foundations of musical aesthetics mcewen

8/6/2019 Foundations of Musical Aesthetics McEwen

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ML

CORNELLUNIVERSITYLIBRARY

MUSIC DP.PAP^


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Cornell University LibraryML 3845.M14The foundations of musical stheticsior.

3 1924 022 202 810


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Cornell UniversityLibrary

The original of tliis book is intine Cornell University Library.

There are no known copyright restrictions inthe United States on the use of the text.

http://www.archive.org/details/cu31924022202810


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Zbt /Dnslc Xoper'g XibrargEDITED BY

A. EAGLEFIELD HULLMUS. DOC. (OXON.)

THE FOUNDATIONS OF MUSICAL^ESTHETICS


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THE MUSIC LOVER'S LIBRARYA series of small books on musical subjects

in a popular style for the generalreader. Crown 8vo

Edited byA. Eaglefield Hull, Mus. Doc. (Oxon)

A Short History of Harmony. By Charles Macpherson, F.R.A.M.Music and Religion : a Survey. By W. W. Longford, D.D., M.A.Everyman and His Music. By P. A. Scholes.Foundations of Musical Esthetics : or, Tiie Elements of Music.By J. B. McEwen, M.A., F.R.A.M.The Voice in Song and Speech. By Gordon Heller. With Fore-word by Herbert Thompson.The Power of Music and the Healing Art. By G. C. Rothery.Modern Pianoforte Technique : the Science and Art of Piano-

forte Playing. By Prof. S. Vantyn.The Story of British Music. By C. Antrobus Harris. With two

plates.The Philosophy of Modernism, in its Connection with Music.By Cyril Scott.Shalcespeare : His Music and Song. By A. H. Moncur-Sime.With a frontispiece.A Century of Welsh Music. By J. Graham.Modern Music ; Its Aims and Tendencies. By R. H. Myers.Kegan Paul, Trench, Trubner & Co., Ltd., London.


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THE FOUNDATIONS OF MUSICAL ESTHETICS

With numerous Musical Illustrations

If thou wouldst be famous, and rich in splendid fruits,Leave to bloom the flower of things, and dig among the roots."

Fifth impicssion

LONDONKEGAN PAUL, TRENCH, TRUBNER & CO., LTD.BRO.\nWAY HOUSE, 68-74 CARTER LANE, E.G.W6

OR THE ELEMENTS OF MUSIC 3SY

SIR JOHN B. McEWEN, M.A.FELLOW AND PROFESSOR OF MUSICAL COMPOSITION IN THE

ROYAL ACADEMY OF MUSIC, LONDON.


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Printed in Great Britain by Ebenezer Baylis and Son, Limited,The Trinity Press, Worcester, and London,


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CONTENTSCHAP. PAGE

J Introductory iII Musical Sound .... g

III Equal Temperament ... jgIV Tonality and Scales ... 27V Harmony 43VI The Rhythm of Contrapuntal

Music 57VII The Principle of Rhythmic

Balance 75VIII Musical Form . . - . w gb

Bibliography .... 123


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THE FOUNDATIONS OFMUSICAL ^ESTHETICSCHAPTER I

INTRODUCTORY

The word " aesthetic," which originally meantperception by the senses, has had its meaningparticularised so that it usually is associatedwith perception of a specific kind. In thissense it is applied to the appreciative attitudeof the discerning mind towards the beautiful inart and in nature.

Philosophy has spent not a little time andtrouble on the attempt to formulate and definethe essential nature of the beautiful ; but whatone regards as beautiful, another will either lackinterest in or even positively dislike, and suchattempts, therefore, have not been particularlysuccessful.

This conflict of tastes is particularly notice-able in the case of the Art of Music. One age


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2 THE FOUNDATIONS OF MUSICAL ESTHETICShas its ideals which are oftenif not usuallyopposed to those of the succeeding generationpeople in one country will take pleasure in atype of music which appears incomprehensibleto those of another; and, even in the case ofindividuals of the same time and place, whatone may admire and love another will abhorand detest.

In the case of Music, therefore, it seems well-nigh hopeless to attempt to formulate or definewhat is the " beautiful," and I have no intentionin this little book of trying such an unpromisingtask. Each of us has his or her own ideas ofwhat constitutes musical beauty, and in mostcases the criteria on which our judgments arebased are not themselves fixed but are in a stateof flux and development.Many people, it is true, seem obliged to adopta fixed standard of artistic value to which theyrefer and on which their artistic judgments de-pend, and strenuously endeavour to preventany change in, or deviation from, the rigorousformulae which regulate their musical thinking.An enlightened and progressive attitude is,naturally, for such, an impossibility, and theinevitable and necessary developments of Artpass unnoticed or misunderstood.Some aesthetic standards, however, are neces-


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INTRODUCTORY 3sary, and if they are allowed to share in the in-evitable process of developmentif they areliving, not deadassist that process by givingit both direction and progressive energy.

It is not even necessary that the musicianshould be able to formulate clearly what arethe conditions and factors in a work in virtueof which it appeals to him as beautiful or thereverse. To reduce these aesthetic values toa clean-cut statement of relations intellectuallyapprehended, would, by that very act, tend toinduce reference to dead and mechanicalstandards. The feeling of the beautifulis something which is intuitive, and whichneither needs to be explained, nor can be ex-plained, in terms of reason. In fact, it is some-thing apprehended immediately, " perceivedthrough the senses," and can no more be " ex-plained " than those sensations which we callheat, cold, sweet, sour, etc.The Art of Music as practised in countries

which owe their culture and civilisation toWestern Europe is the outgrowth of a body ofdoctrine and dogma which is extremely elabor-ate and complex. But for the fact that muchof it is obviously derived from convention andcustom rather than from natural law, it mightalmost be called a Science. It is very doubtful,


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4 THE FOUNDATIONS OF MUSICAL ESTHETICShowever, if the feeling for the beautiful inMusic is more keen in the case of the individualexpert in the niceties of this quasi-science thanin him who is entirely ignorant of its laws andconventions.The pleasure which the expert derives from

a musical work may probably be a feeling morecomplex than that experienced by one who iswithout any technical knowledge, but in manycases it is distinctly affected by the purely intel-lectual satisfaction one derives from thedexterous solution of technical problems.

However, just as the complete realisationof the Art-work cannot be reached by intel-lectual process alone, but demands some im-mediate response from the sensuous side of themind, so the appreciation of such a work asArt is impossible without some intellectual re-action which enables the perceiving mind to" understand " the work presented. Otherwiseit would be possible to create Art-works com-posed of things which give rise to tastes, smellsand tactile sensations. If a piece of musicwere apprehended simply as a number of sens-ations of hearing, simultaneous and successive,the result to the hearer would be on a par withthe condition in which a gourmand is left aftertraversing a more or less elaborate menu.


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INTRODUCTORY -This intellectual process, however, need not

be a self-conscious one, i.e., a process in whichthe mind examines, compares and cataloguesthe sensuous effects exhibited in the Art-work.In most cases there is a background of refer-ence of which the mind is not immediately con-scious.Even in the most extreme cases where there

is an entire lack of what one might call technicalknowledge, appreciation of a musical work im-plies the presence and influence of certainlimiting and defining categories of musicalthought in the mind of the hearer. Some ofthese seem to rest on natural law in the sensethat they are in conformity with the physicalfacts which give rise to musical sound, or withthe way in which the human mind works;others, per contra, seem to be neither naturalnor necessary, but have been implied by thevarious courses which the development of themusical sense has taken.The function or purpose of these categories

if one may use the word purpose in such aconnectionis to unite the purely sensuousmaterials of Music into a whole, more or lesscoherent and consistent. This function in theearliest stages of the Art was probably filled bywhat may be called the principle of Emotional


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6 THE FOUNDATIONS OF MUSICAL /ESTHETICSConsistency. The very earliest attempts ofman to produce a musical work were no doubtco-ordinated and controlled by this funda-mental principle, and it is no less operativenow than it was in prehistoric times.

This primitive principle, however, has beensupplemented by other principles which pertainmore to the intellectual side of the mind. Inall cases where musical art exists, even in arudimentary state, its materials have been insome way codified and arranged so as to be-come capable of being placed in relations intel-lectually apprehended, so presenting featureswhich the mind can seize, remember and recall,and becoming, therefore, in the process capableof idiomatic and consistent treatment.

These supplementary principles are of twokinds ; of which the first is concerned with re-lationship between musical sounds from thepoint of view of Pitch, the second is concernedwith relationship from the point of view ofDuration or Time.From this broad and general classification

are derived and developed the special princi-ples which regulate and co-ordinate modernmusical thought. The particular kind ofmusical perception which we call the "ass-thetic " perception implies a reference of the


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INTRODUCTORYArt-work to these regulating principljss. Theseprinciples, therefore, are the Foundations ofMusical ^Esthetics.


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CHAPTER IIMUSICAL SOUND

The study of the nature of musical sound andof the relationships other than those of purelyan aesthetic kind, which exist between differentmusical sounds, has occupied a good deal ofthe attention of the physicist, and a whole de-partment of scienceAcousticshas grown upwhich has for its object the investigation of thefacts and problems involved.The student will find in the bibliography at

the end of this book a list of works which hemay consult for full and detailed informationon this subject. The following resume of thefacts and the accepted theory is included forthe sake of the general reader.The word Sound, as usually employed,

means the sensation we experience when thenerves of the ear are excited.^ It is also used to

1 The physiological processes which accompany the sensation ofsound are very obscure and are not fully understood. The pro-gress from what we call a sensation to a perception is essentiallypsychical rather than physiological, and t^" nervous impulse

8


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MUSICAL SOUND 9denote the cause which excites this sensation.Between what are called Noises and MusicalSound there is a distinct difference which isuniversally appreciated. The physical factsupon which this difference depends may be setout as follows :When a sonorous body is ina state of vibration these vibrations when trans-mitted to the ear give rise to the sensation ofsound. In most cases the transmitting mediumis the air, which is set into vibration by the son-orous body. In the case of noise these atmos-pheric movements are irregular, in the case ofmusical sound they are regular and periodic.That is, in the case of musical sound the vibra-tion is a movement which recurs regularly atequal intervals of time. Helmholtz's defin-ition of musical and unmusical sound is" Thesensation of a musical tone is due to a rapidperiodic motion of a sonorous body; the sen-sation of a noise to non-periodic motion."(Sensations of Tone, Chap. I).which is first generated in the organ of hearing no doubt under-goes profound changes in its passage up to the higher centres inthe brain, where it becomes a perception. So that, although thereis, at least, one plausible theory formuiated to explain our per-ception of the qualities of sound, based on the anatomical struc-ture of the aural apparatus, there is little doubt that this by itselfis not wholly adequate, nor that, in the end, our appreciation ofthe character and qualities of a sound is what (for lack of a bettername) we may call psychical. That is, it involves much more thana mere impressionthere are interior processes which cannot beexpressed in physiological terms.


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lO THE FOUNDATIONS OF MUSICAL .ESTHETICSA regular vibration system possesses :

(a) A definite Period,(b) A constant Frequency,(c) An Amplitude,(d) A characteristic Mode.

The Period of a vibration is the time taken inthe execution of one complete vibration; i.e.,the time which elapses between that instantwhen the moving body is at a certain positionand the instant when it next occupies the sameposition and is moving in the same direction.The Frequency is the number of such periodsper second ; in musical theory this is generally

termed the vibration number; i.e., the numberof complete vibrations performed by the mov-ing body, per second.The Amplitude of a vibration is the extent

to which the body moves from its position ofrest.The Mode or manner in which the vibration

is executed is of great importance from a prac-tical point of view, and may vary infinitely.

Musical tones differ from one another in(a) Force or loudness,(b) Pitch,(c) Quality or timbre.


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MUSICAL SOUND IIThese characteristics are directly connected

with and dependent on the peculiarities of thevibration system which are enumerated above.The Force depends on the amplitude of thevibration and is proportional to the square ofthe amplitude.The Pitch depends solely on the length of

time in which each vibration is executed; or,to put it in another way, on the number of vi-brations in any given time. The second istaken as the time-unit, and the number of vi-brations per second is called the vibration num-ber of the sound.

Force and Pitch are independent of eachother, so that two tones may have the samepitch and differ in force, or may have the sameforce and differ in pitch.The Mode of vibration is of great import-

ance in the consideration of musical soundbecause on its character depends what we callthe Quality or Timbre of the sound. Theinfinite variety of Quality which may existamong musical sounds is due to the factthat the sounds produced by nearly everymusical instrument are not simple or singletones of one determinate pitch, but are what arecalled compound tones consisting of an assem-blage of such simple tones. In this assemblage


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1 2 THE FOUNDATIONS OF MUSICAL /ESTHETICSthat simple tone which is the lowest, and gener-ally the loudest, is called the fundamental orprime, and by its pitch we judge the pitch of thewhole compound musical tone. The otherhigher simple tones present are called harmonicupper partials, or simply upper partials, or har-monics.

These upper partials occur in a regular seriesforming with each other fixed intervals in thefollowing order of pitch :

I Fundamental tone.The Octave above No. i.The Fifth above No. 2.The Fourth above No. 3.The Major Third above No. 4.The Minor Third above No. 5 etc.,

etc.

The complete list of the upper partials of thesound written as C on the Bass Staff is dis-played in the following scheme :

S 2Z* 2Z"^ J 4 S 6 T 8 9 /O // IZ 13 /4 15 r6The note written as B flat in the above is in reality slightly flatter.


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MUSICAL SOUND 13The number of vibrations executed in any

given time by any of the upper partials of afundamental tone, relative to each of the vibra-tions of that tone, is indicated by the figurewhich shows the position of that upper partialin the series. Thus, the first harmonic of anysoundthe second sound in the series and the8th above the fundamentalhas two vibra-tions to every one of the fundamental; thesecond harmonicthe third sound in the seriesand the 12th above the fundamentalhas threevibrations to every one of the fundamentaland so on.

It is not necessary that all these upper par-tials should be present in every musical sound.Those which are present, however, be they fewor many, must occupy positions in conformitywith the above series; thus, a sound may con-tain Nos. I, 3 and 5 only, all the others beingabsent; or i, 4 and 8, etc., etc.; but in no casecan a tone intermediate in pitch between anytwo consecutive numbers of the series make itsappearance. With certain exceptions everymusical sound is in reality a compound of afundamental tone with a number of upperpartials, and the Quality of such soundsdepends on


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14 THE FOUNDATIONS OF MUSICAL /ESTHETICS(a) The number,(b) The order, and(c) The relative intensities

of the partial tones which are present.These three are quite independent of one

another, and compound tones which are appre-hended as of the same fundamental pitch maydiffer amongst themselves as regards any or allof these three possibilities. It is therefore ob-vious that the possible number of differentqualities is infinitely great, as alteration in anyone of these constituent factors will producealteration in the quality of the resulting sound.The various characteristics of musical sound

enumerated in the preceding part of this chap-ter have so far been considered only from whatone may call the objective point of view, butit will be useful to glance for a moment at thesubjective conditions under which these charac-teristics are apprehended, so far as it is possibleto specify these.With regard to the force of a musical sound,

we naturally and easily conclude that the forceis really a measure of the energy of the vibrat-ing system, or of the distance of the vibratingsystem from our ear.With regard to duration we as naturally con-

clude that the continuance of the sensation of


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MUSICAL SOUND 1sound depends directly on the continuance ofthe vibration.With regard to pitch, however, there is noobvious explanation of the manner in which thisis appreciated by the ear, and what are thelimits of such appreciation is a matter which isnot at all clear or apparent. Helmholtz hasformulated the theory that certain parts ofthe structure of the ear are capable of beingsympathetically excited by sound, and that forevery degree of pitch there is a locality in theear which responds and by its response givesrise to the sensation of that particular pitch.This theory would also serve to explain to someextent how the ear appreciates quality ortimbre, on the basis that quality is directly de-pendent on the presence of certain upper par-tials or harmonics along with a fundamentalsound.

It is, however, not unreasonable to supposethat just as the eye has to undergo what istermed a process of " accommodation " invisualising objects at different distances, andjust as the subjective feeling of effort or straininvolved in the process of accommodation isthe measure of the distance, so the physical re-action in the organ of hearing to external stimu-lus, may involve an effort or strain in the nature


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1 6 THE FOUNDATIONS OF MUSICAL iESTHETICSof an accommodation which will serve as anaid to the appreciation of both pitch and quality.Such power of accommodation may be derivedfrom and developed by experience until it be-comes automatic, and like most automatic ac-tions does not directly enter into consciousness.

Pitch recognition varies much in differentindividuals. Some few are said to exist whocannot discriminate at all between high and lowsounds. At the other extreme are individualswho have what is called the faculty of " abso-lute pitch." Between these two extremes comeall degrees of pitch recognition.The ability to recognise " absolute " pitch

is, however, really a very long way from beingan absolute ability to recognise pitch. Vari-ations in pitch are infinite and the human mindis finite. Pitch discrimination is really amatter of difference of degree, not of kind.Some individuals can recognise pitch to withina semitone or even less. Others cannot identi-fy pitch within much larger limits. What isinvolved is simply the power of identification,and although some degree of development ofthis power is necessary to the musician, it isnot the sole or even the chief desideratum.What is really necessary is that he should pos-sess a high degree of appreciation of the rela-


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MUSICAL SOUND 1/tions which exist between the limited numberof sounds in our musical system, which are co-ordinated and formulated into an artistic pro-duct in conformity with a definite process ofselection. Just as the painter must be able toappreciate truly the relative values of light andshade and colour, and the relations whichunderlie the lines of perspectivehe does notrequire either to know the absolute distancesbetween the objects of his landscape in termsof some arbitrary standard, or even to be pos-sessed of a particularly keen or potent vision.

Musical sounds considered from the subjec-tive side, are in the first instance sensations.That is, they are the result of the action of cer-tain stimuli on the sense of hearing. As suchthey are realised immediately and individually,and have no artistic function or value in them-selves. It is only when they enter into con-sciousness as a statement of relations, ex-pressed or implied, that they become the subjectof artistic arrangement and manipulation.

Just as colour, qua colour, is the sensationaldescription of the effects of light vibrations ofcertain wave lengths on the sense of sight, sothe apprehension of musical sound is simplythe reaction set up in the organism to certainphysical stimuli.


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1 8 THE FOUNDATIONS OF MUSICAL ESTHETICSA single musical sound calls forth a single

reaction, which, if it were unique in experience,would have no meaning or value other than itssurface value as a sensation. But, becausethat particular kind of stimulus which gives riseto musical sound may vary infinitely in detailwhile retaining its general character, we experi-ence a corresponding infinity of musical sensa-tions, all partaking of that general qualitywhich we call musical, but varying amongstthemselves as regards details of individualcharacter. The regulation and co-ordinationof these differences, and the understandingand expression of the relationships which existbetween the various musical sensations are theproper business of the 'Ait of Music. Puttingit in the most general way, the Art of Musicconsists in the arranging of successions andcombinations of musical sounds of varyingpitch, quality, force and duration, according tocertain principles some of which seem to beessential and necessary, while others are unes-sential, conventional and temporary.


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CHAPTER IIIEQUAL TEMPERAMENT

The relationship between two sounds with re-gard to pitch is called the interval betweenthem. The number of possible intervals isabsolutely infinite. In practice the limitationsof the human senses restrict the number of suchintervals employed in any musical system.The limits, for practical purposes, betweenwhich musical sounds used in European musicare arranged, are, on the one hand, that soundwhich has 27.5 vibrations per second (the lowestA on the largest pianoforte), and on the other,that sound which has 4,000 vibrations persecond, roughly speaking.

It is necessary to realise that the peculiarcharacteristic of musical sound which we callpitch is a quality which can be definitely de-scribed only as a rate of vibration. Also, thatwhile each separate rate of vibration corres-ponds to an individual and definite pitch, thenumber of possible rates of vibrarion is abso-

9


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20 THE FOUNDATIONS OF MUSICAL ESTHETICSlutely infinite. Here, in fact, we touch on thatmysterious thing called Continuity, and itshould not be overlooked that, although thesounds employed for musical purposes arecomprised between definite limits, and associ-ated in definite relations, yet from the inferiorto the superior limit the pitch series is in realitycontinuous. So that to represent graphicallythe change of pitch from the lowest to thehighest sound, we must use a continuous line :e.g.

4000

27"5

In all musical systems this rise in pitch isarranged in discontinuous steps^which arecalled intervals^because only by so doing canthe mind give definiteness to its musical think-ing. The graphic representation of such 3


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EQUAL TEMPERAMENT 2system will, therefore, imply a figure like thefollowing, in which ascent in pitch is indicatedby a series of discontinuous steps.

In modern European music these steps areequal, and there are twelve such to the octaveso that each stepor semitone, as it is calledis equal to the twelfth part of the interval ofthe octave. This system of fixing pitch iscalled the system of tuning by Equal Temper-ament.The interval between two sounds takes its

character from the numerical proportion be-tween the rates of vibration of each sound.This ratio is generally stated as a fraction,which is called the vibration fraction of theinterval. Thus, the interval of the octave isproduced between two sounds the upper ofwhich has two vibrations to every one of thelower. The vibration fraction of the interval


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22 THE FOUNDATIONS OF MUSICAL ESTHETICSof the octave is, therefore, 7i- A ratio of threevibrations of a higher sound to two of a lowercharacterises the interval of the perfect Fifth,the vibration fraction of which is, therefore, ^gjand so on. The musical classification of inter-vals as concords or discords corresponds to theratio between the rate of vibration associatedwith each of the two sounds concerned. Thesimpler the ratio, the more concordant theinterval.The following is a list of the intervals found

within the octave with the vibration fractionsof these intervals :


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EQUAL TEMPERAMENT 23


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24 THE FOUNDATIONS OF MUSICAL /ESTHETICSis unsuitable for the employment of complexharmonic process. Instead, we use what iscalled the system of Equal Temperament, inwhich the interval of the octave is divided intotwelve precisely equal semitones. In such asemitone the ratio between the rates of vibra-tion of the two sounds concerned is i : 1.059approximately* ; so that the ratios of the variousintervals in the octave are successively in termsof the ascending powers of 1.059.The relations between the sounds in theEqually Tempered scale are exhibited in thefollowing table :

1 To seven plares of dttjimalsi"oi;q463i.


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EQUAL TEMPERAMENT 25


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26 THE FOUNDATIONS OF MUSICAL /ESTHETICSis based on what is essentially a compromise,and every work on Acoustics bewails thenecessity. However, what the artistic side ofMusic is concerned with is the use of sounds incertain broad relations of combination and suc-cession in such a way as to outline and express,not definite relations of quantity or value, butthe fluctuations of human emotion, which can-not be stated either quantitatively or qualita-tively. Much of this desire for what is calledtrue intonation is based on the assumption thatconsonance in the mathematical sense of theterm is in itself a thing of beauty ; and that themore vigorous stimulus to the sensibility whichthe so-called roughness or discordance makesis in itself undesirable and unpleasantas-sumptions that the musician would probablyhesitate to endorse. The most perfect conso-nances are just those which from a musicalpoint of view are dull, vapid and uninteresting;and the suffrages of any modern audiencewould clearly indicate which is now felt as themore " beautiful " of the twothe simple con-cordant harmony of the ancients, or the highlycoloured texture of modern dissonant music.


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CHAPTER IVTONALITY AND SCALES

A SINGLE sound is an acoustical fact, and theentire series of sounds which forms the basisof our musical system is, from this point ofview, simply a collection of facts. Beforethese sounds can be used for artistic purposesit is necessary that they should be conceivedin such a way (as far as pitch is concerned)that they combine to form a complex whole.The unifying principle under which they are socombined is called the principle of Tonality.The facts of Pitch and of Pitch differencesare objective; they exist apart from the mind

which perceives them; but this feeling ofTonality which unifies and co-ordinates thesepitch differences, is not identical with themusical sensation but accompanies this sens-ation and arises out of it by the subjective re-action of the mind.The feeling of Tonality arises when we view

27


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28 THE FOUNDATIONS OF MUSICAL iESTHETICSa collection of sounds of different pitch as onewhole, bound together in relations which arerendered definite and consistent by the fixationof one central point to which these relation-ships are all referred.

Perception or recognition of anything as awhole implies reference of each element or partof it to some fixation point, which, however,need not be in the foreground of consciousness.This fixation point need not be in the actualfocus of attention at any one time, but mayexist as a back-ground of reference only. Therelationship of the separate parts or elementsto this fixation point unifies the whole.As an illustration of this principle let us

think of the figure of a circle. We call up amental picture of a figure so constructed thatin it there is one point such that all linesdrawn from this point to the circumference areequal.


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30 THE FOUNDATIONS OF MUSICAL ESTHETICScentre. Conversely, the change in the Tonalcentre implies a corresponding change in themanner in which any sound impresses the mind.

In a succession of musical sounds each mem-ber of the succession in turn comes into andmoves out of the focus of attention, but theunifying of such a succession from the pointof view of pitch is accomplished by the factthat each sound is referred to some fixationpoint or tonal centre, and is realised accordingto the relations subsisting between it and thiscentre.

Thus, if we take a succession of differentsounds :

we can produce a distinct number of differentimpressions, according as we regard eachdifferent sound in turn as the fixation pointor tonal centre of the whole. For example,by loading any one of these sounds with extraemphasis or tone, we can strongly direct theattention towards the sound so emphasised,and the whole succession tends to form oneindividual group centred round this strongly


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TONALITY AND SCALES 31accented sound. By changing the sound em-phasised the succession can be made to suggesta series of different tonalities.As another illustration of the same principle

take the sound:

iand refer it in turn to a succession of differentkeys or tonalities, C, B, A, etc., etc. In eachcase the single sound C is accompanied by aspecific feeling which is extra to the sensationof definite pitch, and which is different in eachcase. This specific feeling is caused by thedifferent relations exhibited between this soundC and the central sound of each new tonality.A point of considerable importance is thatthis feeling of Tonality and the manner inwhich it appeals to the musical sense are notfixed and definite for all time, but are subjectto the process of evolution and development.If we examine music composed in the courseof the last 600 years we cannot fail to observesigns of this process of evolution. From theearliest times, even in the dim ages of whichwe have no record, some such unifying prin-ciple must have been at work, and in the


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32 THE FOUNDATIONS OF MUSICAL ESTHETICSmusical system which immediately, precededours and from which our modern system de-veloped we can trace the active influence ofsome such principle of tonality, although itwas felt and expressed in a direction differingfrom that in which we now realise it.

In the music of the early Middle Ages theprinciple of tonality manifests itself under aform purely melodic. That is, the relation ofthe component sounds of a work to the appre-hended centre of gravity is always successive,never simultaneous. From the operation ofthis principle resulted the diversity of "modes"which characterised ancient music. The diff-erent modes, of which there was a compara-tively large number, owed their individualityto the reference of a fixed series of sounds tovarious members of this series, in turn, as thetonal centre. The monochord, which was em-ployed for the purpose of training singers,served to " standardise " the intervals whichwere used in artistic music, and the soundswhich formed these intervals collected into aconsecutive series constituted a scale whichcould appear successively in the differentmodes by the simple expedient of taking adifferent member of the series as the centreof gravity of the system.


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TONALITY AND SCALES 33It is possible even for us who have our

minds saturated with harmonic conceptions torealise something of the operations of thisprinciple. Thus, if we arrange the white notesof the pianoforte in such a way that each issuccessively realised as the centre of gravityof the whole series, we can group the othersounds so that their mutual relations are under-stood by reference to that particular soundwhich for the time being is regarded as thetonal centre. Naturally, the chosen centremust be insisted upon and confirmed, other-wise the more usual arrangements of ourmodern system will tend to re-assert them-selves.The ignorance of this principle and the

vicious tendency to regard tonality throughthe limitations of the major and minor scalesare responsible for the maltreatment of muchof the old folk-music which was invented by apeople ignorant of these essentially harmonicschemes. The following setting of an oldScottish tune which the arranger has made toend outside of its proper tonality is a shockingexample of this musical "Procrustes' bed":


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34 THE FOUNDATIONS OF MUSICAL ^ESTHETICS

m ^3Qe

?-^ Sh

r^^( ^:-i / g

r"r"- -^

4 ^^ ^rf^s=? ^^ imtead r ff^Tonality, according to mediaeval music, andmusic which is invented or composed by peoplewithout harmonic prepossessions, must be real-


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TONALITY AND SCALES 35ised as stated melodically. The very first be-ginnings of harmony were not the result of con-scious or directed endeavour, but aroseaccidentally as a by-product of operations di-rected to quite other endsand it is doubtfulif the human ear, at this period, could ade-quately realise the harmonic effect of even thesimple common chord. In the earliest har-monic music there was not so much an attemptto harmonise a melody as to perform the sameor different melodies at different pitches. Inall probability, at first, the performers were forthe most part unconscious of any harmonic ef-fect at all.

Eventually, with the development of the artof Counterpoint, musicians acquired consider-able skill in the combination of different me-lodic lines, but the individual parts which com-posed the musical structure were combined onwhat may be described as negative harmonicprinciples. That is, the conscious effort of thecomposer was that these parts should combinein such a way that dissonant combinations wereeither avoided altogether, or that such discordsas did occur should have a purely ornamentalfunction, and be capable of solution by melodicmovement.

In the best examples of these works the oper-


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36 THE FOUNDATIONS OF MUSICAL /ESTHETICSations of the principle of Tonality are still fehmelodically. Each part or voice conforms toa tonal scheme which, centring round a particu-lar sound, in the series, is realised as a definitemode. It was even possible for more thanone mode to be employed simultaneously.

However, with the development of the har-monic sense which followed the perfecting ofthe contrapuntal method, the composer eventu-ally reached a point where it is obvious thatthere was an embryonic realisation of the rela-tions between chords as chords. The first ef-fect of this new power of realisation was to leadto harmonic experiments, which often appearcrude and tentative, but the modern realisationof Tonality, which binds into a consistent andproportioned whole both the successions andcombinations used in music, is not apparent.On the other hand the composer had evolvedsome realisation of harmonic relations, althoughthe fact that this is confined to the relations ofonly such combinations as appear in immediatesuccession makes these works sound to our earssomewhat vague and incoherent.The principle of Tonality in modern music

is chiefly realised in connection with harmonicrelationships which it controls and defines. Itserves not only to connect up the constituent


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TONALITY AND SCALES 37notes of individual chords, but to control therelationships of successions of such chords.With reference to the first of these two func-tions, there are certain natural facts which con-firm our system and enable us to regard it asfounded on something more authoritative thanmere custom and convention.

It is a fact, as has already been pointed outin Chapter II, that most musical sounds arenot simple and single, but when they occur arealmost invariably associated with other soundsof different pitch. These subordinate sounds,or harmonics, or upper partials, form what istermed the Harmonic Series of the fundament-al sound from which they are generated. Refer-ence to p. 12, where the complete HarmonicSeries of C is given, will show that the first twosubordinate sounds in the series, excluding theoctave and double octave of the generator, arethe fifth and third from C. The summation ofthese three sounds gives us what is called theMajor Common Chord. In the formation ofthis chord the three individuals, C, E and G," fuse " into and form an entity which is felt assingle and individual, not merely as the aggre-'gate of these three sounds. Similarly, theother sounds which occur in the HarmonicSeries may be combined to form chords, and


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38 THE FOUNDATIONS OF MUSICAL ^ESTHETICS

practically all the characteristic combinatiensof modern music can be obtained in this way.The Harmonic Series presents a whole sys-

tem of sounds which is based on the generatorand in which the determining factor with re-gard to any one sound is the relationship itbears to this one fundamental sound. Fromthis point of view, therefore, Tonality is impliedin every single sound.

However, when we come to consider thisprinciple of Tonality from the point of view ofharmonic successions we find it is strengthenedby association with a further important princi-ple, viz., that of Progression. This principle,stated briefly, is that every sound in the limitsof a definite tonality is naturally attracted toand tends to progress either directly or indi-rectly to the centre of the tonal systemthekey-note and its derived harmony. Musicalconfirmation of a tonal centre necessitatesprogression to that centre, and the degree ofrelationship between any sound in the systemand the centre of that system is measured bythe tendency of this sound to proceed to thetonal centre.Now, every sound most naturally tends to

proceed to that other sound in the HarmonicSeries of which it is the first " foreign " upper


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TONALITY AND SCALES 39partial, viz., the fifth'. So, any chord tendsmost naturally to proceed to that chord whichis derived from the note a fifth below the rootof the first. Thus, the harmony derived fromthe note G tends most naturally to proceeddirectly to the harmony derived from the noteC; the harmony derived from C tends to pro-ceed to that derived from F ; and so on.Writing the twelve sounds of our system so

that each note is placed next to that note towhich it is in this sense most closely related,we get a scheme like the following : this suc-cession may be described as the scale of rela-tionship.

^^^Centre

The sounds arranged in the above sequencepresent the note C as the centre point of thetonality, which is thus seen to be a structurein equilibrium round this centre point, the

I The term " foreign " is used here because the first upper par-tial, the octave from the fundamental, introduces no new elementinto the series.


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40 THE FOUNDATIONS OF MUSICAL ^ESTHETICSbalance being maintained by the equal distri-bution of sharper and flatter sounds on eitherside of the centre.The last sharp, F sharp, and the last flat, G

flat, have the same pitch in the system of equaltemperament. This sound is on the extremelimits of the key, and its tendency of progres-sion to the key centre is very slight. Its chieffunction is to assist in defining change of ton-ality ; appearing as F sharp when the change isto the sharp side, and as G flat when the changeis to the flat side.

Although the B on the sharp side and the Dflat on the other are near the limits of the ton-ality, yet the melodic connection between thesenotes and the key-centre (to which they act asleading notesthe one upwards, the other,downwards) is very pronounced.The choice of any other sound as key-centre

will show a corresponding re-arrangement inthe functions of the constituent notes. Thefollowing is the scheme arranged round thecentre F sharp :

I o '^ ^ ItfV go l^'^ '^^XTTSI ^^ ^^


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TONALITY AND SCALES 4While the sounds in the key have the natural

relations just indicated, the notes efeployedin that scheme which we call a scale are simplya selection from the twelve notes of the key.This selection may be made according to anydesired system; some seem to be more naturalthan others. The Major scale, for example,seems to most of us moderns to be derivedfrom a peculiar necessity of the musical sense.But this is certainly not the case; only ourharmonic prepossessions contrive to make usthink this. In fact, the making of scales seemsto be almost entirely a matter of taste, and theonly difficulty for the modern composer whichlimits his choice is the solution of the niceproblems in harmony raised by the use of theseunusual scales. Even that difficulty is fastvanishing with the general loosening of har-monic necessity which is characteristic ofmodern practice. In fact, one of the mostpopular of these new scale forms is just thatin which no single sound in the whole selectioncan progress to its nearest relative, becausethat relative is omitted. If the student will lookagain at the notes of the key of C as writtenout on p. 39, he will notice that the omissionof every alternate note will produce that fa-vourite scheme of the modern composerthe


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42 THE FOUNDATIONS OF MUSICAL /ESTHETICSWhole-tone scale. Of course, such omissionat the same time eliminates that note to whichevery note of this scale would most naturallytend to progress in accordance with its acous-tical relationship. However, this peculiaritysuits the characteristic fluidityif it is notthe cause of itof most music written in thisformula.

or

7i ^ ^


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CHAPTER VHARMONY

In the preceding chapter it has been stated thatthe feeling of tonality, or key, in modernmusic is a realisation of relationships betweenthe twelve sounds with which our system oftuning provides us. These twelve sounds areunified into one whole by the relationshipswhich they severally bear to one centralsound. This whole is organised so that eachsound fills a place and function relative to thistonal centre different from that occupied byany other sound.The tonality, therefore, may be likened to

a constellation in which we find a definitecentre sound with eleven other subordinatesounds grouped round this centre, each oc-cupying its own particular place in the systemand filling its own particular function. Be-tween this central sound and the others, andbetween each of these others, there are definitedegrees of relationship, and the order of the

3


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44 THE FOUNDATIONS OF MUSICAL .ESTHETICSrelationships is indicated by the arrangementof the sounds grouped round the central sound.

The key, therefore, is realised as a structurein equilibrium which is stable as long asthe special relationships of the subordinatesounds to the tonal centre are maintained. Ifthese special relationships are interfered withthe whole tends to break up and re-crystallizeround some fresh centre.

Just as, in the limits of the tonality, thereare degrees of relationship between individualsounds, so there exist similar degrees of re-lationship between the harmonies derived fromthese individual sounds. As the closest pos-sible relationship exists between two soundsnext together in the above series, i.e., betweentwo sounds which are a fourth or a fifth apart,so the closest possible harmonic relationshipexists between the harmonies built up on twosuch sounds. This fact is independent of theparticular quality of the harmonies involved,or of the simplicity or complexity of the par-ticular combinations.


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HARMONY 45To put it concretely, any harmony derived

from the sound G is related in the closest pos-sible manner to the harmony derived from C,and also to that derived from D; and so on.As in the case of single sounds this relation-ship is felt as a tendency to progression. Afirst chord progresses when it is immediatelyfollowed by another chord, and although inmost modern music any one chord may be fol-lowed by any other, there are, in practice,certain limitations which are generally ob-served. These limitations arise from the factthat the relationships which exist betweenconsecutive harmonies must be realisable ifthe progression is to sound logical. If therelationship is so obscure that it cannot berealised, or realised only with great difficulty,the progression will tend to sound illogical,until familiarity has established and confirmedthe relationship. For this reason new pro-gressions take time to be understood generallybefore they become absorbed into the common-places of musical expression. For this rea-son, also, no limit can be set to the develop-ment of musical resource in this direction.The vast majority of musicians will alwaysfind the commonplaces of expression adequatefor their needs; and the mind which is indi-


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46 THE FOUNDATIONS OF MUSICAL ^ESTHETICSvidually perceptive will always light on hiddentreasure in the shape of undiscovered harmonictruth.

It must, however, be borne in mind that re-lationships between sounds are felt not onlyharmonically but also melodically. Certainindividual constituents of a harmony may pos-sess certain melodic tendencies, in virtue ofthe relationships existing between them andthe rest of the combination. This is the casewith all kinds of discords, but particularly withthose discords which we call unessential. Thenature of these unessential discords is such thatthey form unstable constituents of what areotherwise stable combinations. They were in-vented and chiefly used in the days when theonly relationships distinctly apprehended weremelodic relationships; before tonality in themodern sense, as conditioned by harmonic re-lationships, was developed and realised.

J3l -^ J J ,12Z S^^e-In the above progression, the chief deter-mining factor is the necessity for simplifying


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HARMONY 47and clarifying the complex harmonic relationsby melodic movement. Thus at + the G whichappears and adds complication to the harmonyfinds its solution in the melodic progression toF, one of the simple constituents of the har-mony.Such extraneous notesthe first discords

to be consistently used by the early composersfilled the purpose of decoration or melodicembellishment, supplying that element of "pro-gression" which in the earliest music waslacjiing in the harmony as a whole. In fact,this feeling of logical and necessary progres-sion is mostly lacking in old music, in whichharmony was an accidental circumstance re-sulting from the endeavour to perform two ormore melodies simultaneously; or, if it is pres-ent, is only realised and stated melodically;i.e., the relations of single sound to singlesound are present, but no feeling for harmonicrelation, as we understand it, is traceable.The conception of key or tonality as a con-

nected system of related sounds revolvinground a definite centre, and permeated by thisprinciple of progression to that centre was ab-sent from the minds of the early composers,who regarded music from quite another standpoint.


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48 THE FOUNDATIONS OF MUSICAL /ESTHETICSSuch are the fundamental features of the

early contrapuntal style as compared withmodern idiom, and these conceptions are stillmaintained to some degree in the exercises instrict counterpoint which the student is calledupon to perform. Strict counterpoint is anattempt to construct music from which the twomodern principles of rhythmic balance andharmonic differentiation are excluded. Theadvantage of such exercise is often not obviousto the student who is apt to rebel at what heconsiders the artificial dullness of counterpoint.But in principle the practice of counterpointis of considerable value, especially in modemtimes when the musical idiom in vogue owesso much to, and is so much influenced by theall-pervading pianoforte, in that the task set is,roughly speaking, to "melodize" a succes-sion of harmonies without the complicationwhich is added by the necessity of observingthe principles of rhythmic balance and of de-finite harmonic progression.As this little book does not attempt to deal

exhaustively with any of the subjects intro-duced, but has the pretension rather of givinga general presentation of the main facts onwhich modern musical art Is based, no endea-vour need be made to indicate the complex


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HARMONY 49and elaborate theory of harmony which we oweto Day and Macfarren, and which is the found-ation for most of the teaching in this country.The chief fact in harmony is the ' ' common

chord," and the effective treatment of the" common chord " inside the limits of tonalityis the first principle of harmonic discrimination.

All the elaborate and highly complex detailsof treatment which are embalmed in the text-books can be reduced to one or two very simpleand general principles.The first of these is that no combination of

soundsno chord, as we call such^has anymusical significance in itself. Such musicalsignificance as it possesses depends entirely onthe fact that ii either initiates, continues orcompletes a movement. This is emphaticallythe case in rhythmically conceived music, inwhich harmonic progression occupies a com-paratively secondary place.In the second place, this harmonic move-ment is executed with general reference to thetonality as a whole, and with specific referenceto the place or function in the tonality of theparticular harmony concerned. In otherwords, the progression of any harmony is con-ditioned by (i) the relationship existing be-tween it and the centre of the key system; and


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50 THE FOUNDATIONS OF MUSICAL ESTHETICS(2) by the fact that it is concerned either withthe initiation, the continuation or the comple-tion of progression.

This is a matter which for the most part hasbeen ignored by the text-books, which as arule are content to isolate a number of com-binations, freeze them into immobility, andthen proceed to lay down laws according towhich they are supposed to be treated.

It is rather curious and instructive that thisdogmatic statement of the so-called "rules ofharmony " is made most authoritatively in thecase of the more complex dissonant combina-tions. The treatment of the simple commonchords is mostly dealt with vaguely and theformulation of precise rule is reserved for thecomplex dissonances. But, as a matter ofmusical fact, the more complex combinationsare in reality only decorated and ornamentedforms of the simple chord, and the implicitfunction and relations of the former with re-gard to the tonality are identical with the func-tion and relations of the simple chord on whichthey are based.To illustrate this point: the Dominant triadin the key has the special function of suggest-ing immediate progression to the key-centre,towards which it stands in the closest relation-


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HARMONY 51ship. Similarly, any of those elaborate com-binations which by association with this Domi-nant chord partake its character, share its re-lationships and tendencies.The order of harmonic relationship viewed

from the key-centre corresponds to the orderof relationships which exist between the indi-vidual notes of the tonality illustrated anddealt with in the preceding chapter.The connection between two harmonies isdirect and immediate when they are derivedfrom notes the one of which is a fourth belowor a fifth above the other. Thus, the harmonyderived from G is immediately connected tothat derived from C, and also to that derivedfrom D. The tendency of progression towardsC is stronger than towards D, because the noteG is the first foreign upper partial of C. Suchprogression may be termed Centripetal, be-cause the feeling is progression towards thecentre. Progression from the harmony of Gto that of D, however, is Centrifugal and isaway from the key-centre. The former ofthese is the more natural because of theattraction towards the key-centre. In the caseof the latter the progression is maintainedagainst this attraction, and therefore, this typeof progression requires a definite output of


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52 THE FOUNDATIONS OF MUSICAL /ESTHETICSmusical energy which prevents it from sound-ing so natural or necessary as the other.Harmonies derived from sounds separatedby other intervals than these are less directlyrelated and their juxta-position tends either toproduce an effect somewhat inconclusive:

$ 2r ^or to create an implicitif not an explicit-feeling of contradiction.

i 231In this latter case care must be taken to counter-act this feeling of key contradiction by specialmanipulation of the melodic progressions.# SHowever, even in the case of such a progres-

sion as the last, harmonies not directly relatedcan be forced into a kind of direct connection


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HARMONY 53by the use of what may be called chord-fusion.By this term is meant the simultaneous em-ployment of more than one simple chord. Suchsimple chords then blend into a more complexcombination which may take on itself the char-acter and relationships of either of the originalsimple chords. Thus, the chord of G is thenearest relative to that of C, while the chordof D is related only indirectly to that of C;if we fuse the chord of D with that of G weproduce a complex dissonant combinationwhich in virtue of the presence in it of theharmony of G is directly related to the har-mony of C :

$ 1This fact of chord-fusion renders possible

the logical use of any combination of the notesof the key. As the chief fact in the idea ofTonality is the implicit and explicit tendencyto progress to the key-centre and as the directprogression to this key-centre takes place onlyfrom the Dominant harmony, such chord fu-sion is mostly carried out on the basis ofDominant harmony. But it is equally possible


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54 THE FOUNDATIONS OF MUSICAL /ESTHETICSon Other basses, and so long as the dissonantcombinations so formed receive an appropriatesolution, and so long as the relationships inthe tonality are clearly observed and attendedto with reference to progression, such com-binations are mostly quite satisfactory.

Proceeding a step further in the considera-tion of musical relationship brings us to anotherspecial feature of modern musicmodulation.Just as the single notes of our system enterinto definite and consistent relations with oneanother, and just as the harmonies derivedfrom these notes form specific relationshipswhich define and fix tonality or key; socorresponding degrees of relationship exist be-tween the various aggregations of single notesand harmonies which have been co-ordinatedinto a series of keys or tonalities.These degrees of relationship are strictlyparallel to those established between the single

sounds and harmonies of any one key. Justas the closest relationship exists between a noteand those other notes from which it is separatedby the intervals of a fifth and a fourth re-spectively, so the closest relationship betweenkeys are these in which the tonal centres ofeach key are separated by the above intervals.

Similarly, as in the case of single notes the


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HARMONY 55degree of relationship gradually diminishes as.we proceed from the key centre outwards inboth directions; so, a precisely parallel andanalogous modification of relationship proceedsas we move from the key whose central pointis C to the keys whose tonics are successivelythe other notes in the scale of relationship.At this point it is necessary to interpolate a

caution to the reader to avoid confusing theterms key and scale.There is only one key or tonality associated

with each tonal centre but there are possiblea very large number of scales. The scale isonly a selection of the notes of the key; and,while the mode of selection has a very im-portant influence on the effect of any piece,it has practically no influence on the generalprinciples of relationship formulated above.The term key is a comprehensive term whichincludes the whole material of the system; the

term scale is a term applied to a particularmode of selection of this material. The twomodes in common use at present are the Majorand Minor scales; but the only reason for theprevalence of these in modern music is thefact that the solution of harmonic problem iseasier and more apparent in these two modesthan in any other.


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56 THE FOUNDATIONS OF MUSICAL /ESTHETICSModulation in the proper sense of the term,

takes place, therefore, between keys, not be-tween scales. To go from one mode of a keyto another mode of the same key, is like chang-ing from one room to another of the samehouse ; to go from one key to another key is, onthe contrary, a radical change involving afresh scene and a fresh outlook.

This fact of key relationship is used by themodern composer for the purpose of givingshape or " form "as it is calledto his work.According to the practice of the early classicalcomposers only changes involving very simplerelationships were commonly used. But themodern composer allows himselfas in theuse of harmony^practically any change helikes.

This side of the matter will be dealt withmore fully in the later parts of the book underthe consideration of the principles of musicalfotm.


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CHAPTER VITHE RHYTHM OF CONTRAPUNTAL MUSIC

So far, the matters dealt with in the precedingchapters have been concerned with those princi-ples of musical thinking which refer to rela-tionships between musical sounds from thepoint of view of pitch. But the relationshipswhich exist between sounds, considered fromthe point of view of Time or Duration, are ofat least equal potency and significance in thescheme of modern musical art.

^Esthetic principles concerned with time re-lationships between sounds are the basis ofwhat is called Rhythm in music; and the sys-tematic combination of these with principlesdealing with Pitch relationships constitutes theessentials of that side of musical constructionwhich is termed musical Form. Modernmusical art is practically the result of the com-bined and simultaneous operation of these t\iocontrasted " codes "as they may be calledthe one relating to sounds as they occur in

57


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58 THE FOUNDATIONS OF MUSICAL /ESTHETICSpitch, the other to sounds as they occur in time.The discovery and full formulation of these" codes " of aesthetic principles were long andtentative processes, during which the musicalsense of mankind developed from a conditionthat can only be described as primitive into onecapable of appreciating the subtleties of a verycomplex art.

Without going into the details of this processof developmenta matter somewhat outsidethe scope of this bookit is proposed in thischapter to give a general sketch of the coursewhich this development has taken, chiefly withreference to the foundation principles ofrhythm.

There is no doubt that the chief factor whichconditioned the earliest development of music-al art was the fact that it was essentially a vocalart. Instrumental music of a primitive kindprobably existed from very early times, but itis doubtful if it was ever self-sufficient or inde-pendent until comparatively modern times.Such as it was in the earliest times, it was inall likelihood used only as an adjunct to activi-ties which were not in themselves musical, e.g.,dancing, hunting, ceremonial functions, etc.The technical limitations of the ancient instru-ments were, besides, too serious to allow much


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THE RHYTHM OF CONTRAPUNTAL MUSIC 59liberty or variety in performance; in fact, theonly instrument which was sufficiently undercontrol and sufficiently responsive to be used forartistic purposes was the human voice.

So far, then, as the artistic development ofmusic was concerned, it is fairly obvious that thedirection in which this extended and the rateat which it progressed were to a very large de-gree conditioned by the facts that the early mu-sicians were singers, and that their music wascomposed for and performed by voices.The time outline of the earliest vocal music

was determined by the syllabic quantities ofthe words which were sung. So long as themusical outline was a simple setting of thewords, and so long as the performance wasstrictly in unison, or by different voices movingstrictly in some consecutive or parallel intervalsuch as the fourth or fifth, no special time no-tation would be necessary. But when themusical outline became more complicated, andwhen musicians learned the art of combiningtwo or more melodies characterised by con-trasted directions or rates of motion, somemethod of regulating and indicating the relativetime values of the sounds had to be used inorder to maintain the music in its proper proportions.


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6o THE FOUNDATIONS OF MUSICAL /ESTHETICSThe first efforts of the musicians who invent-

ed our notation were, from this point of view,confined to the production of such symbols aswould indicate clearly very simple quantitativerelations; and the music they composed, forwhich this notation was required, was built upentirely of successive sounds which were ren-dered continuous and unified into a series by the

.

simplicity of ratio in time value which existedbetween them.

Sounds exactly the same length stand to oneanother in a relationship immediately appre-hended. Sounds the time values of which are insimple ratio, e.g., 1:2 or 1:3, present rela-tionships comparatively easily apprehended;and successions of such sounds can be summedup into a continuous unity when some furtherco-ordinating principle relating to pitch isoperative.The early musicians were so influenced in thechoice of the time outlines of their compositionsby their realisation of verbal quantities, thatsome of them of set purpose attempted toformulate regulations for musical rhythm basedon the syllabic quantities of the words sung.A certain Jean Antoine de Baif (1532- 1589)wrote some " Chansons Mesur6es " which wereset to music by contemporary composers In


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THE RHYTHM OF CONTRAPUNTAL MUSIC 6these verses de Baif indicated with the signs- yj the " longs " and " shorts " of each of hislines, and the composers chose such musicalvalues as corresponded to these quantitativesigns.As a specimen of this procedure the fol-

lowing example,* quoted by Vincent d'Indy(Cours de Composition Musicale), is repro-duced.The verses with their quantitative indication

are:Li bsr arondS mfisag^re dfi la gaye saizon

Est venfl, je I'ay veflt116 v6le mducheletes, elle v6le mduchgrons.The musical setting is:

i q: ZL32 ^a bdiS roTtde mesa-^- rede la^ i/e JizS^-zon1S>- TT^^Jst ve-nu. /e Cat/ veu, El-le uo U mouifie^/e- tes. el- -le vo- le m&ucherons

.

' Le Printi^mps," by Claudin L. Jeune (Les Maftres Musiciensde la Renaissance francais>*).


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62 THE FOUNDATIONS OF MUSICAL /ESTHETICSThe fundamental principles on which this

systematization of musical value is based areoperative even at the present day, althoughthe strict proportions insisted on by theory arenot always observed in practice, being modi-fied by the operation of the modern feeling forbalance in structure and determinative pro-gression.We find, therefore, at the date when coun-terpoint was the natural and indeed the onlymeans of expression at the command of theartistic composer, that the time outline ofmusic was regulated by a system the chief ad-vantage of which was that it co-ordinated thevarious melodic lines which combined to formthe structure. The sounds in this time outlinewere related to one another in the very simplestarithmetical proportions, and although thesevalues could be manipulated within consider-able limits, they were yet, in the end, all re-ducible to some statement of very simple pro-portions.The musical phrase, in contrapuntal music,

was a succession of sounds modelled on words,the individual sounds showing some variety oflength, but all lengths related in very simpleproportions. It was, therefore, regulated asregards extent by the number of words sung;


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THE RHYTHM OF CONTRAPUNTAL MUSIC 63as regards outline or syllabic pattern, by thevalues of the syllables of these words. Be-tween the lengths of the component phrasesof a contrapuntal work, there was, consequent-ly, no necessary relation: some might be long,some short. The chief factor in performancewas the necessity for the due and proper allot-ment of time value to each syllable, so thatthe requirements of harmonic combinationmight be complied with.

Latterly, no doubt, some greater freedomwas used, both in the modelling of the musicto the words, and probably in actual perform-ance. Thus, instead of building up the phrasefrom a series of elementary "longs" and"shorts" each corresponding to one particu-lar syllable, the later contrapuntists showedoften a fine sense of melodic decoration andfeeling for contrast in the construction of thephrase. Thus the following outline shows avery high development of this feeling forbeauty in line:

ik


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64 THE FOUNDATIONS OF MUSICAL /ESTHETICSWith regard to the composition of such con-

trapuntal works, as a whole, the main principleobserved was what may be described as theconsistent maintenance of continuity. It mustbe remembered that the artistic problem to besolved at that time was the combination ofsimultaneous melodic lines, differing, it is true,as to the time values of their constituentsounds, but all characterised by a similarfluidity and by an equal absence of definiteand regular articulation. Each musical phraseconformed to the outline of the verbal phrasewhich it illustrated. More or fewer words didnot matter; the elasticity of the musical outlineenabled it to expand or to contract accordingly.The problem of unifying the whole work andof reducing the feeling of discursiveness en-tailed by the peculiarities of the style, wassolved by a self-sacrificing adherence to certainmelodic formulae, and by the more or less per-sistent recurrence of a limited number ofphrases. The principle of Imitation which isinherent in a vocal style of composition wasfreely used; at first, in a manner somewhatcasual and restricted, but latterly, subject tocertain definite and characteristic regulations.The full systematization of the contrapuntalidiom was reached in the Fugue, a form which


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THE RHYTHM OF CONTRAPUNTAL MUSIC 65has persisted right down to modern times, andwhich, though mostly associated now with aninstrumental medium, was in its origin basedon and derived from the conditions and ne-cessities of vocal music. Even in works ofthis type which were written for instruments,in the details of which the technical characterof the instruments exercised a very importantdetermining function, the principle which oper-ated was essentially the principle underlyingearly vocal music. That is, continuous state-ment and amplification of statement, with noregular articulation indicating balance andsymmetrical design as a whole and co-ordinat-ing all the separate parts. The absence of anydefinite feeling for tonality based on the co-ordination of the relations in pitch betweensimultaneous sounds, and the ignorance of thegreat modern principle of key relationshipemphasised the same features in this earlymusic.

These features and the peculiarities of de-sign which they connote are still to be seen inthe more modern contrapuntal music. Butthey are, in such modern music, supplementedby other features of which the early exampleswere entirely innocent. The radical changesin the outlook of the musician occasioned by


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THE RHYTHM OF CONTRAPUNTAL MUSIC 67fug-al. Such works as the Preludes to theEnglish Suites of Bach, and a good dealwritten by even the most modern composers,are based on structural principles identicalwith those which underlie the fugal form.Fluidity of outline, the lack of balanced ar-ticulation, and the assiduous maintenance ofcontinuity proclaim the near kinship of suchpieces to the Fugue, and indicate their descentfrom the original vocal music of the early con-trapuntists.The problem presented to the performer by

such pieces is fairly complicated and admits ofno very definite solution. In the next chapterit will be shown how the "elocution" of therhythmically balanced work is a matter ofphrase identification, and how the applicationof the broad principles of rhythm renders pos-sible this identification of phrase. In thiscontrapuntal music, however, there are nodirect means by which we can always authori-tatively decide this important question ofphrase outline. Built on vocal idioms whichoriginally owed their phrase outline to the de-finition of words, modern instrumental musicin this idiom has no verbal associations whichcan serve as a guide to the performer. But,if the performance of such works is to convey


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68 THE FOUNDATIONS OF MUSICAL .ESTHETICSany meaning, there must be present in everycase phrase outline and definition of some sort..Due regard must therefore be paid to the con-trasts of pitch and of time outline so as to en-sure a significant performance. Most of thedislike which the unsophisticated have towardscontrapuntal music is traceable to the fact thatmany performers imagine a fugue is to be"rattled" through from beginning to endwithout colour or contrast; excepting perhapsan extra amount of emphasis on the reappear-ances of the subject.The contour of the melodic line will usually

give more or less obvious indications as to"interpretation." The following illustrationsmay help to make this point clear. If a certainvoice or part consists entirely of repetitions ofthe same sound identical in pitch and in value

lj# **M Mm*we would have an undifferentiated successionwhich we might divide up in any way, and inno one way rather than in any other. Just asthere is no particular reason if we wish to di-vide up a straight line why we should divideit into any particular number of parts ratherthan into any other.


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THE RHYTHM OF CONTRAPUNTAL MUSIC 69But suppose that in the series of sounds

there are some sounds which are differentiatedfrom the others by time value :

ior by pitch :

&f T m mor by both time value and pitch :

% rxrur,'P y P "n*"then such differences, especially if they occurregularly, produce points in the successionwhich can be regarded as indicative of someshape.

Just as if the straight line referred to aboveshould now become curved:

Now, although continuity is maintained mthe curved line just as much as in the straight.


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70 THE ^ OUNDATIONS OF MUSICAL iESTHETICSthere are featureschiefly associated withchange of directionin the curved line whichlend themselves to the indication of possiblearticulations. The parts into which this curvedline then articulates need not be balancedeither in themselves or with reference to eachother, but the important point is that by takingadvantage of the differences in direction, etc.,the line can be reasonably regarded as an ag-gregate of the several parts so obtained, andcan so acquire a character and an individualityof its own.According to the same principle the char-

acteristic features of any melodic successioncan afford indications as to how that successionmay be articulated and so acquire anaesthetic individuality, although the parts soarticulated may neither be internally balancednor present any balance with reference to eachother.The fact that, in much modern music which

is composed in the contrapuntal idiom, thesubject matter is conceived on the basis ofrhythmic balance, predisposes the mind of thecomposer to a development in which this char-acteristic feature of modern musical thought ismore or less prominent. The regular employ-ment of sequential imitation in such works is


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THE RHYTHM OF CONTRAPUNTAL MUSIC 7also ascribable to the desire of the composerto present this development under conditionswhich, in their formal aspect, convey this feel-ing of balance, while at the same time main-taining the continuity of progression. Thefollowing examples illustrate these points.The first four are subjects of fugues byBach, and it will be felt that the natural ar-ticulations which they display are such thatthe feeling of a balanced statement com-pounded of distinct and individual balancedunits is maintained in each expression.

m m* m * ^ m-JH^ ^


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THE RHYTHM OF CONTRAPIfNTAL MUSIC 73Bach: Fugue in A minor


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74 THE FOUNDATIONS OF MUSICAL /ESTHETICSBach : Forty-eight Preludes and Fugues.Book IL, No. I.mh i=ri ^=r^ ^

^ *fIJ^ l ,-

' i ^^ ^^^^^

IJ J- m^^ efc^ 55


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CHAPTER VIITHE PRINCIPLE OF RHYTHMIC BALANCE

The artistic music of the Middle Agesbywhich is meant music other than folk-musicwas a sophisticated form of expression de-veloped wholly and solely from the vocal side.Whatever may have been the case in the tunesand " chansons k danser " sung by the people,the feeling for rhythmic balancearising outof the symmetrically balanced physical move-mentwas rigorously tabooed by the eccle-siastics who were the professional musiciansof these times. The associations of the dancewith the profane and ordinary common life ofthe people disposed the ecclesiastical musicianto a method of expression in which this dis-trusted secular influence could not in any de-gree be traced.

This result was further achieved by the de-velopment of the contrapuntal method of com-position, in which the artistic problem to be

75


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76 THE FOUNDATIONS OF MUSICAL ESTHETICSsolved was the combination of simultaneousmelodic lines, varied, it is true, as to the valuesof their constituent sounds, but all alike dis-tinguished by fluidity of outline, the absence ofdefinite and regular articulation, and the simi-larity of texture which results from the use ofcommon melodic formulae. The musical artof this period resembles in its lack of definitedesign the oriental decorative "arabesques"in which the eye is confused and the attentionhypnotised by the multiplicity of interlacinglines, now convergent, now divergent, butwithout any subordination to a general prin-ciple of shape or perspective.The rise and development of instrumental

music, however, were the means of introducinga new and important factor into the situation.As vocal music had attained to a very con-siderable development before the composerthought of writing for instruments, the naturalresult was that the earliest compositions forinstruments were based solely on the maturedvocal idiom. In other words, they were theexact counterpart of the prevalent vocal com-positions, only without word*. Divested of thewords which gave the shape to the music, theeffect of such compositions was soon realisedto be far from satisfactory; and, after some


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THE PRINCIPLE OF RHYTHMIC BALANCE "J "Jconsiderable time during which composers ofinstrumental pieces experimented more or lessblindly in the endeavour to dig out some prin-ciple of design from the technical effects pecu-liar to each instrument, the eventual solutionof the problem was found in the performanceof musical pieces types of which had been inexistence all along, but which had been un-recognised by the professional composers.These were found in the dance tunes sung andplayed by the people.A dance tune, unlike the vocal type ofmelody, has its root and origin in bodily move-ment and gesture. In the primitive dances,such movements were, no doubt, of a com-paratively obvious and simple type; and, asperformed by an assemblage of people eitherin the course of some mystic or sacred rite, orpurely as a social diversion, consisted of theregular and periodic repetition of some seriesof movements. The simplest of all dances isthe March, in which the body of the dancermoves in cycles each of which contains twosimple movements. With more complexdances the series of movements is more com-plex, but all possess this feature in common,that after the series is completed the body ofthe dancer is in the same relative attitude as it


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78 THE FOUNDATIONS OF MUSICAL ESTHETICS

was at the beginning of the series. In the caseof dances performed by one individual thecyclic character of the movements need not beso apparent nor so necessary, but in dances inwhich a number of individuals take part thiscyclic arrangement is a necessary condition.When an assemblage of people performedthe same dance at the same time, the task of

co-ordinating the movements of the differentindividuals was probably accomplished byshouts and cries; just as the drill-serjeant co-ordinates the step of the recruits with " LeftLeftLeft." These primitive shouts natural-ly developed into some kind of simple sym-laetrically balanced song, which derived itssymmetry from the regularly balanced move-ments which it served to co-ordinate.When the mediaeval composer, therefore,had tried vocal idioms as a basis for instru-mental composition and had found the unsatis-factoriness of such a method, the most naturaland obvious thing for him to do was to fallback on that kind of music probably alreadyassociated in some measure with instrumentalperformance, and write dance music; i.e.,music which is constructed on the basis ofregularity and balance of rhythmic statement.The combination of this new principle with


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THE PRINCIPLE OF RHYTHMIC BALANCE 79the paraphernalia of the contrapuntal styleproduced a species of composition in whichsometimes the one idiom seems to be para-mount, sometimes the other : where certain sec-tions or divisions of the work are conceived onthe basis of regular rhythmic articulation, andwhere in other divisions the natural fluidity ofthe contrapuntal style re-asserts itself. Inmany cases the dance shape was adopted inits entirety but by sophisticating the treatmentthe composer concealed the somewhat obviousorigin from which it derived.

In order that a rhythmic progression maybe felt as balanced it is necessary, in the firstplace, that the mind should attend to the pro-gression in a peculiar way; and, secondly, thatthere should be inherent in the progressioncertain natural arrangements and proportionswhich can intuitively be realised as balancedand symmetrical.

Before proceeding to the consideration of thepurely musical side of such a progression it isnecessary to consider briefly what is impliedin both these conditions.A rhythmic progression is a succession oisounds which unfolds itself in time, and which,

in virtue of the definiteness and simplicity ofthe relations of value existing between these


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60 THE FOUNDATIONS OF MUSICAL /ESTHETICSsounds, serves as a measure of the extent andrate at which time passes. This extent andrate are, however, relative rather than abso-lute. In such a progression two things areessential: first, the existence of sounds in suc-cession; second, the existence of definite andsimple relations of value between these suc-cessive sounds.

If the sounds of a succession present amongstthemselves relations of value which are notdefinite nor simple the succession ceases to berealised as rhythmical. In European musicthe relations of value which must exist in orderthat a progression may be felt as rhythmicalare of a very simple nature; viz., representingratios of i: 2, 1:3, 1:4, etc'The consideration of a series of sounds in

succession may be associated with two differentforms of mental activity. In the one case thedirection in which this activity is chiefly exer-

' In oriental music, the development of which has been on linesdivergent from those followed by European music, the relativevalues of successive sounds are frequently very complex, and theoriental musician seems to be able to apprehend the complexproportions implied by such values, and to feel as rhythmical pro-gressions which we at present cannot so realise. (Of. The Thoughtin Music, Appendix A). Even in our European music these com-plex relationships in value are met with in what is called " TempoRubato," but there the apprehension is assisted by the operationof this very principle of rhythmic balance.


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THE PRINCIPLE OF RHYTHMIC BALANCE 8cised may be described as backwards; the out-look is retrospective. That is, each sound asit comes into and passes out of the focus ofperception has its value and place in the pro-gression assigned to it according to the re-lations which exist between it and those soundswhich have preceded it. No definite attemptis made to forecast to any extent the outlineof what is to follow it. To illustrate figura-tively: the attention of the listener is like thatof a person who is proceeding through acountry with his back to the direction of pro-gression. As each object comes in its turninto his field of vision he realises it in its rela-tions to that part of the landscape which he hasalready seen, but forms little or no idea of itsrelations to that which is still to come.The simplest musical example of this kind

of attention is in the apprehension of the fluidprogression typical of counterpoint:


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82 THE FOUNDATIONS OF MUSICAL /ESTHETICS

$Cj ^ '^ ~J Jl j^T-J^^^ ^=B^ r etcm -jr.t TTThe apprehension of progressions like the

above is almost entirely of the type described.So long as each sound entering the focus ofattention stands in easily understood relationsof quantity to its pred

foundations of musical aesthetics mcewen

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