale, or mode, and
thence to trace the origin of the fundamental rules
of harmony, as the completion of melody, in the
same source as that to which we have traced the
commencement of all melody itself.* In so doing
it will be convenient to drop the term harmonics
and non-harmonics as far as possible, and to speak
* I need hardly add that the words melody and harmony are
used in their technical sense, melody meaning an agreeable suc-
cession of single sounds, and harmony an agreeable succession of
compound sounds or chords. I should, however, remind the
student that the terms harmony and counterpoint are not the
same in meaning. Counterpoint is the agreeable succession of
two or more distinct but combined melodies, moving sometimes
singly, but for the most part in chords; while in simple harmony
the chords move in masses or bodies of sound.
52
53
of the notes in the scale by their more ordinary
names, as the second, third, fourth, &c., counting
upwards from the note which is the lowest note in
the octave, which we now call the key-note, as
designating the pitch, or sharpness, of the whole
series of tones and semitones.
49. All keys, the student should be reminded,
are precisely like one another in the relationship
of their various portions or elements. They only
vary in the different rapidity of the vibrations of
the atmosphere which produce their fundamental
notes. In a perfectly tuned pianoforte the diffe-
rence which some persons imagine they feel in the
quality or influence upon the mind of various keys
is the effect of the modulation of the chords with
which the different melodies are harmonised, and
not of the different relative relationships of pitch
between the separate notes of the octave. What
is the source of these variations I shall endeavour
by-and-by to point out. For the present we are
only concerned with the origin of the minor dia-
tonic scale, which is as follows:-
550
This is the minor scale in its essence.
It is
54
varied in different ways by different writers, being
sometimes converted into the major in descending,
together with sundry alterations of the sixth and
seventh notes, both in ascending and descending.
Its essence, however, lies in the alteration of its
third note (the natural E of the major scale),
which is flattened a semitone; producing the
minor common chord of
&
000
instead of the major
Todo
50. The effect upon the mind of this alteration
in the diatonic scale, both in unaccompanied
melodies and in harmonies, is remarkable. The
flattened third is found prevailing to a large extent
in the unaccompanied melodies of semi-civilised
nations. Of the old Celtic tunes which are
familiar to the English ear, very many are clearly
arranged upon some species of strange scale in
which the flat or minor third is strikingly pre-
dominant. At the same time, it cannot be denied
that to the ordinary uncultivated ear of us moderns,
and especially to the young, harmonised melodies
55
in a minor key are distasteful, conveying an
impression of sadness and dulness in contrast with
the brightness and cheerfulness with which they
like to associate all music not of a funereal kind.
The essentially plaintive and pathetic quality
of music in a minor key is, however, full of its own
charm to the cultured ear, and especially as we
grow older and love the poetic expression of the
sadness and tragedy of human life. Various
natures, also, as they vary in their inner qualities,
so they vary in the general tone and sentiment of
the music they love. But, on the whole, it is
undeniable that the minor chord is grave, sad, and
plaintive, in contrast with the brilliant and joyous
qualities of the corresponding major.
51. How is this? How are these two apparently
contradictory facts to be accounted for? How is
it that such strikingly dissimilar emotions are
excited by the alteration of the position of a single
semitone in the diatonic scale, the whole sentiment
of a musical composition being dependent upon the
placing two intervals of three and four semitones
respectively, either before or after one another.
In the major scale we have four semitones between
C and E and three between E and G.
a ㅎ
​56
In the minor we have three semitones between
C and Eb, and four between Eb and G, in both
cases the whole interval between C and its
fifth, G, remaining the same, namely, a total
of seven semitones. Whence, then, this change
from sorrow to joy, by this apparently trivial
alteration ?
52. I think that the fact may be accounted for
when we trace the minor scale to its origin. Its
prevalence in the tunes of earlier civilisation is
due to the circumstance that the earliest instru-
mental scale was defective and was practically
destitute of the semitone, and that harmony was
unknown. The minor quality of the antique
tunes is a peculiarity of melody only, and the
presence of the major third as the essential element
of the common chord, formed by the unison of
the key-note with its two predominant harmonics,
now called the third and fifth, was not known.
The major third, when entering simply as a
single note into the course of a melody, was
often quite unable to modify that singularly
abrupt and unfinished quality which is popularly
57
thought to be the “minor" sentiment of ancient
song:
and which really resulted from the
presence of the Bb or “minor seventh” in
the scale.
53. Let any one take the original instrumental
scale
to
f
9
and see what he can make of it in the way
of tunes without any chords, and mark how odd,
quaint, sad, and even grotesque will be the
ordinary character of his work. I have already
mentioned the Fourth Gregorian tone for the
Psalms as a most characteristic example of the
cast of the melodies to be yielded by the early
scale, but it deserves fresh attention as indicat-
ing the true character of those antique airs.
Hobo
2 크
​bo
bo
Who does not here feel at once that it was the
repetition of the Bb, and still more its position
in the closing phrase, which gave to the music
of many centuries and thousands of years ago
just that wild rough-hewn character which is
popularly, but erroneously, supposed to constitute
them melodies in the modern minor key.
58
54.
Aĩ the same time, the ear of composers
su constantly habituated to this same phrase
--that is, to the use of the flat third, treating the
G as the starting note of this portion of the scale,
begins to regard the minor third as a natural
sound, owing to the ease with which the note
C and its fifth G were interchanged by the
subtle processes of the musical ear.
The ear
which was familiar with the sequence
to
을
​easily came to accept the sequence
although the flat E was not yielded by the
natural sounds of any tube or string. Rudeness
and roughness of interval were so habitual to
the ancient ear that it readily acquiesced in the
peculiar interval which is characteristic of the
'true minor scale wherever it occurred, and when-
ever the voice was able to free itself from the
obligation to sing in unison with a pipe or horn.
59
55. But the moment that harmony is attempted,
all this is changed. The law of the composite
harmonic character of all sounds popularly
supposed simple comes into operation. Let us
play as follows:
d
bo
Ped. fa PP
The ear being filled, not only with the single
sound of C, but with all the harmonics which are
sounded with it, feels suddenly depressed at the
addition of the E), for the reason that no Eb is
found in the harmonics.
Nor is the effect altered if we play as follows:--
d be:
ei
Ped. t
The ear still refuses to accept the union of the Cwith
the Eb as otherwise than sad, although it accepts
precisely the same union of two sounds, separated
by three semitones as eminently sweet and soothing,
when the note C is followed by the minor third
孟 ​f
instead of the minor third
g
IZ
60
56. It is obvious, therefore, that the difference
between the impression produced by the interval
of the one minor third from that produced by the
other must be sought elsewhere. The fact that
the note C actually forms one of the two notes in
the case where the interval sounds sad, while in
the other it is altogether absent, only makes the
phenomenon itself the more remarkable. As I
have said, then, the explanation is to be found in
the composite character of the note C, whose
harmonics take such complete possession of the
ear that they exclude from it that very sensation
of sweetness which it finds in the minor third
f
even where the C is not sounded, When it hears
a similar minor third in the form of
repeated. The peculiarly plaintive or gloomy
quality of music harmonised in a minor key is,
therefore, this, that it is practically composed of
thirds which are felt to be extremely discordant,
because the ear incessantly refers them to some
fundamental note with which they are in discord,
while it admits the very same thirds to be
61
practically concords when it unconsciously refers
them to some other note. At first sight, of
course, it sounds paradoxical to assert that two
notes, when sounded together, should sometimes
affect the ear as discordant, and at others as
agreeable, and that this variation should be the
consequence of the mere sounding of one single
note a short time before they are sounded.
Nevertheless, so it is. Thus the double notes
Eb and C, sounded together immediately after AB,
thus-
produce a totally different sentiment on the mind
from that which they produce when sounded after
G, thus-
In the former case the ear is filled with the
harmonics of Ab; in the latter it is filled with
those of G. And upon this fact depends the
whole fabric of the musical art, including all the
rules for modulation and harmony which the skill
of ages has now elaborated.
57. Harmony, let me repeat, is the agreeable
succession of chords, and not merely the agree-
62
able sensation produced by the sounding of
certain different sounds at the same moment.
And being thus a succession of chords, as long as
a phrase remains in any one key the ear is per-
petually referring all that it hears to the
fundamental note of that key, and is treating
all combinations of sounds as concordant or
discordant, according to their relation to that one
fundamental sound. And I cannot too strongly
urge upon the student the recognition of this
fact, reminding him that it is because the dia-
tonic scale is a necessary physical development of
the composite sound of this key-note, that the
ear perpetually refers all harmonics with a less
forcible but yet quite real feeling to the sounds
comprised in the sequence called the diatonic
scale itself.
58. To understand how it is that such mighty
results can spring from such an apparently
inadequate cause, the student must next learn
what it is that constitutes the essential difference
between a concord and a discord. It is now
recognised by nearly all scientific theorists that
much that has been written on the varieties of
concords and discords is simple unmitigated
jargon, which serves only to confuse the mind
63
and teaches the student nothing. His memory
is burdened by a multiplication of technical
distinctions and figures, while he finds himself no
nearer than before to a practical skill in writing
either melody or harmony; and he secretly asks
himself whether it is credible that the great
masters invented their wonderful inspirations and
new combinations under the direction of all these
artificial rules of musical grammar, which they
ever had at their fingers' ends. Especially is the
student bewildered at the disagreement of different
theorists as to whether certain chords are con-
cords or discords, whether they are authorised by
rigid musical law, or are tolerated under the term
of musical licence; with other similar sources of
confusion.
59. Yet, after all, there is not the smallest
difficulty or mystery in the matter, when once we
realise the truth that the agreeableness or dis-
agreeableness of a combination or sequence of
musical sounds depends upon certain laws of the
atmosphere and their influence upon the brain
through the ear. No amount of theoretical
writing would make the effect of a cool grey upon
the eyesight the same as that of a bright yellow,
and the union of the red flowers and green leaves
64
in a bed of scarlet geraniums produces an influ-
ence upon the brain through the retina which no
human ingenuity or perverseness can change.
And so it is with concords and discords. We are
so framed by nature that when two notes are
sounded together, of which the one is produced by
a series of atmospheric waves, moving twice,
three times, four times, five times, &c., as fast as
those of the other sound, the two waves mingle
with one another so as to produce certain varied
effects of unity and repose, and the mind, affected
by the ear, is satisfied. In arithmetical language,
whenever the speed of one such succession of
atmospheric waves is the exact multiple of another
succession, the two melt into another and form a
combination of sounds which touch the heart of
every man and woman whose physical organisa-
tion is not more or less imperfect. In the same
way, when the one series of atmospheric waves is
not an exact multiple of the other they cross and
clash with one another, causing, when minutely
analysed, an incessant series of interruptions in
their continuity, which annoys and distresses the
mind and excites a desire for some change in one
of the notes which shall lead to a concordant
union without any violent destruction of their
relationship. If more than two notes are sounded
65
together the case is the same, only that the
emotions excited are deeper, and the demand for a
change to a condition of rest is more imperative.
A concord is thus simply the union of sounds
which are multiples, more or less few in number,
of some fundamental sound; and a discord is a
combination in which this relation does not exist at
all, or to an unappreciable extent. Chords are thus
more or less discordant, while the limit at which
the practically concordant become physically dis-
cordant can hardly be ascertained. It is also
certain that whatever theorists may say the
ear is most completely soothed and receives
the most complete sensation of harmonious
union when the chords lie between certain
narrow limits of consonance and dissonance,
and that beyond the interval of the fourth
semitone the ear begins to lose its complete
sense of repose.
60. It is further to be noticed that the harmonics
to which so much reference has been already made
are produced by vibrations which are exact
multiples of the lowest sound produced by any
tube or string. Thus, if the note
TO
F
66
is produced by a string which vibrates sixty-four
times in a second (which is a pitch sometimes
adopted in tuning the pianoforte), the first
harmonic
-which is the octave of the fundamental sound
-is produced by 128 vibrations in a second ; the
third harmonic
by 192 (three times sixty-four) in a second; the
fourth,
by 256 (four times sixty-four); the next,
by 320 (five times sixty-four), and so on, until all
musical sound becomes a hideous scream. And
thus it is that the harmonic notes which have been
adopted as the chief elements in the diatonic
scale, as a vehicle of tune, are in concord with the
keynote when sounded together in chords, so that
they are also essential elements of all harmony.
67
The common chord is simply a union of the sounds
which are the most important multiples of the
lowest fundamental note; and all harmony, being
in its essence an agreeable succession of chords,
must start from this chord or must return to it.
When new keys are introduced by the introduction
of a flat or sharp, the same principle must still
prevail. The common chord of the new key
immediately takes possession of the ear, and
requires that every discord which is connected
with it shall at once be so treated as to tend
towards a submission to its demands. This
change of each discordant chord, either directly
or by one or more intermediate steps, into the
concord to which it is related, is what is known as
its “resolution”.-the term which the student so
frequently meets with in all discussions on musical
science.
61. The next question which presents itself for
solution is the principle upon which chords should
follow one another, whether as concords or as
discords, or as alternations of concords with dis-
cords. And first of all, is there any such principle ?
Or are the rules of harmony which musical
grammarians and theorists have laid down to be
regarded as the mere arbitrary regulations of what
68
is absurdly called “learning," but which has no
pretension to be respected as the scientific
knowledge of musical truths? For example, there
is a certain note in the diatonic scale—the fifth-
which is felt to bear a specially close relationship
to the key-note, in determining the movement of
the chords which may be made to flow from it.
For this reason it is termed the dominant, a word
which has far more sense and meaning than many
other musical words. *
62. In answering this question I must again
request the student's attention to the nature of
* What can be more ridiculous, for instance, than to call a fifth
a "perfect fifth," and an interval which is a semitone less in
measurernent an “imperfect fifth"? This latter is not a fifth
at all. We might as well call a French franc an “imperfect
shilling;" GE is simply the fifth note in the diatonic scale of the
key of C, and Gb is not in the same scale at all. In the absence
of any complete and self-consistent system of notation, it is
necessary to give to the Gb. some name or other. To call
it a flat fifth would undoubtedly be unscientific, because, as I have
said, it is not a fifth at all; but at least it would not be so
misleading to the student as to call it an imperfect” as
compared with a “perfect" fifth, which latter term is about
as nonsensical as it would be to talk of a round circle or a female
woman. Undoubtedly, from the imperfections and inconsistencies
of our nomenclature, we are sometimes put to great straits
when we wish to avoid the use of a phrase which conveys some
untruth. Thus, what is this interval
69
that movement of the atmosphere which produces
the effect upon the mind which we call music.
The sensation of a musical sound is the effect
of a series of extremely rapid and delicate blows
struck upon the drum of the ear and thence
conveyed to the brain by the movement of the
surrounding atmosphere. It is as truly the effect
of a series of blows as the fall of a tree before
a gale is the result of the violent movement of
the atmosphere. These blows, as has been said,
produce mere noise when they do not follow one
another at exactly equi-distant intervals of time.
It is only when the intervals are equi-distant that
the effect is a musical tone; and the faster the
rate at which these blows succeed one another
the higher or more shrill is the pitch of the
sound they produce.
63. Now it is obvious that when the blows
simultaneously struck by two different waves or
to be called ? It is a fifth, counting upwards in the scale.
But it is not a fifth in the sense in which
is a real fifth, viz., seven semitones. Happily, a great deal
of music is read and played without the use of any names for
chords and intervals at all. And so let this interval between B
and F remain without any strictly logical designation of its own.
70
columns of air come very closely to one another
the sensation of identity of sound must be much
stronger than when the moments of impact are
wider apart. The effect upon the brain of a blow
doubled in force at every alternate stroke must
be greater than that which is doubled only at
every third stroke, and greater still than that
which is doubled at every fourth stroke. And
this lessening of the sense of unity must continue
to increase the more distant become the moments
at which the strokes are doubled. When, again,
their simultaneous strokes cease altogether, and
the moments at which the two waves strike the
ear never actually agree in time, or (to use the
more convenient Greek term) synchronise, then
it is that the brain becomes conscious of a strange
sense of irritation and distress, and longs for
some change which will reduce all this irregularity
of atmospheric movement to order. Nor is it
enough that distinctly synchronising sounds should
be added to these discordant sounds. The ear is
not satisfied until the non-synchronising sounds
have altogether melted into others which syn-
chronise, at whatever intervals this synchronising
may occur. Discords are thus half-way between
music and noise. The movement of each atmos-
pheric wave continues uniform in speed, but the
71
apparent absence of all order in their combined
movements, and the extent to which these waves
clash with and impede one another, produce a
harshness of effect which causes positive pain
to the sensitive ear, unless regarded strictly
as a transitional period in the even flow of more
concordant sounds.
64. Apply these truths, then, to the sequences
of the diatonic scale, and disperse it into its
harmonics. It then stands thus :
C C
сі
G
C! E G" Bb C D E
G:11
Lood
a
2a
3а
4a 5a
ба
7a
8а
ga
Іоа ІІa
That is, if the lowest C vibrates a times in a
second, the next C, which is marked C! , vibrates
twice a times in a second. In other words, if the
two notes are sounded together, at every second
vibration the ear is struck by a double stroke.
If C and G are sounded together, the ear receives
the double stroke at every third vibration, because
the waves which produced G move three times as
fast as those which produce the lowest C.
If C (written in the bass clef) and E (written in
the treble clef) are sounded together, the impact
72
of the twofold blow occurs at every fifth vibration,
because the wave of. E is repeated just five times
as fast as that of C, and so on all through the
whole series of harmonics.
65. What is the result ? When notes an
octave apart are sounded together, the listener
is conscious of a singular mingling of identity and
difference between the two sounds. An unculti-
vated ear thinks they are the same, differing only
in loudness from the same notes when taken
singly, while the cultivated ear can trace the
exact ratio between the slower and the quicker
vibration. When, however, the low C is sounded
in unison with the first G, counting upwards, a
totally different sensation is created. The sen-
sation of identity is lost, but a strange and
pleasant sensation of agreement and unity is
awakened, and the mind feels as if it had got
possession of a new idea, so to say. If the reader
will not think me too metaphysical
or too
mystical, I will say that the introduction of the
reinforcement of tone at threefold intervals, in
place of the monotony of the twofold union, gives
birth to a certain subtle sense of freedom, and
awakens the hidden consciousness of the power
of modulation into life. Nor will the thoughtful
73
theorist deride what I am saying. He knows
that the whole mystery of the inexplicable charm
of the movement of complicated harmony is the
result of the unconscious application of the
subtlest laws of sound to the expression of human
intelligence and emotion, and that the greatest
masters are those who by a species of inspiration
have felt their way along the path of musical
development, through their gift of understanding
the endless variations of the delicate relationships
possible between concordant and discordant
chords.
66. Leaving this digression, however, I must
call the student's attention to the fact, now made
clear, that there are real differences between the
degrees in which certain unions of notes are con-
cordant, resulting from the variations in frequency
with which their vibrations simultaneously strike
the ear.
It is obvious beforehand, from the
harmonic law to which I have been referring, that
such would have been the case, and, in reality,
every body feels it to be so. Whatever theorists
may say, everyone feels that the union between
C and G, that is, the concord of the fifth, as it is
usually called, is more strongly concordant than
that of a third, whether a major or a minor third;
74
and that consequently a relationship exists be-
tween a key-note and its fifth more intimate than
that which is possible between any other two
notes in the diatonic scale. And the reason is
perfectly clear and intelligible to any one who will
take the trouble to study the arithmetical relation-
ships of the sounds in the scale. The twelfth of
the key-note, or that which, for practical purposes,
is the fifth (the distance between the twelfth and
the fifth being just one octave), vibrates three
times as often as the key-note itself. But the
third of the key-note, which is really the seven-
teenth (omitting the two intervening octaves),
vibrates five times as fast as the key-note, being
the fifth harmonic. .
e
That is, while in the case of the fifth, or G, the
blows struck by the sounds are doubled at every
third blow, in the case of the third, E, they are
doubled at every fifth blow, the impact of the
intervening blows being enfeebled and confused.
In the case of the minor third, G E-
在 ​f
75
-the impression of concord is still feebler. The E
vibrating five times as fast as the fundamental
note, and the G vibrating six times as fast, the
G and the E sounding together will strike the ear
simultaneously only once in thirty vibrations, as
any schoolboy who has learnt the elements of
fractions will understand.
67. But this is not all. While the strokes of
the fundamental note C
are reinforced by the strokes of the G
at every third vibration, they are also reinforced
by strokes (less powerful, it is true, but quite
effectual) from the next G
at every sixth vibration, so that, in fact, the vibra-
tions of the C are doubled at every third and
trebled at every sixth vibration, while the concords
of the major and minor thirds remain as just
76
stated. Similar results follow from the reinforcing
influences of all other harmonics in their various
degrees.
68. The great practical result is, however, what
I have pointed out, namely, the irresistible
influence of the fifth, or dominant, the moment
we wish to add a fresh chord to that which
already fills the ear, even if only a single note has
been sounded by a tube or string. If instead of
merely sounding the single note C we have
sounded the common chord, by adding the third
and the fifth, the influence of the fifth is all the
more commanding through the operation of the
same harmonic laws in reference to the fifth (G)
and the third (E). The fifth must therefore be
made the fundamental note of the new harmony,
and must become the root of a common chord of
its own.
No other combination of sounds satisfies
the ear to the same extent; while so satisfied is
the ear with the new common chord based upon
the fact that the introduction of the seventh,
absurdly called the “major seventh," which was
so intolerable to the ear when sounded alone,
immediately after the fundamental note, becomes
positively agreeable, imparting a peculiarly bright
and as it were pungent delicacy of flavour to the
77
combination thus created. At the same time,
every person with a cultivated sensibility to music,
who will analyse the effect of the new common
chord upon his ear, will feel that the effects of
the new third and of the new fifth are not the
same.
While in the chord
000
the effect of the D is soft, that of the B4 has a
piquancy of its own, and imparts a sense of
brightness to the change.
CHAPTER IV.
Chords made up of a series of thirds.—The necessary influences
of the chords of the dominant and of the flat seventh.
Naked fifths.
69. We are thus brought to the following
elementary conclusions: First, the diatonic scale
is an arrangement of intervals which is necessary
to the development of melody, and the adoption of
the common chord as the first step in the creation
of harmony is rendered equally necessary, through
the laws of the vibration of all musical sound.
70. Secondly, harmony, like melody, consisting
in the agreeable succession of chords, the first
condition for the invention of a new chord must
be sought in the elements of the common chord
already in existence. In the predominance of the
fifth, above all the other harmonics, this requisite
condition is supplied to us, and in the application
of the laws of the common chord to this new
basis must be sought the conditions for a further
development of harmonic combinations.
71. Thirdly, inasmuch as all harmonics are the
physical effect of the vibrations of the lowest
78
79
sound of the series, that sound is really the
root from which all combinations must be treated
as growing. Every possible chord, whether
concordant or discordant, having a tendency,
resulting from the endless possible combinations
of harmonics, to move in some special direction,
the recognition of some one note, either struck or
implied in any chord, as its “root," is not a
caprice of musical theorists, but is involved in the
unchangeably composite character of every simple
musical sound. Every alteration in the relative
position of the various notes in a chord is therefore
rightly called an "inversion" of its natural
position. And whether or not the student
proceeds to the study of the many names by
which musical grammarians designate the various
chords employed by modern composers, it ought
never to be forgotten that the ear is always
conscious of the want of some low note to which
any two or more successions of harmonics must
be referred.
72. Hence the remark that is so often made
as to the superior skill of all the great masters
in the treatment of the bass part of their writings.
With all inferior composers the bass, however
correct, is frequently weak and ineffective; where-
80
as with the great men the bass presents a union
of tunefulness, strength, and naturalness which
thoroughly satisfies the ear and practically sustains
the melody. Hence, also, the remark which
appears so strange to the beginner, that a melody
to which it is impossible to add a good bass is in
itself a worthiess tune.
73. The recognition of the common chord of the
fifth or dominant being thus established as the
first step in the formation of harmony, two ques-
tions immediately present themselves. On what
principle shall we build up and analyse our
chords, taken singly? And on what principle
shall we unite them in a regular succession, so as
to recognise the relationship between the two dia-
tonic scales of which they must frequently be
composed ?
74. First, then, on what principle shall we
build up and analyse our chords ? As a matter
of fact, they are concordant and discordant in
very various degrees. Whatever names may be
given to them by theorists and grammarians,
the ear is conscious of a large variety of sensa-
tions produced by different chords; a variety,
81
moreover, which is materially affected by the
relative positions of the different notes which
make up a chord. These changes, which, as
has been said, are termed the “inversions" of a
chord, unquestionably indicate the existence of
some subtle influence exerted by some physical
cause, which is by no means explained by the
usual custom of calling a chord by some bewilder-
ing arithmetical name. Of what elements, then,
is a chord composed ?
75. Surely there is but one reply which is in
accordance with physical facts. Every chord
is made up of a series of thirds, termed technically
major and minor, and consisting respectively of
four and of three semitones. A simple analysis
of the elements of the composite quality of the
fundamental single note leaves us in no doubt
about the matter. Natural harmonics constitute
a union of thirds, so far as the ear can practically
detect their existence in actual music. And it is
only with actual musical possibilities that we
are concerned. As in painting a picture we are
not concerned with the qualities and effects of the
prismatic hues as presented to the eye by real
light, but only with the hues of coloured solid
objects, so it is with all musical writing. And
G
82
the great fundamental fact which is thus presented
to us is this harmonic chord :-
6
in which the three lower notes here written in the
bass staff need not be unnecessarily referred to,
as being repeated in their octaves in the treble
staff; with this reservation, that it is to these
lower sounds, and above all to the lowest C, that
all the upper sounds are referred by the ear. For
this same reason it is that it is unnecessary to
include the higher harmonics, as they are so feeble
in sound that the ear is not practically affected
by their existence.
76. Here, then, is an overwhelming flood of
sound, made up entirely of thirds, which compels
us to reject all other theories as to the composi-
tion of chords, and includes, in addition to another
chord hereafter to be discussed, all the chords
which need be mastered by those who are seeking
only for first lessons in harmony. In this com-
bination of five notes, beginning with the three
lowest, we get the common chord; the addition
83
of the next third furnishes us with the chord
which is called that of the flat or minor seventh,
while with the addition of the D we obtain the
chord of the ninth. In the study of these chords,
with the addition of that which is called the
diminished seventh, the beginner will find
abundant illustrations of the essential nature of all
modulations, and will be able to furnish himself
with materials for all the composition which he
may like to attempt for himself.
77. Here, however, I must reply to one or two
objections which may be made to this view of the
necessary analysis of all chords. · A chord, I would
remind the reader, is a combination of sounds
on which the ear is willing to dwell as an essential
portion of the structure of a piece of harmony.
It must be distinguished at the outset from any
passing notes which would be painfully discordant
if dwelt upon, but which are found agreeable and
suggestive when taken rapidly, so that the ear
is just conscious of their momentary presence, and
that is all. But these passing notes are difficult
to use agreeably, and the beginner should have
nothing to do with them, except to notice and
enjoy the charming effects which they produce
in the hands of the great masters.
84
66 How
78. And this brings me to reply to a difficult
question, which an intelligent student might
naturally make to the adoption of the principle
that all chords are made up of thirds.
can you reconcile your principles," he will say,
6 with the fact that all unisons are regarded as
identical in their nature when forming portions
of a harmony?” In this chord of the seventh
you have a Bb reckoned as a third above the
G and a third below the D. Well and good. But
what is the relation of the Bb and the D to any
other C in unison with the C from which all these
thirds are reckoned? Why may not this following
combination of C and D
be reckoned as part of a chord, and why is
it regarded as simply a hideous discord ? Why
may not chords be regarded as
partly of seconds, as well as of ninths and
sevenths ?
made up
79. I reply by recurring to the great fundamental
law of the composite harmonic character of every
single sound, involving the equally fundamental
law of the difference in the degrees of consonance
85
and dissonance between certain concords and
discords. The interval of the ninth
is unquestionably a discord; but it is not nearly
so strongly discordant as the interval of the
second
although in each case the notes are a C and a
D sounded together. This statement may seem
strange at first sight, but the fact is undeniable,
and the reason is this : that the note C
is the effect of vibrations four times as fast as
those of the fundamental sound C
while the next C
은
​is the effect of vibrations eight times as fast as
those of the fundamental C; the D
86
being the effect of vibrations nine times as fast
as those of the fundamental C. Consequently,
while in the chord of the ninth the two waves
of vibration synchronise once in every thirty-six
(4 X 9) strokes upon the ear, in the chord of the
second they synchronise only once in every
seventy-two (8 x 9) strokes. When, therefore,
the two sounds of C and D (in the treble clef)
are treated as the interval of the ninth, that
is, divided from one another by four thirds,
the ear recognises a closer approach to a concord
than when they are only separated by a single
tone. And hence the complete chord of the ninth
is felt to be a partial approach to that common
chord of the third and fifth, towards which all
chords, whether concords or discords, necessarily
are felt to move by the natural laws of sound.
The adoption of a division of all chords into
combinations of thirds is, therefore, not merely
a useful practical device for the grammatical
analysis of chords, but is forced upon us by
the fact that in every case the ear necessarily
refers all sounds to a certain fundamental note
or rest, from which nature deduces her own
chords in thirds only, until the sounds she pro-
duces are too faint to impress themselves upon
the ear.
87
80. Following the guidance of nature, we are
next led to the consideration of the chord which
is commonly called the chord of the minor
seventh
This is one of those terms which have been
introduced into musical nomenclature by a
sort of hap-hazard, but which have either no
meaning at all or a false meaning, and which
serve only to confuse the student. According
to the dictates of nature, this chord is simply the
chord of the seventh. It is the seventh note in
the diatonic scale, so long as it approximately
retains the actual sounds produced by nature.
When the interval of the seventh is simply
lessened by the sharpening of the C-
0000
the chord is rationally called the “ diminished
seventh," into which the unmeaning terms
major” and “minor” are not intruded. But
the quality and functions of this “diminished
seventh"
are very different from those of the
real seventh, and our consideration of them must
be for the present postponed. In the meantime
88
I shall take the liberty of calling the seventh of
nature the flat seventh, as sufficiently 'showing
what it is without the adoption of the terms
'major" and " minor."
81. The flat seventh, then, is a note which
refuses to have its claims for recognition absolutely
set aside so long as it remains in harmonic
connection with the diatonic scale of C. In draw-
ing up that scale musicians have summarily
abolished this seventh, and have substituted for
it another note which writers have usually called
the major seventh, as if after all it was the seventh
of nature. This introduction of a semitone, as the
last division of the scale previous to the return
of the first note in the form of its octave, has
been shown to be necessary in order to fashion
a scale thoroughly serviceable for the purposes
of melody. But
i
"Naturam expellas furcâ, tainen usque recurret ;'
which saying of Horace may be thus freely
rendered: “You may condemn the seventh of
nature to exile, but it will not cease sounding
in your ears nevertheless." The fundamental C
goes on producing as its seventh harmonic a
sound nearly the same as the Bb of the complete
89
chromatic scale, while the ear insists upon regard-
ing this interval of a flat seventh as something
very nearly akin to a concord, notwithstanding
all the nomenclature of theorists, who regard
musical science as something apart from nature.
This union of
C and Bb, let it never be forgotten, is nearly
a concord, the strokes of the Bb falling upon the
ear almost exactly seven times as fast as those
of the C; and as long as that C goes on sounding,
the Bb goes on sounding too; and thus, when the
C is silenced, it has accustomed the ear to this
peculiar interval and prepared us to receive it
again with pleasure whenever naturally introduced
without violating the grammatical rule of the
scale as a fixed succession of sounds. This scale
is, as has been shown, the result of a compromise,
made necessary by the irreversible facts of har-
monics; and we must never forget that the position
and power of the seventh are the consequence
of this compromise, and that the phenomena of
90
acoustics render all strictly logical identification
of theoretical scales with the mysteries of musical
sound, as apprehended by the mind, impossible.
82. The first result, therefore, of the presence
of the flat seventh in the harmonics of a funda-
mental note is to increase the influence of what
is called a minor third in all harmonious pro-
gressions. In the chord of the third and fifth,
consisting of one major and one minor third, the
concordant element is stronger in the major than
in the minor. But the addition of the Bb, that is,
the addition of another minor third, so that the
composite sound which the ear takes in consists
of one major and two minor thirds, habituates the
ear to the sentiment, so to say, of the minor third,
and prepares it for the immense influence of this
interval in all the processes of modulation.
i
83. Nor let the reader imagine that this state-
ment is whimsical or fanciful. The processes
of modulation, by which all modern music works
its marvellous charms, are in reality the result
of a long and careful culture of the sensibility of the
ear—that is, of the brain through the nerves.
And the modulations and chords which are so
captivating to our ears, and which would have
91
been rejected as hideous by the greatest masters
three hundred years ago, are all to be traced
to some subtle connection with the elementary
laws of physical sound which the present genera-
tion has learned to feel.
84. And hence it is, if I may be permitted a
practical digression, that it is so necessary for
the formation of a perfectly liberal and sensitive
musical taste that the student should acquaint
himself, sympathetically and progressively, with the
works of the great masters, from Palestrina to
Beethoven. He will then understand that all the
progress which has been made is nothing but a
development; each advance having been simply
a trial of new effects, under the guidance of an
ear familiar with the simpler combinations of
sounds, and trained in the use of the practical
resources of the art while still limited in its
liberties. Those who believe in the hereditary
transmission of acquired qualities in the brain
would hold that we of the nineteenth century are
born with brains fitted to comprehend and enjoy
Beethoven's choral symphony to an extent which
would have been impossible to the brains of the
people of the sixteenth century. But be that as
it may, it is certain that the music of this century
92
can only be thoroughly understood, criticised, and
estimated at its true value by those who know
the great works of the past in their complete
sequence and their historical and musical growth.
85. Returning, then, from this digression, it is
our duty to ascertain, if possible, what further
influence has been exerted upon musical art by
this presence of the flat seventh in the midst of a
scale, and of harmonies from which it has been
forcibly excluded. As I have pointed out, it has
strengthened the position of the minor third as an
element in the construction of harmony; but it
has done more than this. It has contributed
materially to that recognition of the varying
degrees of consonance and dissonance, which,
though only partially, if at all, recognised by
theorists, constitute the basis upon which the
development of the art has been conducted. The
force or strength of a concord depending physi-
cally upon the frequency with which its sounds
synchronise in their strokes upon the ear, every
introduction of any interval which familiarises the
ear with a concord which is less concordant than
any previously known, is practically the introduc-
tion of a new delicacy or subtlety of modulation,
and lessens the strong contrast between the
93
concord and the discord, as such, which is so
powerfully felt in the first steps of modulation.
86. Now, as has been already shown, in the
major third
the strokes of the two sounds synchronise at every
twentieth vibration, while in the minor third
f
they synchronise only at every thirtieth. But
when the chord of the seventh is completed, we
have another minor third
英
​in which the strokes synchronise only at every
forty-second vibration; the B flat vibrating seven
times while the G vibrates six times. Here,
therefore, is a new combination which is recognised
by the brain as nearly concordant, but which yet
tends to a dissonance more decidedly than does
the minor third already recognised; and thus also
we get at the reason why the effect of a chord
upon the mind depends so much upon the relative
position, or, as it is termed, the inversion, of its
94
component notes. In reality, the further each
third is removed from the fundamental note from
which all the notes are harmonically derived, the
less close becomes the relationship of each pair of
sounds; in other words, the more their original
concord tends to become a discord.
87. Here, too, we see that it is impossible to
lay down any precise rules for the “resolution" of
discords into their allied concords under all circum-
stances, and amid the endless varieties of the
treatment of complicated chords by the great
writers. The fact is, that the intervals of which
these chords are made up are not the same in
reality when differently inverted, and still more
when they stand at widely different intervals from
the deep fundamental note. Certain rules must
be observed in the change or resolution of a discord
into its nearest concord in a few simple cases.
But these rules no more tell us what must be
done in all possible combinations than the rules
for constructing a sentence, in which the nouns,
adjectives, and verbs shall all be used grammati-
cally, will suffice to enable us to comprehend the
majesty of Milton's verse, or the delicate graces
of Addison's prose. Modulation is like the colour-
ing of pictures: no rules can thoroughly teach
1
95
it. We may instruct the young painter in the
peculiar effect of green and red, of yellow and
purple, of orano
of colour upon the retina; but the beauty of the
colouring of a picture depends upon a multitude of
little combinations and contrasts, upon which
none but the mind of the true artist can decide.
88. Thus it is that the skill with which the
difficult notes in a harmony are (as it is called)
dispersed” is one of the surest tests of a com-
poser's right to be called a master in his art.
Notice the striking difference between the effect
of the same notes in the scale of two octaves, as
thus dispersed
8
and the same notes as here rearranged-
D
In the second arrangement the G, which is the
96
second harmonic in natural sound, is placed
where it comes in nature; in the first arrange-
ment the E is made to sound where it has no
place, and the result is that the effect of the
second arrangement is full and satisfactory, while
that of the first is bald and awkward. Compare,
again, the impression of fulness, richness, and
ease which the best writers can produce with a
few notes or instruments, with the mere loudness,
effort, and uneasy changefulness of others, whose
music is, nevertheless, tolerably good in its way.
Haydn is certainly not one of the greatest masters,
and to place his violin quartets on a level with
those of Mozart and Beethoven would be absurd ;
but yet how surprising is the impression of fulness,
ease, and completeness which he contrives to
convey by his skill in the arrangement of his
chords. There is no remarkable profoundness or
tenderness in his thoughts, but in what is termed
“style" in writing he is unsurpassed. And it is
the same with the handling of the orchestra in
"The Creation." And all this because he instinc-
tively felt that the impression produced by a chord
or an interval depends not only on its treatment by
itself, but upon its subtle relation to the composite
harmonies generated by the lowest notes with which
his melodies and modulations were connected.
t
97
89. The ear, in truth, incessantly modifies the
application of the rules of rigorous musical techni-
calism. Books may tell us that all minor thirds
consist of three semitones; and so they do on
paper, and viewed as individual and imaginary
sounds. But in harmony, that is, when combined
in real music, the ear cannot help referring them
to some one common fundamental note, and
feels that
is not the same portion of a complete chord as
ܕ
ODI
90. The fact appears to be that the two intervals
which the ear loves the best, as suggesting the
idea of repose and completeness, are the major
third
and the minor third
and that no other major or minor thirds in the
scale are equally satisfactory. The moment a
H
98
minor third becomes less concordant than in this
special position, it begins to suggest sad and
plaintive thoughts, and is transformed into the
first minor third in the minor diatonic scale.
And it is the same with any interval more wide
than the four first semitones in the diatonic scale,
The fourth-
again, is an unsatisfactory combination in itself,
because, as has been already shown, the F has
no natural harmonic relation to the C, and because
the strokes of the combined vibrations synchronise
at far distant intervals in their strokes upon
the ear.
91. Further, although we have banished the flat
seventh from our diatonic scale and substituted
a sharpened seventh for the sake of giving com-
pleteness to our octave, yet the ear cannot lose
all sensation of the original seventh, and an
incessant conflict goes on between nature in her
simplest form and nature as modified by art. The
ear having once thoroughly taken in this interval
of the real seventh acquires a tendency to accept
all modulations whereby it reasserts its original
influence. Thus, as soon as the fifth is felt to
99
furnish a solid basis for the construction of a fresh
chord of the seventh, from which the original B2
has been banished, thus
of
the memory of the old banished note still lingers
on and makes the ear willing to accept a fresh
point of departure from the original key of C
into a kindred scale where the Bb resumes its
position, although there is no“ blood relationship”
of the new key-note F to the sound. This new
note F being once admitted as the fundamental
sound, the C falls at once into its place as the
second harmonic, and thus the first “flat key"
takes possession, and we are conscious of an
influence upon our emotions quite different in kind
from that which results from a modulation into
the nearest "sharp key." Nobody will deny the
reality of the difference of the two kinds of
modulation in affecting our minds, and I venture
to think that the explanation I have here given
is at least partly its true explanation. A modula-
tion into the nearest flat key is felt to convey a
sensation of repose, because the harmonic flat
seventh has regained its place in the general
movement of both melody and harmony.
100
92. Here, too, is perhaps the right place for
pointing out the reason why the naked fifth is
not an agreeable combination, unless some special
reason can be assigned for its use in peculiar
circumstances. It sounds hard and colourless,
for the simple reason that it is too strongly con-
cordant, and lacks those delicate shades of dis-
sonance without which we may be impressed,
but are not pleasantly moved. In the octave the
strokes upon the ear are reinforced at every
alternate blow, and we do not feel any effect of
harmony at all. In fifths, which are to the
ear the same as twelfths, every third blow is
reinforced by an additional stroke, and the ear
seems, in a sort of physical sense, to suffer, until
the soothing influence of the comparatively dis-
sonant intervals of the major and the minor third
are combined with the vigorous assault of the fifth.
In the case of horns and trumpets this want of the
assimilating tone of the third is less felt, because
the horn and the trumpet are instruments of ex-
treme resonance, and the whole series of harmonics
are produced with a clearness which fills up the
naked fifth with a gentle force peculiarly their own.
93. Thus, then, we are brought to recognise
the intimate relationship between the natural
ΙΟΙ
diatonic key of C and its dominant G on the
one side, and a similar relationship with the
key of F on the other. They both arise from
the composite character of the fundamental C,
whose harmonics generate an overwhelming
fifth in company with an intruding but necessary
sharp seventh, and which, at the same time,
suggests the recognition of the real seventh and
the banishment of the intruder, by the invention
of some new arrangement of tones and semi-
tones. From the same study of the nature of
sound we have learnt the necessity of regarding
the lowest note in every chord as the root from
which it springs, and the inclination which the
ear feels to resolve every strongly dissonant
combination into some more consonant interval,
to be itself in the end resolved into the one most
satisfactory chord of all, that is, the chord of the
third and fifth, oddly called the common chord.
We have also seen that the ear requires the
occasional use of a further union of thirds in the
chord of the seventh, and in the judicious use of
these several chords and their modulations the
first elements of all harmony are comprised.
CHAPTER V.
Key-relationship in complicated harmonies.
94. The reader will thus have seen that it is in
this long lingering hold upon the ear, which is
retained by any full sounding note, that I believe
that the solution of many of the difficulties which
seem to beset the theory of music, as a reality, is
to be found. It is not enough to regard a sequence
of single notes or chords as mere collections of
sounds taken in pairs or threes, just as we cannot
discuss the colouring of a picture by noticing only
the juxtaposition of each separate set of tints. The
eye is affected, it is true, by the prismatic divisions
of light, according to certain sharply defined rules;
but the methods by which the mind is moved by
the endless possible combinations and modifi-
cations of these lines is dependent upon certain
subtle truths of broad and wide application, which
no literal and regular teaching can communicate.*
95. A very interesting illustration of the truth
of the theory here advocated is supplied to me by
the concluding paragraph of Mr. Sedley Taylor's
* See some excellent remarks bearing on this subject in the
eleventh chapter of Dr. Stainer's “ Theory of Harmony."
102
103
زو
« Sound and Music.” After the very pertinent
remark that “unquestionably the ear's order of
merit is not the same as the mechanical order,"
Mr. Taylor says, “I am inclined to attribute the
predilection of the ear for thirds and sixths, over
the other concords, to circumstances connected
with its perception of key-velations, though I am
not able to give a satisfactory account of them."
Yet Mr. Taylor himself supplies an illustration
which leads to that very comprehension of the
effect of key-relationship whose power he feels.
96. He quotes the concluding bars from the
final chorus of Bach's “ Passion according to St.
Matthew” as supplying a case of a discord which,
when isolated, is so intensely harsh that it is at first
difficult to understand how any preceding or suc-
ceeding concords could make it at all tolerable;''yet,"
as he justly adds, "the sequence in both the phrases
cited is of the rarest beauty." They are these :-
ru
he
sauf
te, sauf - te
ruh.
1
104
4
ob 3
4
8 8
As Mr. Taylor says, the chord marked with the *
in each phrase, taken by itself, is excruciating;
yet, as used by Bach, “it is of the rarest beauty.”
Guided, however, by the principles here insisted
on, the reason is really clear. If we sit down to
the piano and play over the passage, we feel at
once that it is through the withdrawing from the
harmony of the dominant fifth * (Bb in the first
passage, G in the second) in the last chord of the
first bar that the extraordinary sense of harshness is
felt in the sudden discord with which the next bar
opens; and that at the same time it is the marked
re-introduction of the same fifth in the tenor part
which at once makes the ear feel that the sudden
break in the movement is only momentary, and
was introduced by Bach for the purpose of giving
a sensation of piquancy to the even flow of the
passage. How smooth and vocal is the whole,
and above all how beautiful is the rhythm of the
* The passages are here in the keys of ED and its relative
minor, C; though the signature still indicates the key of Bb.
105
second soprano, will be seen strikingly by singing
or playing each one of the parts by itself.
97. And there can be no doubt that Bach did
really make special provision for intensifying a
sense of continuance in that same fifth, in order to
carry on the sense of quiet waiting and gentle
movement, until the final close of each passage in
the common chord. If we turn to the preceding
bars in the chorus, we find the very fifth itself,
filling the ear with voices and double basses for
two previous bars, and dropped only for a moment.
The whole passage of six bars is, in fact, nothing
but a prolonged cadence; and by dwelling upon
the preparatory dominant the mind is preparing
itself for the final close, after its long tension
amidst the scenes of the tragedy through which it
has been carried. And it is thus by a master-
stroke of the poetic art that Bach gives to his
final movement that “ lengthened sweetness long
drawn out," which, in conjunction with a perfect
manliness and intelligence, is the characteristic of
this wonderful chorus.
98. It is to be noted, further, that, with equal
power and propriety, Bach first impresses us
irresistibly with a sense of the rest and repose to
106
which Jesus has attained through the gate of
agony and death, leading us up to that particular
phrase which has been here quoted, in the major
key; and then repeats it and finally concludes
in the minor, so as to leave upon the mind the
recollection that it is a tragedy which it has been
really witnessing. All through the work, in truth,
this mingling of the sympathies of those who
stand by with the agonies of the sufferer has
been expressed with the rarest skill. This is the
secret of the repetition of the famous chorale,
“O haupt voll blut und wunden," so many times,
though with varying words and harmonies. It is
the voice of the heart, which, though it cannot
actually share the pangs of the sufferer, yet makes
them its own so far as love and sympathy can
make them. Then at last, when the “ Passion"
is over, it is natural to continue this drawing out of
each emotion up to the last; and so the few final
pages assume the character of one long, varied,
interrupted, and, finally, completed cadence,
during which the ear lingers tenderly upon the
dying strains, still willing to dwell upon each
fresh short phrase and modulation rather than to
bring all to its final close. And it is by this
persistent sounding of the dominant again and
again, and in different ways, that this loving,
107
lingering feeling is sustained. Thus, as I have
said, with profoundly artistic skill, just when it
seems that the last thought of the drama shall be
one of repose and peace, we are brought back to
the recollection that after all it has been a tragedy
at which we have been present, by the re-intro-
duction of the minor key, including that same
strange discord which we have before noticed, in
which the dominant plays the same important
part, and completes the breadth, the unity, and
the expressiveness of a piece which is certainly
one of the most dramatic choruses that have ever
been written.
CHAPTER VI.
First attempts at harmonies.-Consecutive octaves and fifths.
99. It has been already remarked that it is in
the judicious use of the common chord and the
chord of the seventh, and of those of the most
closely allied keys, that the student will find him-
self able to use, as well as to understand, the
simplest and most important movements of
harmony in aid of melody. Some little explana-
tion is next necessary as to what is meant by
this judicious use.
100. The first rule to be observed—and, indeed,
it is a principle rather than a mere rule-is this,
that all harmony should be regarded as the com-
binations of separate individual parts or “voices,"
as they are often called in continental music: a
term which is better than our own, because it
conveys the idea of the free individuality of each
part. And this freedom, when used melodiously,
is the very soul of good harmony. In all the
best harmony, from a fugue or symphony down
to the simplest part-song, even the uncultivated
ear recognises a sort of tunefulness, ease, and
108
10g
unity which it misses in inferior compositions.
It is, perhaps, in a quartet of voices or strings
that we feel especially the individuality of the
movements of each part, in which each preserves
its own distinct character, never makes an ugly
phrase, and yet never disregards its duty towards
its brother voices or instruments. Yet in orches-
tral works on the largest scale the same variety
in unity is to be observed. Flutes, hautboys,
clarinets, and bassoons (the quartet of wood
instruments); trumpets, horns, and trombones
(the brass section); violins, violas, violoncellos,
and double basses (the strings) : each as a body,
and each as a single instrument, preserves its
individuality, is never ugly, and yet contributes
its portion to the complete effect of the whole
with ready submissiveness.
101. The most surprising of all masterpieces
in this art of combining completeness with
individuality are, as I think, the great choral
works of Bach, especially his “Matthew Passion,"
his “John Passion," and his mass in B minor.
No writer has ever succeeded in combining
accompaniments marked with such strong indi-
viduality and force of melody with vocal parts
equally individual and equally intense in tune, while
ΙΙΟ
yet the combination of the vocal and the instru-
mental parts appears to the ear as natural, simple,
and complete, as if one was little more than an
expansion of the other.
102. This, therefore, is the idea with which
the student should begin all practical attempts
at harmony. Every part should move agreeably
when taken by itself, as well as when taken in
conjunction with others. In the next place, the
use of octaves should be sparing in harmony
of three parts, and requires much care in harmony
of four parts. It is usual to lay down the rule
that consecutive octaves, that is, octaves which
move in the same direction, either upwards or
downwards, must be avoided only because they
doriọt add to the harmony. But it appears
to me..that they are often equally useless, or
indeeit Bjectionable, when they are not con-
secutive:** The one question to be considered is
as to the degree in which they reinforce the
various portions of a harmony in its irrevocable
union with the harmonics of its fundamental
notes.
103. Far more important, however, is the rule
which forbids the use of consecutive fifths; a rule
III
in which every one acquiesces, but of which I have
never seen any satisfactory explanation. Take
these notes, for instance :-
are they not positively hideous ? They are con-
demned as “consecutive perfect fifths." Then
take these two
which are tolerated as a “perfect fifth,” followed
by an “imperfect fifth.” They certainly have
not the effect of perfect repose and completeness,
but they are agreeable, and seem naturally to Isad
to something else which will close the musical
phrase.
104. Now, first of all, why is the first succession
hideous ? Each of the two fifths is a strongly
marked concord. Surely there must be some
reason in the nature of atmospheric movements
why they should be so intensely disagreeable
when they follow close upon one another? I
think the reason is to be found in that same
II2
fundamental fact upon which the theory of this
little book is founded; the fact, that is, that the
harmonics of a note linger far longer in the ear
than has been generally supposed. And thus it
is that when the two notes of the second fifth
手
​are sounded, they are felt to be utterly in discord
with the whole series of the harmonics of the first
fifth
Let me once again urgently press upon the
student the recollection that what we are dealing
with are actual sounds, and not names and
distinctions upon paper; and that when we have
made up a complete set of seven notes, three of
whicho do not exist in the real sounds struck by
the fundamental note, nature has still been too
strong for us, and has filled our ear with her own
real tones. When, then, we drop two of the
most important of the real tones in a scale, and
suddenly give forth two other sounds, of which
not a trace is as yet sounding in our ears,
the effect is awkward, harsh, impertinent, and
positively repulsive. The sounds of the second
II3
事 ​●
fifth are nowhere,* and have no acoustical
connection whatever with those of the first fifth,
and are therefore, unless their intrusion is con-
cealed with rare skill, extremely unwelcome.
105. But, it will be said, how do you, on this
theory, account for the fact that a sequence
consisting of a “perfect" and an “imperfect "
fifth is not nearly so disagreeable, although
neither of the two new notes
至
​to
exists in the original harmonic scale ? The
objection is a very fair one, but I think it can be
answered.
106. In the first place, the interval called an
imperfect fifth is no fifth at all, except upon
paper.
It has no
no relation in reality to the
* The student should be reminded that the note D does enter
as a harmonic higher up in the scale
but that its sound is very faint indeed. A delicate ear will, more-
over, at once notice that it is the A in the second of the
consecutive fiſths which is so extremely disagreeable.
I
I14
perfect", fifth, which consists of seven semi-
tones, and by nature exercises so powerful an
influence upon all harmony that it is justly
called the dominant. The “imperfect” fifth
consists of six semitones, and is no more a real
fifth than (as I have said) my next-door neighbour
is
my
cousin because his house happens to join
on to my own. But it is not enough to call
attention to our faulty nomenclature.
notion is true, that it is the intrusion of two
perfectly new sounds which makes the second
fifth so unpleasant, the same reason ought to
make the entrance of the “imperfect" fifth
equally unpleasant, inasmuch as neither the F
nor the Bh is found in the natural scale of
harmonics.
If my
107. Now it is not maintained that the passage
from the “perfect" to the “imperfect" fifth is a
sequence on which the ear likes to dwell. The
second fifth is felt to be emphatically a passing
sound, and is pleasant only as leading the ear
onwards with as little delay as possible to some
new chord. It will be enough, therefore, if we
can detect some tolerably distinct and real con-
nection between it and the original harmonic
sounds, so that although the succession is slightly
115
strange it may be made fairly welcome. Now
is it not the case that when the “imperfect "
fifth
is sounded the ear is conscious of a certain
connection between those two notes and the G
next below them? I do not think I am at
all fanciful in so saying. While there is no
lingering sound to connect
and
f
the retention of the C, thus-
>
or of the G, thus-
sounding simply like a blunder; the retention of
the G in the second case, thus-
के
so
116
or its addition an octave below
1
8 랑
​sounds perfectly natural. Hence I conclude that
the loud sound of the second harmonic G
is still lingering in the ear and mingles with the
new fifth, as the root note of the chord of the
seventh
the moment it is sounded, and thus furnishes
a bond between the "perfect” and “imperfect "
fifths, which is wanting in the case of the two
“perfect” fifths.
108. At any rate, practically there is no difficulty
in judiciously advancing from a “perfect” to an
“imperfect” fifth, while the student will do well
rigorously to avoid all consecutive" perfect
fifths. It is quite true that they are occasionally
used by the greatest writers, but it is in peculiar
circumstances, in which some prevailing chord
117
in the phrase, or some peculiar modulations in
the general harmony, or some quaint colouring
which the writer desires to give to his melody,
makes this progression not merely tolerable, but
agreeable. These exceptional cases are simply
illustrations of the principle that the essence of
music is pleasantness and beauty, that whatever
is ugly is bad, and that in certain cases combi-
nations, which almost invariably are ugly, through
the subtle operation of the physical laws of sound
become actually agreeable. At the same time
they can only be safely indulged in by the
experienced composer whose ear has been refined
and his dexterity sharpened by long and various
practice.
CHAPTER VII.
Equal and unequal temperament.-Claudio Monteverde.-The
diminished seventh.
Tog. One more chord remains for discussion,
which is not of an elementary kind, but which
cannot be overlooked in these "first lessons”
because of its vast practical importance, and
because it holds a position peculiar to itself in the
structure of all harmony; the chord, that is, of
the diminished seventh, written in the key of C,
thus-
oood
The student will see at once that whereas from
C to Bb is the interval of the flattened seventh in
the diatonic scale, counting upwards, the interval
is shortened one semitone at the lower end by
sharpening the C, and the whole chord is thus
rightly called the diminished seventh. This
chord has the peculiarity of consisting of three
“minor thirds," as they are called ; that is, of
three times three semitones; and its introduction
by Claudio Monteverde, early in the seventeenth
118
ΙΙ9
century, is the most important event in the whole
history of musical modulation. Before, however,
referring in detail to his work, it is necessary that
we should come to some conclusion as to the one
great question which still divides musical theorists,
and which must be determined before musical
theory can ever be brought to be a rational and
scientific system.
110. In approaching the question, I must beg
the student to give his careful attention to one of
the most astonishing phenomena in all physical
science, because until it is understood all that
follows and indeed all that has been hitherto
implied—is mere waste of thought and labour.
As has been pointed out, all those peculiar
sounds called octaves, and which are so like and
yet so different, are the result of vibrations of
the air, which are exactly double multiples of
the vibrations which produce the octave sound
immediately below it. If the lowest sound is
produced by thirty-two vibrations, the first octave
will be produced by sixty-four vibrations, the next
by one hundred and twenty-eight, the next by
two hundred and fifty-six, and so on. At the
same time, a peculiarly concordant sound, though
less concordant than the octave, is produced by
I20
each of the other multiples of the lowest sound.
Thus, three times the lowest produce the twelfth
(or fifth); five times produce the seventeenth (or
third), and so on.
III. But now, here appears this surprising
circumstance. It would naturally be supposed
that if we were, on tuning a pianoforte upwards
in exact octaves from C to C and so on, always
forming each succeeding octave by producing
twice the vibrations of its predecessor; and if,
when we had reached the first G (the twelfth),
we continued the same process of tuning from
G to G upwards in double multiples, the sounds
ultimately reached by the octaves of G, when
they and the octaves of C came together, would
be exactly in tune, each sound being the result of
the same number of vibrations. To put it in
ordinary arithmetical language, five times twelve
is exactly the same as twelve times five. But the
wonderful thing is this, that in tuning the piano-
forte it is not so. The final G is found to have
slightly overshot the final C, and consequently all
along from the first it has been impossible to tune
any two keys in exactly correct consonance, if
they are to agree with one another. If we tune
a D an exact fifth from the G below it, and the
I21
C next below the D an exact octave from its own
lower octave C, the interval between the upper
C and D, side by side in the diatonic scale, is
found just a shade more than two exact semitones;
and the accomplished violin player, who can
produce every possible shade of tone upon his
strings, does in fact make his C# not absolutely
identical with his Db.
112. But now comes the tug of war. This
theoretical difference between the two notes
which are identical on all keyed instruments runs
through the whole diatonic scale. We may, if we
please, insist upon regarding D# as a different
note from Eb, FH as different from Gb, and so
on; because when we are writing music in a
particular key we only write the notes which are
in the diatonic scale, treating all others as acci-
dentals. Nevertheless, whether we write, for
instance, F# or Gb, the sound produced by the
player is the same.
* Mr. Bosanquet's Enharmonic Harmonium, exhibited at
South Kensington in 1876, is, so far as I know, the only
successful attempt that has been made to construct an actual
musical instrument in which all the keys in the chromatic scale
are tuned in strict adherence to harmonic law. To say nothing
of the necessary accuracy of arithmetical calculation, the inventive
and constructive skill here displayed are really wonderful.
I22
113. In the early days of musical science, how-
ever, it was just the same as in all other matters
of science. Men looked at one or two facts, and
constructed a vast theory on paper, in harmony
with these one or two facts, and set all others
aside as unworthy of the attention of the
“learned.” Musical theorists knew that in theory
G# is not absolutely the same sound as Ab, but
they did not know that if we do not treat them
as practically identical, all tuning of keyed instru-
ments and all harmony would be impossible. They
invented the absurd notion about the "perfection"
and the “imperfection” of certain intervals, and
assumed that all music is ungrammatical which
is not based on this fancy; while, as a matter of
fact, the ear actually likes the “imperfect " better
than the “perfect” intervals. What was this to
them, however, inasmuch as they regarded music
as a deduction from the multiplication table, and
not as a combination of sounds agreeable to the
human ear, and adapted to kindle into life our
deepest emotions? They were like the old school
of doctors, who insisted that a sick man should
die if their orthodox medicines did not cure him.
114. It is the same with the old musical
doctors. They do not hold that the office of
123
the musical art is to convey musical sound, but
that its function is to enforce musical scales. It
is useless to argue with them that if, as a matter
of musical fact, except in one exceptional case out
of a million, G# is Ab, the two sounds must be
treated as identical, in all musical grammar which
can pretend to be really scientific. All really con-
sistent theorists insist that music is a question of
sound and not of paper; that it is useless to treat
of two sounds as if they are not in reality the
same, when in all practical cases they are the
same; and that until writers on the science of
music recognise this truth, and devote their
inventiveness to such modifications of the unfor-
tunate old nomenclature as shall show that
sounds which are the same had better be
called the same, the study of music as an art
founded on a strict observance of complicated
phenomena will always be a needlessly bewilder-
ing puzzle.
115. The student, then, should at once grasp
the truth that inasmuch as by the laws of sound
it is impossible to tune all the intervals in a piano-
forte in exact tune, the only rational device is to
make them all slightly inaccurate in an equal
degree. This is what is called the method of
124
equal temperament, meaning that all the keys are
equally “tempered” or modified. And this is
what is always done by a thoroughly competent
tuner on the pianoforte, though it has only lately
become general in the tuning of organs, in which
it was the custom to distribute the necessary
errors unequally among different keys, so that in
some chords the discords were dreadful. And
what I am now urging is that theorists as well as
tuners should once for all put away this old notion
of calling notes by their wrong names, as far as
it is possible. They should incessantly remind
themselves and those who follow them that for
practical treatment in the way of modulation F#
is Gb, and G# is Ab, and that it is physically
impossible that they should be anything else.
Doubtless owing to the hand-to-mouth method by
which our nomenclature and practice have grown
up, and the unscientific ignorance of the age when
harmony first grew into infant life, the difficulties to
be encountered are in some degree insurmountable.
But they may be materially lessened by our
steadily bearing in mind the facts of the case,
and remembering that in music it is very
common to call two things by quite different
names, though in reality they are absolutely one
and the same.
125
116. Although it is thus difficult, indeed, to
persuade many persons that when an interval in
actual performances always is of a certain length,
it should be treated as longer or shorter, according
as it happens to occur as a flat or a sharp in some
arbitrary scale, the student will only require to be
reminded of one or two considerations in order
to see that any practical system except that of
equal temperament is impossible. In the first
place, the theory of unequal temperament bases
its pretensions on the notion that all concords
should be as strictly consonant as the laws of the
atmosphere allow, in each individual case and taken
separately. Yet it is the fact that concords never
are taken separately, except (and then almost
always only in theory) by an extremely skilful
violin player, playing alone. Every sound which
has any appreciable resonance always produces
a discord by its own harmonics, so that what the
ear hears is a multitudinous flood of waves,
beautiful in their influence upon the ear, but
banishing to the winds all notions of arithmetical
accuracy in tune. It is the same as with a lovely
picture. In regarding it as a whole, one never
sees the clearly-marked, accurate hard outlines ;
but rather a myriad gradation of tints, melting
one into another. In the case of an orchestra,
126
the production of dissonance is still more marked
and universal. The air is filled with resonances,
which violate all pretence at concordant rigorism.
The minute distinctions between sharps and flats
are lost in a wilderness of sounds, in which the
broadly-marked forms of the tempered diatonic
scale absorb all others; while even in the diatonic
scale itself the most fastidious ear cheerfully
enjoys a generalisation of sounds which is enough
to set the hair of the antique rigorist on end with
horror.
117. If it is urged, as it sometimes is, that this
is not ideal music, I only reply that we are
dealing with music as Nature has made it; and
that inasmuch as Nature has very ignorantly
made us love gently dissonant intervals, we, if we
are wise, should follow Nature's guidance.
• Why has not man a microscopic eye?
For this plain reason: man is not a fly."
So writes Pope ; and we can only add in the
same spirit, “Why has not a man a micracoustic
ear?" Because the sensations of sound are
designed to be the results of atmospheric
vibrations moving at a fixed rate, and not as
rapidly as lightning, and they are to be heard in
127
large masses and by many people at once. And
such being the case, the laws of musical modula-
tion have taught us that peculiar invention which
we call equal temperament, and with which we
are quite contented.
118. Again, how strange it is that those who
imagine that what they call pure harmony is
alone to be endured, always overlook the effect
of the reflected sounds from the walls of a
building! However accurately the minutest
gradation of the diatonic scale may be observed
by a violin player, they are lost the moment they
mingle with one another through their own
reflected movements from the sides of a room.
If a violin player is to maintain a spotless purity
of intonation, he must perch himself upon the
top of the spire of Salisbury Cathedral. It would
not be enough for him to stand in the middle of
Salisbury Plain, for the sounds reflected from
the earth would injure the absolute faultless-
ness of his intonation. Sound, let us remember,
takes only a single second to travel above a
thousand feet, so that it actually takes only a
second for a note to pass from one end of
Winchester Cathedral to the opposite end and
back again.
128
119. What, then, must be the effect of this law
in any ordinary concert room? All the music
that is sung or played reaches the listener not
only as a flood of direct sounds from the singer or
player, but also as reflected sounds from the
walls, the direct sounds reaching the ear quite
appreciably before the reflected sounds, and
producing a confused mixture of tones. When
music is played out of doors, especially not in a
street, these reflected sounds are much lost, and
the effect is poor and thin, while in reality it is
simply much less confused.
120. Hence the comparative value of the
different positions in a concert room. The best
places are those in which the direct sounds from
the musicians reach the ear as nearly as possible
at the same moment with the reflected sounds.
This is the reason why the seats in the curved
orchestra at St. James's Hall, London, are the
best seats for hearing the instrumental music.
The atmospheric waves reach the ear reflected
from the wall behind, almost simultaneously with
those which come direct from the instruments,
and the effect is thus not only loud but clear.
With the songs it is not so good, because the
singer turns his back upon the orchestra, so that
129
none but reflected sounds ever reach it. For
similar reasons the seats which are about one-
half or one-third of the distance down a concert-
room are not so good as those which are quite at
the end of the room ; for although it is quite true
that the farther the atmospheric movement is
prolonged the feebler become its strokes, yet
this diminution of force is more than compensated
by the increase in the exactness of time with
which the direct reflected strokes reach the ear.
And thus it is that in a building with various
galleries, passages, and arches, no one can say
beforehand where the sounds from the orchestra
will be best heard. In our present ignorance of
the laws of acoustics as applied to architecture,
no one can foretell in what odd and unexpected
nook or corner strange reflected waves will so
converge from various quarters as to produce
the most distinct and agreeable, or the most
bewildering, combinations.
121. Here, therefore, we surely have sufficient
ground for maintaining that the preservation of
a really unequal temperament is purely visionary.
It is enough to see that in the first place nature
refuses to silence her harmonics, and secondly
that it is much more true to say that walls have
K
130
voices than that they have ears. In harmony,
therefore, we are satisfied to assume that every
fourth semitone in the chromatic scale is a major
third, and every third semitone a minor third,
by whatever letters, sharps or flats, those intervals
may be designated as a matter of convenience ;
and that, moreover, this interval
-here written as a sixth-is in reality a diminished
seventh, as sounded in actual performance.
122. Such was the conviction, whether or not
he fully understood what he knew (for to know
a truth is not necessarily the same thing as to
understand it), of Claudio Monteverde, whose name
I have already mentioned as the chief founder
of the art of modern music. Born at Cremona
in 1698, it was not till he was about fifty or sixty
years old, when he filled the post of Chapel-master
of the Court of Mantua, that he had astonished
the musical world of his day by the boldness
of the modulations in his madrigals, and above
all by the practical introduction of a union of
131
three minor thirds, which is now known as the
diminished seventh.* In this chord
2
10000
lies the essence of all modern modulation. It is
the most seductive of discords, and is so peculiar
in its quality that the ear almost lingers on it as
if it were a consonance.
123. Its physical composition is this, that to
three notes, which are the chief harmonics in the
fundamental note, it adds a fourth, by displacing
the fundamental note itself, the interloper being
in violent discordance with the fundamental note
as repeated in all its octaves. Thus, while E
and G and Bb
in all their permutations, produce a combined
sound in which the ear is struck at the same
moment by the combined atmospheric waves at the
same frequently recurring intervals, these same
alternations of united and clashing waves are here
* A full account of the work of Monteverde is to be found in
Fétis's “Biographie Universelle des Musiciens."
132
accompanied by a fourth sound (C#), which is
always in violent discord with their own funda-
mental note (cb), and whose strokes are yet
synchronous with their own individual strokes
at intervals of no very wide distance.
124. What was it, then, that suggested this
combination to Monteverde's mind ? I imagine
that it was his adoption of the theory of equal
temperament before his time. Whatever his
teachers (for whom he clearly had no great
veneration) might have said, he insisted upon
regarding A# as the same thing as Bb. And,
therefore, in his ears, whatever there was upon
his desk,
0.01.
was identical with
Dividing this interval into two equal portions,
each a minor third, he added another minor third
at each extremity of the chord, completing an
entire octave, and inventing the startling novelty
of the diminished seventh. This, then, is the
special characteristic of the diminished seventh,
133
that it enables us to divide the octave into four
equal intervals, each of three semitones in length,
and thus becomes the most natural and universally
applicable of all instruments for modulation when
we wish to preserve the peculiar sentiment of
dissonance in its sweetest form.
125. Consequently, from the lowest to the
highest notes in a range of diatonic scales, this
same uniformity of division is preserved, a
uniformity of division into sections of twelve
semitones being effected by the diminished
seventh, following one another to any extent.
And thus it is that the diminished seventh pre-
sents us with the two essential elements of
musical expressiveness in a degree unrivalled
by any other chord.
It unites an absolutely
isochronous stroke of discords, in themselves not
violently dissonant, with a uniformity of division
of intervals throughout the whole length of the
pianoforte key-board or orchestral scale. Thus it
lends itself to all kinds of suspensions and passing
modulations, which answer to the multitudinous
tints in a garden or landscape, and which create
a sense of a rich fulness of life, without any
sense of painful elaboration. Many chords, too,
apparently difficult to handle, are seen to be in
134
reality nothing but diminished sevenths, when
their real nature is ascertained by the free
application of the doctrine of equal tempera-
ment, and the student has learnt that his chief
concern is with musical sound as it exists in
reality.
CHAPTER VIII.
The pedal point.
126. One more subject remains which ought
not to be passed over even in first lessons in
harmony, though it is usually reserved for a more
advanced stage of the study. I need hardly
remind the student that my aim has been to
place before him, as intelligibly as possible, those
elementary ideas of which all music is the
development, leaving to him to pursue the subject
in more elaborate treatises. I wish to show him
what are the fundamental physical facts upon
which all music rests, and how it is that the
mind is led to regard certain sounds and com-
binations as the vehicles by which it expresses
its emotions, and delights to have these emotions
excited. Why it is that the mind is moved by
one class of atmospheric vibrations rather than
by another no mortal intelligence can say, just as
no one can tell why the retina and the mind are
affected by red in a manner different from that in
which they are affected by green. It is not very
many years since adequate attention was drawn
to the fact that our sensations of colour, and
135
136
con-
indeed of form, are materially affected by the
permanence of the impression which is made
upon the retina of our eye by every object that is
presented to it, whether we ourselves are
scious of it or not. Even now it may be doubted
whether painters, decorators, and designers are
sufficiently alive to the undeniable phenomenon
that, in reality, the moment we look at any
coloured object there simultaneously begins the
formation upon the retina of an image (technically
termed the spectruin) of that object in a colour
which is compounded of the two remaining (or
complementary) colours in the prism, or rainbow.
The moment we look at a blue object an orange
image (orange being compounded of red and
yellow) begins to be formed on the retina, and
mingles with the blue object, on which we con-
tinue looking; with the consequence that the
longer we look the duller does it appear, being
mixed with more and more of the orange image.
And so with all the others, the result being that
the complete and enduring effect of any combina-
tion of colours in a wall or a dress or a picture,
when steadily looked at, is produced by a large
number of spectra mingling with the colours
themselves before us, in a degree little contem-
plated by the original designers.
137
127. Just so it is with the secrets and the
ordinary rules of musical compositions. Ideas
are prolonged and melted into one another to an
extent which cannot be brought within the regular
rules for the management of chords and the
resolution of discords, while in effect these very
discords themselves are the result of that desire
for lingering on certain notes or phrases, beyond
the extent to which they would seem to be
desirable, according to the ordinary rules of
harmony. It is to this propensity that the student
should direct his attention at an early stage of his
studies, both to enable him to analyse and enjoy
the works of great musicians, and to assist himself
in his first efforts at modulation and composition.
128. There are various forms which this love
for the prolongation or suspension or repetition of
a note or phrase especially exhibits itself. And it
is to be especially noted that the desire for
prolongation itself is in strict harmony with that
prolongation of the complete harmonic dissonant
concord, on which I have so much insisted in this
little work. The secret of modulation is the
fitting of one chord into another by a species of
growth, much more than the mere addition of
sound to sound according to the regular rules of a
138
system of architecture. Among these chief forms
are (I) the simple suspension of one note of a
chord, so that it constitutes a discordant element
in the succeeding chord, and requires a definitely
marked resolution; (2) the continuance of a
sustained note through a whole phrase, or a
considerable portion of a phrase; (3) the long-
sustained low note, technically called a "pedal,”
which frequently forms the finale of a fugue, and
which is usually the fifth of the key-note, and is
sounded steadily on while a series of chords rolls
onwards in a strange sequence of discords and
concords; and (4) the repetition through many bars
of one note, or one or two notes close to each other,
by which a composer seeks to impress some intense
emotion upon the hearer, apart from the general
melodies or apparent sentiment of the piece.
129. The simple sustaining of one note of a
concord while the following concord is struck, so
that a discord is formed which the ear imperatively
requires to have resolved, is common in all
good part writing, and it was one of the principal
instruments for modulation employed by the early
ecclesiastical and madrigal writers. Among later
writers its effect becomes almost glaring in the
well-known Italian psalms of Marcello, while its
139
use in the “Recordare" of Mozart's Requiemn is an
illustration of the astonishing skill with which
that wonderful man could unite the peculiar
gravity and stately form of Palestrina with his
own unapproachable tenderness and delicacy in
the development of the melody of the moderns.
The phrase towards the end of the “ Recordare,"
Inter oves locum præsta, may be especially mentioned
as an example of the difference of emotion which
is awakened by harmonies in which the artifice
of suspension is scarcely used at all, coming
immediately after a series of passages in which
the resources of counterpoint and the free handling
of chords are employed with all Mozart's refine-
ment and skill. Then all at once, in a ravishing
melody simply harmonised, the passion of the
suppliant finds its climax in the final prayer.
130. The "pedal point," or point d'orgue, as it is
called by French writers, is a striking illustration
of the truth of the principle which I have been
endeavouring to advocate, namely, the irresistible
inclination of the ear and mind to refer every
phrase and harmony to some great root-note from
which all spring, and to which they have a
perpetual tendency to return. As it is through
the influence of the dominant that the listener
140
is first led from the vast original harmonic chord
into all the seductive paths of modulation, so it is
in the pedal point that he finds delight when
that dominant note is established as a basis, while
every variety of chord and melody winds onwards,
irresistibly attracted, half willingly and half way.
wardly, to its final rest.
131. But there is another development of the
same principle which may profitably be examined
by the student without waiting till he has advanced
further in his labour. Now and then, in the
writings of the greatest choral and orchestral
masters, we find passages in which this same
device is adopted for seizing and retaining the
emotions of the hearer by the prolongation of some
one chord or closely united chords, by way of
gradual climax, and with all that elaborate counter-
point which superficial persons imagine to interfere
with intense expression of feeling. The noblest
masterpiece of this kind with which I
acquainted is in the twofold opening movement
of the " Credo” in Bach's Mass in B minor. For
the last sixteen bars, from the moment of the
entrance of the trumpets, a mighty flood of
harmony seems to be circling round and round
the common chord of D (in which the piece is
am
141
written), while the sopranos sing a brilliant melody
that flows onwards and upwards with as much
ease and unembarrassed tunefulness as we feel
in Beethoven's latest masterpieces. And all this
is in truth an exposition, with an eloquence
which no spoken words can reach, of belief in
Him who is the maker of all things visible and
invisible.” In all music I know nothing else so
expressive and so sublime.
132. Another instance, quite in a different
style, of the power of intensifying an emotion
by this persistence in the use of a single idea is
to be found in the celebrated song in Gluck's
Iphigenie en Tauride, where Orestes gives expres-
sion to the peace which he imagines to fill his
heart, which is still beating with a dread of the
vengeance of the unappeased Furies. His words,
and the melody to which he sings them, are all of
peace; but throughout the whole song the viola
plays a restless syncopated movement, almost
all on the dominant, betraying the self-deception
of the miserable heart, and leading up to the
chorus of the Furies, who burst upon him. Here
we have an illustration of that power which the
mind unquestionably possesses of being conscious
of two, three, or more distinct simultaneous
142
musical ideas, expressive of equally distinct human
emotions, and alike resting scientifically on the
fundamental fact that all music is necessarily more
or less made up of dissonances, and that a pure,
unadulterated consonance would be, compared to
the multitudinous mingling of grand and tender dis-
cords, as the north wind is to the southern breeze.
CONCLUSION.
a
133. Music, then, is an art founded on
science. It is something more than an ingenious
arrangement of sounds, designed for pleasing the
mind through the ear, according to the fancies
of a body of composers, like the art of dress, or,
to a considerable extent, like the art of decorative
painting. It is the latest of all the arts which
human ingenuity has created, probably because
of the complicated and subtle character of the
scientific facts on which it is based, and of the
slowness with which the mechanism by which it
expresses itself in its instrumental form has been
brought to maturity. It was almost as easy
mechanically to cut the marbles of the Parthenon
out of the quarry, as it is to carve the latest displays
143
of the modern sculptor's incapacity; but it would
have been physically impossible for the musicians
of Athens to play a symphony of Beethoven.
134. The cultivation of music as an art has
thus been practically a struggle to build a
structure of thought and emotion upon the basis
of a most imperfect knowledge of the laws of
sound. These laws are of the most subtle kind,
and are often thought at first to be contradictory
in character. Even now they to a large extent
elude analysis, and the modes in which the
molecular elements of the atmosphere act and
react upon one another, and upon the brain
through the ear, are far from being adequately
comprehended.
135. It is, however, upon the hidden processes
by which these molecules do act upon one another
that the effect of music upon the mind depends ;
and the drawing up of a code of rules in strict
accordance with the facts which science thus
gradually discovers is the duty of the musical
theorist and teacher. And here, as in so many
other varieties of man's achievement, the artist
and the theorist are often at variance, both with
one another and with the scientific student of
144
atmospheric phenomena. The history of music
for the last four hundred years, and before that
time music cannot be said to have existed as an
art, is the record of the incessant enlargement of
our knowledge of the capacities of the complica-
tions of musical sound to express the thoughts
and feelings of our nature. Many have been the
varieties of form which musical compositions
have taken, but the real growth of the musical
art has been in its development of the art of
modulation; that is, of the combinations of
sounds, both together and in succession. In this
growth genius has maintained a perpetual conflict
with pedantry; the rules which have been held
sacred by one generation have been derided as
unmeaning shackles in the course of another
half century; while the victory has been due to
a more or less unconscious perception of the
true relation of sounds to one another, not as
they are supposed to be related on paper, in
treatises absurdly called "scientific," but in the
movements of that marvellous fluid in which we
breathe and move and live.
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