# THE TREATISE ON HARMONY

by F. W. POUND

## Chapter One

### I

"What, mon élève, is the element grossly omitted from all treatises on HARMONY..."

at this point the élève looks up
brightly...

"except the treatise now being composed"...?
the élève continues to regard me brightly... and blankly. No
answer is offered me.

The answer, mon élève, is :

"The element most grossly omitted from treatises on harmony up to the present is the element of TIME. The question of the time-interval that must elapse between one sound and another if the two sounds are to produce a pleasing consonance or an *interesting* relation, has been avoided."

AND YET the simplest consideration of the physics of the matter, by almost the simplest mathematician, should lead to equations showing that

A SOUND OF ANY PITCH, OR ANY COMBINATION OF SUCH SOUNDS, MAY BE FOLLOWED BY A SOUND OF ANY OTHER PITCH, OR ANY COMBINATION OF SUCH SOUNDS, PROVIDING THE time interval between them is properly gauged; and this is true for ANY SERIES OF SOUNDS, CHORDS OR ARPEGGIOS,

### II

The limits for the practical purposes of music depend solely on our capacity to produce a sound that will last long enough, i.e. remain audible long enough, for the succeeding sound or sounds to catch up, traverse, intersect it.

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III

WHY IS THIS QUESTION OF TIME-INTERVALS omitted from all
other treatises on harmony?

Parenthesis for historic survey.

1. Musical theorists are exceedingly conventional, for centuries they went on quoting Franco of Cologne instead of listening to sound.

2. Harmony in Bach's time was a vigorous and interesting matter.

Why?

The answer to this question and to the main question of this
section, is:

The early students of harmony were so accustomed to think
of music as something with a strong lateral or horizontal motion
that they never imagined any one, ANY ONE could be stupid
enough to think of it as static; it never entered their heads
that people would make music like steam ascending from a
morass.

They thought of music as travelling rhythm going through
points or barriers of pitch and pitch-combinations.

They had this concept in their blood, as the oriental has his raga
and his tala. It simply never occurred to them that people
would start with static harmony and stick in that stationary
position.

IV

Hence it has arrived that the term "Harmony" is applied to
the science of chords that can be struck simultaneously; and
the directions for modulations have been worked out for chords
that can follow each other without demanding a strict or even
interesting time-interval between their emission.

In short, Mr. Joseph Corfe produced his

THOROUGHBASS
simplified

and laid open to the meanest capacity ;

he did that over a century ago, and no one detected the fact
till this year (a.d. 1923).

I am told that even Mr. Corfe's work contains errors.

But far be it, far, afar from me to contradict Mr. Corfe, or
that still more illustrious professor, Dr. Schonberg. All that
they have said is, or may be true, and lacking in interest.

Ernst Friederich Richter has said :

"Pure theory can not and
should not concern itself with practice, for it has as sole aim

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the definition of the nature of the divers constituent elements
of the art, without ever treating the special and particular cases
which result from the employment of personal procedures."

Observation :

Aristotle was not a pure theorist.

Sauzay

"Il faut se borner à penser que J.-S. Bach écrivait la musique par certains procédés dont la loi générale nous échappe."

(Sauzay "Le Violon Harmonique", p. 217.)

The secret or part of it probably is that Bach, consciously or unconsciously, never thought of using two chords except as parts, integral parts, of a progression, a rhythmic progression.

## CREDO

I believe in an absolute rhythm. E. P. 1910 with explanations.

In 1910 I was working with monolinear verbal rhythm but one had already an adumbration that the bits of rhythm used in verse were capable of being used in musical structure, even with other dimensions.

Treatises on harmony give you all sorts of recipes for getting from one chord to another (this is more or less reduced to a few simple mechanisms) they do not stop to enquire whether the transit by these means is interesting, or, in a given situation, expressive.

That is supposed to be a matter of creative genius. It is.

## V

Any series of chords can follow any other, provided the right time-interval is discovered. The interesting sequences are probably those that DEMAND very set and definite intervals.

That is probably all we have to say in this chapter.

### Chapter Second

### I

Given proper approach, the progression

is probably perfectly sound. I mean from the point of view of mathematics.

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II

Fortunately this theory of harmony can never be reduced to an academicism. At least it seems unlikely that any mathematician will bother. The mathematics of the case might prove discouraging.

You can reduce the line composition of *La Nascita di Venere* to trigonometric equations; it would make a long charming series. The results might be interesting but they would not help you to draw.

Question

"How did you find those four notes?" said X... in undisguised admiration. "Gee, I wish I had found those four notes."

Answer : By listening to the sound that they made, a thing no pyanist has ever done.

That is perhaps all we have to say in this chapter.

Chapter Third

And possibly the last; for we have probably said about all we have to say. The former treatises on harmony dealt with static harmony, they may have defined harmony as "simultaneous melody" or they may have sought some other definition, but they did not consider that the lateral motion, the horizontal motion, and the time interval between succeeding sounds MUST affect the human ear, and not only the ear but the absolute physics of the matter. The question of where one wave-node meets another, or where it banks against the course of another wave to strengthen or weaken its action, must be considered.

I

The harmony for one instrument is BY NO MEANS necessarily the harmony for another. Good players have always "GOT THE MOST OUT OF" the compositions they played by their subtle seizing of this gaya scienca, and we have said "he has a sense of rhythm" or she "has a sense of rhythm".

II

And again Sauzay : Le fameux Durante, qui a fait tant d'élèves célèbres, ne leur donnait jamais des règles qu'il formulait.

Naturally. When Harmony was alive it was merely a personal give away, it was a bundle of tricks of the trade, the fruit of personal experience, it was A way of getting over a difficulty or managing a turn of expression; it wasn't intended to cramp anyone's style: It was pragmatic, it worked, and each school

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worked its trade secrets to death with the magnificence of
Bel Canto, of music up to Johann Sebastien. The mechanism
was a plus thing, it worked in an open field.

The mess came when it was set up as a fence, and everyone
tried to walk on the rails or climb over it.

They rotted their melodies by trying to find schemes which
"harmonize" according to a concept of "harmony" in which
the tendency to lifelessness was inherent.

*Chapter Fourth* ; corollaries and complications.

Continuing, mon élève; you will probably have noticed by
now a glaring omission on my part.

A SOUND OF ANY PITCH etc...

any chord may be followed by any other provided the right
time interval be placed between them.

The duration of the resolving chord must also be considered ;
and the duration of the various chords in a sequence will be
subject to mathematical computations, if people prefer mathe-
matics to judging the sounds by ear.

THE HARMONY FOR ONE INSTRUMENT MAY NOT BE THE HARMONY
FOR ANOTHER.

Again the competent mathematician could show us that
the vibrations of a' cello where the sound is steadily produced
by a drawn bow will combine in a different way from those of
a horn, a plucked string or an instrument of percussion.

Everybody knows this; but the time is over when we can
give more reverence to a person who can detect slight variations
of pitch, than to one who can detect the difference between

It will make a difference what instrument the sounds are played
on; it will make a difference if one note or several notes are
played louder in the chord; it will make a difference if the
next chord strikes the precedent chord while that chord is
still being propelled from the instruments or if the second chord
strike the other chord as it fades;

and all these things are really in the domain of harmony, that
is of active, not static, harmony;

and as for the workings of the latter; this time element may
upset them or reinforce them in given circumstance.

The so called "laws" of harmony were useful when they were
a bag of handy tools; but if one tries to carry the whole
machine shop, one's mobility will probably suffer.

81

WHETHER COPYRIGHT LAWS ARE DESIRABLE.

To the Editor, *Transatlantic Review*.

Dear Sir,

It is proposed to examine the above question from a single
point of view; namely whether copyright laws further the
production and dissemination of literature.

It has been sufficiently demonstrated that copyright laws further the business of businesslike publishers, and of business-like writers. What remains to be seen is whether they ever did, ever do, or ever can encourage the writing or the publishing of a work of literary merit.

First, what is a copyright law? It is a guarantee given by
the State that the writer or publisher or both of a new writing
shall have undisputed right to exploit the painful possibilities
of the said work for a period of years after publication. (This
right, in most countries, can be ceded or bequeathed.)

It is argued that, although probably very few (if any) literary
artists of consequence would but for their royalties abandon
writing, the law is especially valuable as it affects the publisher.
Publishing books, it is said, is a risky business; few books show
a profit, and it is only in virtue of the exclusivity bestowed by
the copyright laws that the occasional big seller is made to pay
the way of the failures. In other words, without copyright
laws good books would still be written, but they would not be
published. In still other words, it is the occasional big sellers
that make publishing profitable and that enable the publisher
to go on printing most of his books at a loss. And if we repeal
the copyright laws we take all the profit out of the big sellers,
since they would instantly be reprinted by competitive publishers.

Such reasoning is pure nonsense. Book-publishing is a
commerce like any other, and it is as absurd to suppose it cannot
thrive without protection as to imagine that but for patent laws
we should still be lighted by candles. People will want books,
copyright laws or none; and the want will be supplied, in one
way or another. It remains to be seen whether without the
copyright laws it would be better supplied.

Let us look at the business possibilities of book-publishing
under a régime of liberty.

It is to be assumed that immediately on repeal of the copy-
right law there would be a rush to reprint the latest popular

# NOTES FOR PERFORMERS

by William Atheling, with marginalia emitted by George Antheil.

## I. *The Piano*, February 1918

Why indeed the Piano? Apart from bickering over the tempered scale, though one can hardly accept the argument that it is no use bothering over inaccuracy of pitch that only one person in two hundred can perceive, people without absolute and pitch sense do, and do very often, get a certain very definite pleasure from correct playing, even if they are incapable of detecting a single error, or even a series of errors save by a vague dissatisfaction or by an even slighter and more vague diminution of pleasure.

All keyboard instruments tend to make performers of people not born to be musicians; and the very fact that one can play a keyboard instrument quite correctly without in the least knowing whether a given note is in tune or is correct in itself, tends to obscure the value of true pitch. This perception, the first requisite of any player upon strings is therefore left, perhaps, wholly unconsidered by the piano student. The piano tuner is responsible for all that. His services are inexpensive. This argument might be used also against the earlier keyboard instruments although they were never sufficiently loud to drive out and predominate over the rest of the instruments And they did not fill the building.

From initial carelessness about pitch piano-playing has gradually progressed to a carelessness about actual sound. The attention that was centred in earlier music upon purity of tone, upon sound-quality, has been weakened and weakened till I have seen a composer of no small talent utterly impervious to the quality of the noise he was making.

*(I presume the "timbre" is meant. G. A.)*

The notes were in the right order; they followed each other as he intended, he was satisfied.

I long, perhaps not too vainly, for the day when the piano shall be as the hansom, which vehicle it not a little resembles and when the pianist shall be as the cab-driver, so far as the concert hall is concerned. The instrument will abide with

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us yet, for there is the pianola attachment, and if for some
time it is necessary to train acrobats to play Bach-Busoni for
pianola records, surely human invention will lead to, and has
already discovered, a means for making the records direct.
The future composer will do his work, not with a pen but a
punch. "You couldn't pack a Broadwood half a mile," says
Mr. Kipling, but there is always the gramophone.

(I bow gracefully several years. G. A.)

At least "it took me back twenty years." Have we not all,
with the shades of Murger, with the well-known death mask
gaping at us, and with the plaster cast of the drowned girl
hanging in the other corner, have we not all of us known the
charm? (The Schumann quality that has been read into
Chopin by generations of conservatoire young ladies to the
obscuring of Chopin's austerity.)

It was the studio "mood" as opposed to the piano of Sir Frederic Leighton and the Leightonians, the instrument at which the very young mother sits with her numerous well-washed, fresh offspring clambering about her, receiving the cultural rudiments. The pianist in this case has merits.

I do not say that I am above the studio manner ; that I would
not willingly recall the past, forget my bald spot. "Four and
forty times would I," as Mr. Kipling has it, listen to the wailful
note as the more reserved couple wait until it's time to walk
home, and the less reserved, or more "bohemian" couple hold
hands under the sofa cushion,—Jugend, Jugend, Jugend !
and the inefficient illustrator (aged sixty) who once hoped
to paint like Raphael, looks at the ceiling or the performer.

But what has all this to do with the concert-hall ? A certain
crop of female pianists always hoped to produce in the concert-
hall the atmosphere of the studio ; to bring to the hoarse old
gentleman from the Thames valley and to the large-waisted
lady from Roehampton a "breath of the real meaning," to
"show them that life..." and sometimes the female pianist
succeeded... After the final uncalled for encore, when all
but her dearest friends had left the building. Neverthe less
the concert-hall is not the studio. Some musicians may actually
play better in studios, they may get force from the "atmosphere",
or the company may merely blurr the critical senses, but these
things do not concern the concert-hall. The magnetic theory
is invalid.

(In fact the concert-hall has nothing at all to do with the studio.
It is its enemy, thank God. I prefer the excusable boredom of the
classics to the young gentleman who "sketches" Chopin out with
the new knowledge of a Cyril Scott. G. A.)

The magnetic theory is invalid. No performer can rely
on emotionalising the audience.

(One must try as hard as Brancusi's bird. Finished ! Why
worry ? The hysteria is there. G. A.)

Music in a concert-hall must rely on itself and the perfection

MUSICAL SUPPLEMENT

of its execution; it is as it were, under glass. It exists on the
other side of the footlights, apart from the audience. With
apologies to the language, the audience are spectators, they
watch a thing of which they are not part, and that thing must
be complete in itself. They may be moved by the contemplation
of its beauty, they are not moved—or at least can be moved
only in an inferior and irrelevant way—by being merged into
the action of the stage.

(Push this a little further and you have my theory of absolutism,
ffff and pppp are as sentimental as the insufficient painter nuancing
up his messes. G. A.)

I labour this point rather heavily, but it is not a trifle, and
hundreds of musical careers have been muddled simply because
the performers have not understood how entirely the music
must lead its own life:

(My dear E. P. hundreds of musical careers have been ruined
because there was no such thing in these people. G. A.)
must have its own separate existence apart from the audience;
how utterly useless it is to try to mix up audience and perfor-
mance.

(Which all reminds me that I once had a friend who always
said "I might have become a great pianist if..." Tommyrot! G. A.)

March 1918

A concert in a concert-hall is a performance, a presentation
not an appeal to the sympathies of the audience (Yes. G. A.)
It is, or should be, as definitely a presentation or exhibition
as if the performer were to bring out a painted picture and
hang it before the audience (Yes, yes, why not? G. A.)
The music must have as much a separate existence as has the
painting. It is a malversion of art for the performer to beseech
the audience (via the instrument) to sympathise with his or
her temperament, however delicate or plaintive or distinguished.

(By the way that reminds me that the emotionalism you speak
of is the performer's dramatic disguise. When listening to music
why not listen for music. Musical art assuredly can come only out
of the very inmost secrets of musical line. Why not come out
and out with it and say that music is no Goddamn circus. G. A.)

From the "studio" manner (in concert-halls), from the
domestic manner,

(Great mistake to confuse it with music. G. A.)

from the rural church manner, and from the national
festival manner,

(Ditto. Politics is no field for a music critic. G. A.)

may the surviving deities protect and deliver us! They
have not, they do not, but we do not cease to pray that they
may achieve it.

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(The studio manner is the kindergarten method for young radical
ladies. G. A.)

An era of bad taste probably gathers to itself inferior matter
from preceding periods. An indiscriminate rummaging in
the past does not help to form a tradition.

(A splendid turn for Mr. Casella, Maliperio, Prokofieff, and
the Six. G. A.)

A sense of rhythm covers many defects.

(One might say almost all. G. A.)

The pain caused to the ear by occasional horrid sounds is
quickly obliterated in the succeeding flow of the music. Singers
hoping for platform success will do well to notice this.

(This is the whole thing in a nutshell, not only of singers, but
of all platform artists. Ninety per cent of failures are due to
absolute incapability in the primary rudiments of music—rhythm !
How can they hope to be musicians—not even an excuse ! Printed
notes laid before them and keyboard instruments. Everything
laid out and planned for the unmusical ! Back to the troubadour !
I mean ninety per cent are not musicians, trained, born or any-
thing. G. A.)

A drag, a lack of the wave force, deadens, tires, ulterly wears
out the audience. Rhythm-sense is not merely a tempo mesure,
it is not merely a clock-work of the bar-lengths. Measured
time is only one form of rhythm; but a true rhythm-sense
assimilates all sorts of uneven pieces of time, and keeps the
music alive.

I would point out Lawes as an example of how the words
of a poem may be set and enhanced by music. There are
different techniques in poetry; men write to be read, or spoken,
or declaimed, or rhapsodised; and quite differently to be sung...

(By the way, most songs are written for the wrong kind. G. A.)

Words written in the first manners are spoiled by added
music; it is superfluous; it swells out their unity into confusion.

When skilled men write for music then music can both
render their movement, as Lawes does often, tone by tone,
and quantity by quantity; or the musician may apparently
change the word-movement with a change that it were better
to call a realisation. Music is not speech. Arts attract us
because they are different from reality. Emotions shown in
actual speech poured out in emotion will not all go into verse.
The printed page does not transmit them, nor will musical
notation record them phonographically.

(Ha! The famous Antheil notation to the rescue! G. A.)

But, for all that, a certain bending of words or of syllables
over several notes may give an emotional equivalent.

This is an art by itself, differing from poetry, and from the
art of harmony or of counterpoint. Nevertheless, it has occas-
ionally and triumphantly appeared in the world, and is well
worth an effort to recover.

MUSIC IN LONDON

THE "NOVELTIES" OF THE AUTUMN SEASON

by DYNELEY HUSSEY.

Of the new works, which have been performed during the past season in London, about a dozen were interesting either as explorations or as the latest products of established composers. of these several may maintain their places in the repertoire; only one work stands out in retrospect.

These proportions are not so bad as they may appear at first sight—one masterpiece and half-a-dozen good second-raters. One outstanding group need not be discussed. It contains the work of immature composers, who pour out their green-sickness in lugubrious tone-poems written in idioms that were fashionable a decade ago; and of mature dullards, like Reger, whose *Pianoforte Concerto* must be the longest and most tedious specimen of that ill-famed form. The rest may be, for convenience, divided nationally, into French, German and British.

The French School, with its polyglot adhesions from Russia, Spain and the English peerage, has given us nothing of importance. Prokofief's third *Pianoforte Concerto* has some good ideas, but they are always neglected in favour of the reiteration of insignificant phrases, scored in the two-pence coloured style of the tinsel-and-glitter School. The *Avant-Garde* concert was not, one hopes, really representative. Stravinsky, for one, was misrepresented by an early song in the manner of Mousorgsky and by a pianoforte arrangement of the *Puppets' Dance* in *Petrouchka*. This work in its complete form was one of the greatest successes at the Promenade Concerts. Some songs by Manuel di Falla, who does not really belong to this *côterie* at all, showed up the puerility of the rest, which consisted mainly of commonplace tunes made to sound piquant by accompaniments written quite arbitrarily in unrelated keys... With the accidentals omitted, these pieces might, without harm, be included in the *curriculum* of any girls' school.

The Germans put up a much better show. At one end of the scale there is the colossal *Alpine Symphony* of Strauss; at the other, Schönberg's dessicated essence of music, called *Le Pierrot Lunaire*. The *Alpine Symphony* had two perfor-

The real art is only felt by heart to heart.

Instance is immortal

Without one's momental expressions, it is impossible to
express one's purity or reality of moment.

One point creates infinite.

While the state of pure ego is the state of instance, the
expression in this state is expression of immortal.

Expression of a dot will be enough for the refined
sensitive people.

Momental expression which human can do is only a point.

THE FREEDOM (CREATIVE EVOLUTION)

IS THE KEYNOTE OF THE UNIVERSE

It is Slavery to think "White is White", Black is White"
or "Relativeness is Absoluteness", "Affirmative is Negative",
sometimes we stick on logical conventionality and sometimes
break that conception.

While we are surrounded by those contradictory conflicts,
we shall never be free from agony or struggle.

To be bound by 2 meters of body and limited by fifty years
more or less of life, is a conception I wish to be free from and
desire to see the other World.

1, myself, at least, should never be free from anxiety
unless I find some other point of view different from the ordi-
nary common conventional point of view.

There must be another point of view which we never think of.

The artist draws a thing "not as it is", but, "as it appears"
and the effort of the artist is by an arrangement of colours and
lines upon surface; to the eye an impression which will recall
that made by a three dimensional object.

Our conception of space is limited to three dimensions, and
when we attempt to make a drawing, we practically limit ourselves
to two. And it is not at all unthinkable the space is limited to
four dimensions.

The manifestation of "<u>Materialistic</u>" is either
Objective or Spiritualistic. Subjective: But synthesized both
together and transcends.

Is it to be called the Art to express the thing "as it is"
or "as it appears" ?

That will only be specimen of the thing,
THE ART - that must be the manifestation of "Beauty".