ML CORNELL UNIVERSITY LIBRARY MUSIC DP.PAP^ Cornell University Library ML 3845.M14 The foundations of musical stheticsior. 3 1924 022 202 810 Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924022202810 Zbt /Dnslc Xoper'g Xibrarg EDITED BY A. EAGLEFIELD HULL MUS. DOC. (OXON.) THE FOUNDATIONS OF MUSICAL ^ESTHETICS THE MUSIC LOVER'S LIBRARY A series of small books on musical subjects in a popular style for the general reader. Crown 8vo Edited by A. 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. 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 LONDON KEGAN PAUL, TRENCH, TRUBNER & CO., LTD. BRO.\nWAY HOUSE, 68-74 CARTER LANE, E.G. W6 OR THE ELEMENTS OF MUSIC 3 SY SIR JOHN B. McEWEN, M.A. FELLOW AND PROFESSOR OF MUSICAL COMPOSITION IN THE ROYAL ACADEMY OF MUSIC, LONDON. Printed in Great Britain by Ebenezer Baylis and Son, Limited, The Trinity Press, Worcester, and London, CONTENTS CHAP. PAGE J Introductory i II Musical Sound .... g III Equal Temperament ... jg IV Tonality and Scales ... 27 V Harmony 43 VI The Rhythm of Contrapuntal Music 57 VII The Principle of Rhythmic Balance 75 VIII Musical Form . . - . w gb Bibliography .... 123 THE FOUNDATIONS OF MUSICAL ^ESTHETICS CHAPTER I INTRODUCTORY The word " aesthetic," which originally meant perception by the senses, has had its meaning particularised so that it usually is associated with perception of a specific kind. In this sense it is applied to the appreciative attitude of the discerning mind towards the beautiful in art and in nature. Philosophy has spent not a little time and trouble on the attempt to formulate and define the essential nature of the beautiful ; but what one regards as beautiful, another will either lack interest in or even positively dislike, and such attempts, therefore, have not been particularly successful. This conflict of tastes is particularly notice- able in the case of the Art of Music. One age 2 THE FOUNDATIONS OF MUSICAL ESTHETICS has its ideals which are often — if not usually — opposed to those of the succeeding generation ; people in one country will take pleasure in a type of music which appears incomprehensible to those of another; and, even in the case of individuals of the same time and place, what one may admire and love another will abhor and detest. In the case of Music, therefore, it seems well- nigh hopeless to attempt to formulate or define what is the " beautiful," and I have no intention in this little book of trying such an unpromising task. Each of us has his or her own ideas of what constitutes musical beauty, and in most cases the criteria on which our judgments are based are not themselves fixed but are in a state of flux and development. Many people, it is true, seem obliged to adopt a fixed standard of artistic value to which they refer and on which their artistic judgments de- pend, and strenuously endeavour to prevent any change in, or deviation from, the rigorous formulae which regulate their musical thinking. An enlightened and progressive attitude is, naturally, for such, an impossibility, and the inevitable and necessary developments of Art pass unnoticed or misunderstood. Some aesthetic standards, however, are neces- INTRODUCTORY 3 sary, and if they are allowed to share in the in- evitable process of development — if they are living, not dead — assist that process by giving it both direction and progressive energy. It is not even necessary that the musician should be able to formulate clearly what are the conditions and factors in a work in virtue of which it appeals to him as beautiful or the reverse. To reduce these aesthetic values to a clean-cut statement of relations intellectually apprehended, would, by that very act, tend to induce reference to dead and mechanical standards. The feeling of the beautiful is something which is intuitive, and which neither needs to be explained, nor can be ex- plained, in terms of reason. In fact, it is some- thing apprehended immediately, " perceived through the senses," and can no more be " ex- plained " than those sensations which we call heat, cold, sweet, sour, etc. The Art of Music as practised in countries which owe their culture and civilisation to Western Europe is the outgrowth of a body of doctrine and dogma which is extremely elabor- ate and complex. But for the fact that much of it is obviously derived from convention and custom rather than from natural law, it might almost be called a Science. It is very doubtful, 4 THE FOUNDATIONS OF MUSICAL ESTHETICS however, if the feeling for the beautiful in Music is more keen in the case of the individual expert in the niceties of this quasi-science than in him who is entirely ignorant of its laws and conventions. The pleasure which the expert derives from a musical work may probably be a feeling more complex than that experienced by one who is without any technical knowledge, but in many cases it is distinctly affected by the purely intel- lectual satisfaction one derives from the dexterous solution of technical problems. However, just as the complete realisation of the Art-work cannot be reached by intel- lectual process alone, but demands some im- mediate response from the sensuous side of the mind, so the appreciation of such a work as Art is impossible without some intellectual re- action which enables the perceiving mind to " understand " the work presented. Otherwise it would be possible to create Art-works com- posed of things which give rise to tastes, smells and tactile sensations. If a piece of music were apprehended simply as a number of sens- ations of hearing, simultaneous and successive, the result to the hearer would be on a par with the condition in which a gourmand is left after traversing a more or less elaborate menu. INTRODUCTORY - This intellectual process, however, need not be a self-conscious one, i.e., a process in which the mind examines, compares and catalogues the 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 technical knowledge, appreciation of a musical work im- plies the presence and influence of certain limiting and defining categories of musical thought in the mind of the hearer. Some of these seem to rest on natural law in the sense that they are in conformity with the physical facts which give rise to musical sound, or with the way in which the human mind works; others, per contra, seem to be neither natural nor necessary, but have been implied by the various courses which the development of the musical sense has taken. The function or purpose of these categories • — if one may use the word purpose in such a connection — is to unite the purely sensuous materials of Music into a whole, more or less coherent and consistent. This function in the earliest stages of the Art was probably filled by what may be called the principle of Emotional 6 THE FOUNDATIONS OF MUSICAL /ESTHETICS Consistency. The very earliest attempts of man to produce a musical work were no doubt co-ordinated and controlled by this funda- mental principle, and it is no less operative now than it was in prehistoric times. This primitive principle, however, has been supplemented by other principles which pertain more to the intellectual side of the mind. In all cases where musical art exists, even in a rudimentary state, its materials have been in some way codified and arranged so as to be- come capable of being placed in relations intel- lectually apprehended, so presenting features which the mind can seize, remember and recall, and becoming, therefore, in the process capable of idiomatic and consistent treatment. These supplementary principles are of two kinds ; of which the first is concerned with re- lationship between musical sounds from the point of view of Pitch, the second is concerned with relationship from the point of view of Duration or Time. From this broad and general classification are derived and developed the special princi- ples which regulate and co-ordinate modern musical thought. The particular kind of musical perception which we call the "ass- thetic " perception implies a reference of the INTRODUCTORY Art-work to these regulating principljss. These principles, therefore, are the Foundations of Musical ^Esthetics. CHAPTER II MUSICAL SOUND The study of the nature of musical sound and of the relationships other than those of purely an aesthetic kind, which exist between different musical sounds, has occupied a good deal of the attention of the physicist, and a whole de- partment of science — Acoustics — has grown up which has for its object the investigation of the facts and problems involved. The student will find in the bibliography at the end of this book a list of works which he may consult for full and detailed information on this subject. The following resume of the facts and the accepted theory is included for the sake of the general reader. The word Sound, as usually employed, means the sensation we experience when the nerves of the ear are excited.^ It is also used to 1 The physiological processes which accompany the sensation of sound are very obscure and are not fully understood. The pro- gress from what we call a sensation to a perception is essentially psychical rather than physiological, and t^" nervous impulse 8 MUSICAL SOUND 9 denote the cause which excites this sensation. Between what are called Noises and Musical Sound there is a distinct difference which is universally appreciated. The physical facts upon which this difference depends may be set out as follows : — When a sonorous body is in a state of vibration these vibrations when trans- mitted to the ear give rise to the sensation of sound. In most cases the transmitting medium is 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 of musical sound they are regular and periodic. That is, in the case of musical sound the vibra- tion is a movement which recurs regularly at equal intervals of time. Helmholtz's defin- ition of musical and unmusical sound is — " The sensation of a musical tone is due to a rapid periodic 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 in the brain, where it becomes a perception. So that, although there is, 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 itself is not wholly adequate, nor that, in the end, our appreciation of the character and qualities of a sound is what (for lack of a better name) we may call psychical. That is, it involves much more than a mere impression — there are interior processes which cannot be expressed in physiological terms. lO THE FOUNDATIONS OF MUSICAL .ESTHETICS A 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 in the execution of one complete vibration; i.e., the time which elapses between that instant when the moving body is at a certain position and the instant when it next occupies the same position and is moving in the same direction. The Frequency is the number of such periods per second ; in musical theory this is generally termed the vibration number; i.e., the number of 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 of rest. 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. MUSICAL SOUND II These characteristics are directly connected with and dependent on the peculiarities of the vibration system which are enumerated above. The Force depends on the amplitude of the vibration and is proportional to the square of the 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 is taken 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 each other, so that two tones may have the same pitch and differ in force, or may have the same force and differ in pitch. The Mode of vibration is of great import- ance in the consideration of musical sound because on its character depends what we call the Quality or Timbre of the sound. The infinite variety of Quality which may exist among musical sounds is due to the fact that the sounds produced by nearly every musical instrument are not simple or single tones of one determinate pitch, but are what are called compound tones consisting of an assem- blage of such simple tones. In this assemblage 1 2 THE FOUNDATIONS OF MUSICAL /ESTHETICS that simple tone which is the lowest, and gener- ally the loudest, is called the fundamental or prime, and by its pitch we judge the pitch of the whole compound musical tone. The other higher simple tones present are called harmonic upper partials, or simply upper partials, or har- monics. These upper partials occur in a regular series forming with each other fixed intervals in the following 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 the sound 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 r6 The note written as B flat in the above is in reality slightly flatter. MUSICAL SOUND 13 The number of vibrations executed in any given time by any of the upper partials of a fundamental tone, relative to each of the vibra- tions of that tone, is indicated by the figure which shows the position of that upper partial in the series. Thus, the first harmonic of any sound — the second sound in the series and the 8th above the fundamental — has two vibra- tions to every one of the fundamental; the second harmonic — the third sound in the series and the 12th above the fundamental — has three vibrations to every one of the fundamental : and 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 few or many, must occupy positions in conformity with the above series; thus, a sound may con- tain Nos. I, 3 and 5 only, all the others being absent; or i, 4 and 8, etc., etc.; but in no case can a tone intermediate in pitch between any two consecutive numbers of the series make its appearance. With certain exceptions every musical sound is in reality a compound of a fundamental tone with a number of upper partials, and the Quality of such sounds depends on 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 may differ amongst themselves as regards any or all of these three possibilities. It is therefore ob- vious that the possible number of different qualities is infinitely great, as alteration in any one of these constituent factors will produce alteration 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 what one may call the objective point of view, but it will be useful to glance for a moment at the subjective conditions under which these charac- teristics are apprehended, so far as it is possible to specify these. With regard to the force of a musical sound, we naturally and easily conclude that the force is really a measure of the energy of the vibrat- ing system, or of the distance of the vibrating system from our ear. With regard to duration we as naturally con- clude that the continuance of the sensation of MUSICAL SOUND 1 5 sound depends directly on the continuance of the vibration. With regard to pitch, however, there is no obvious explanation of the manner in which this is appreciated by the ear, and what are the limits of such appreciation is a matter which is not at all clear or apparent. Helmholtz has formulated the theory that certain parts of the structure of the ear are capable of being sympathetically excited by sound, and that for every degree of pitch there is a locality in the ear which responds and by its response gives rise to the sensation of that particular pitch. This theory would also serve to explain to some extent how the ear appreciates quality or timbre, on the basis that quality is directly de- pendent on the presence of certain upper par- tials or harmonics along with a fundamental sound. It is, however, not unreasonable to suppose that just as the eye has to undergo what is termed a process of " accommodation " in visualising objects at different distances, and just as the subjective feeling of effort or strain involved in the process of accommodation is the 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 1 6 THE FOUNDATIONS OF MUSICAL iESTHETICS of an accommodation which will serve as an aid to the appreciation of both pitch and quality. Such power of accommodation may be derived from 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 different individuals. Some few are said to exist who cannot discriminate at all between high and low sounds. At the other extreme are individuals who have what is called the faculty of " abso- lute pitch." Between these two extremes come all degrees of pitch recognition. The ability to recognise " absolute " pitch is, however, really a very long way from being an absolute ability to recognise pitch. Vari- ations in pitch are infinite and the human mind is finite. Pitch discrimination is really a matter of difference of degree, not of kind. Some individuals can recognise pitch to within a semitone or even less. Others cannot identi- fy pitch within much larger limits. What is involved is simply the power of identification, and although some degree of development of this power is necessary to the musician, it is not 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- MUSICAL SOUND 1/ tions which exist between the limited number of sounds in our musical system, which are co- ordinated and formulated into an artistic pro- duct in conformity with a definite process of selection. Just as the painter must be able to appreciate truly the relative values of light and shade and colour, and the relations which underlie the lines of perspective — he does not require either to know the absolute distances between the objects of his landscape in terms of 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 such they 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 subject of artistic arrangement and manipulation. Just as colour, qua colour, is the sensational description of the effects of light vibrations of certain wave lengths on the sense of sight, so the apprehension of musical sound is simply the reaction set up in the organism to certain physical stimuli. 1 8 THE FOUNDATIONS OF MUSICAL ESTHETICS A single musical sound calls forth a single reaction, which, if it were unique in experience, would have no meaning or value other than its surface value as a sensation. But, because that particular kind of stimulus which gives rise to musical sound may vary infinitely in detail while retaining its general character, we experi- ence a corresponding infinity of musical sensa- tions, all partaking of that general quality which we call musical, but varying amongst themselves as regards details of individual character. The regulation and co-ordination of these differences, and the understanding and expression of the relationships which exist between the various musical sensations are the proper business of the 'Ait of Music. Putting it in the most general way, the Art of Music consists in the arranging of successions and combinations of musical sounds of varying pitch, quality, force and duration, according to certain principles some of which seem to be essential and necessary, while others are unes- sential, conventional and temporary. CHAPTER III EQUAL TEMPERAMENT The relationship between two sounds with re- gard to pitch is called the interval between them. The number of possible intervals is absolutely infinite. In practice the limitations of the human senses restrict the number of such intervals employed in any musical system. The limits, for practical purposes, between which musical sounds used in European music are arranged, are, on the one hand, that sound which has 27.5 vibrations per second (the lowest A on the largest pianoforte), and on the other, that sound which has 4,000 vibrations per second, roughly speaking. It is necessary to realise that the peculiar characteristic of musical sound which we call pitch is a quality which can be definitely de- scribed only as a rate of vibration. Also, that while each separate rate of vibration corres- ponds to an individual and definite pitch, the number of possible rates of vibrarion is abso- «9 20 THE FOUNDATIONS OF MUSICAL ESTHETICS lutely infinite. Here, in fact, we touch on that mysterious thing called Continuity, and it should not be overlooked that, although the sounds employed for musical purposes are comprised between definite limits, and associ- ated in definite relations, yet from the inferior to the superior limit the pitch series is in reality continuous. So that to represent graphically the change of pitch from the lowest to the highest sound, we must use a continuous line : e.g.— 4000 27"5 In all musical systems this rise in pitch is arranged in discontinuous steps — ^which are called intervals — ^because only by so doing can the mind give definiteness to its musical think- ing. The graphic representation of such 3 EQUAL TEMPERAMENT 2 1 system will, therefore, imply a figure like the following, in which ascent in pitch is indicated by a series of discontinuous steps. In modern European music these steps are equal, and there are twelve such to the octave ; so that each step — or semitone, as it is called — is equal to the twelfth part of the interval of the octave. This system of fixing pitch is called 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 the interval. Thus, the interval of the octave is produced between two sounds the upper of which has two vibrations to every one of the lower. The vibration fraction of the interval 22 THE FOUNDATIONS OF MUSICAL ESTHETICS of the octave is, therefore, 7i- A ratio of three vibrations of a higher sound to two of a lower characterises the interval of the perfect Fifth, the vibration fraction of which is, therefore, ^gj and so on. The musical classification of inter- vals as concords or discords corresponds to the ratio between the rate of vibration associated with each of the two sounds concerned. The simpler the ratio, the more concordant the interval. The following is a list of the intervals found within the octave with the vibration fractions of these intervals : — EQUAL TEMPERAMENT 23 Vibration Fnction Ratio. Unison Vi I : I Minor Second ^7l5 1 : 1 .06 Major Second 78 1:1.125 Minor Third % i: 1.2 Major Third 74 1:1.25 Perfect Fourth 73 1:1.3 Augmented Fourth % I : 1.40625 Perfect Fifth 72 1:1.5 Minor Sixth % 1:1.6 Major Sixth % 1:1.6 Minor Seventh 16/ h 1:1.7 Major Seventh 15/ 1:1.875 Perfect Octave 2 1:2 The above scale, however, is not used in modern music to any extent, chiefly because it 24 THE FOUNDATIONS OF MUSICAL /ESTHETICS is unsuitable for the employment of complex harmonic process. Instead, we use what is called the system of Equal Temperament, in which the interval of the octave is divided into twelve precisely equal semitones. In such a semitone the ratio between the rates of vibra- tion of the two sounds concerned is i : 1.059 approximately* ; so that the ratios of the various intervals in the octave are successively in terms of the ascending powers of 1.059. The relations between the sounds in the Equally Tempered scale are exhibited in the following table : — 1 To seven plares of dttjimals — i"oi;q463i. EQUAL TEMPERAMENT 25 Ratio Unison i: I Minor Second 1:1.059 Major Second I : (1-059)' Minor Third I : (1-059)' Major Third I : (1.059)* Perfect Fourth I : (1.059)" Augmented Fourth I : (1-059)' Perfect Fifth I : (1-059)' Minor Sixth I : (1.059)" Major Sixth I : (1.059)" Minor Seventh I : (1.059)'° Major Seventh i: (1.059)" Perfect Octave 1: (i.o59)i«or I 2 To the scientific mind there is something repugnant in the fact that our musical system 26 THE FOUNDATIONS OF MUSICAL /ESTHETICS is based on what is essentially a compromise, and every work on Acoustics bewails the necessity. However, what the artistic side of Music is concerned with is the use of sounds in certain broad relations of combination and suc- cession in such a way as to outline and express, not definite relations of quantity or value, but the fluctuations of human emotion, which can- not be stated either quantitatively or qualita- tively. Much of this desire for what is called true intonation is based on the assumption that consonance in the mathematical sense of the term is in itself a thing of beauty ; and that the more vigorous stimulus to the sensibility which the so-called roughness or discordance makes is in itself undesirable and unpleasant — as- sumptions that the musician would probably hesitate to endorse. The most perfect conso- nances are just those which from a musical point of view are dull, vapid and uninteresting; and the suffrages of any modern audience would clearly indicate which is now felt as the more " beautiful " of the two — the simple con- cordant harmony of the ancients, or the highly coloured texture of modern dissonant music. CHAPTER IV TONALITY AND SCALES A SINGLE sound is an acoustical fact, and the entire series of sounds which forms the basis of our musical system is, from this point of view, simply a collection of facts. Before these sounds can be used for artistic purposes it is necessary that they should be conceived in such a way (as far as pitch is concerned) that they combine to form a complex whole. The unifying principle under which they are so combined is called the principle of Tonality. The facts of Pitch and of Pitch differences are objective; they exist apart from the mind which perceives them; but this feeling of Tonality which unifies and co-ordinates these pitch differences, is not identical with the musical 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 28 THE FOUNDATIONS OF MUSICAL iESTHETICS a collection of sounds of different pitch as one whole, bound together in relations which are rendered definite and consistent by the fixation of one central point to which these relation- ships are all referred. Perception or recognition of anything as a whole implies reference of each element or part of it to some fixation point, which, however, need not be in the foreground of consciousness. This fixation point need not be in the actual focus of attention at any one time, but may exist as a back-ground of reference only. The relationship of the separate parts or elements to this fixation point unifies the whole. As an illustration of this principle let us think of the figure of a circle. We call up a mental picture of a figure so constructed that in it there is one point such that all lines drawn from this point to the circumference are equal. ! TONALITY AND SCALES 29 If we call up pictures like these:— we realise that these figures are not circles, without definitely formulating as a reason that there is no such central point. In music the single sounds of different pitch are the elements or parts, and these elements or parts are unified into a whole and displayed in some consistent relationship one to another by reference to one single sound as a fixation or central point. This central point is chosen arbitrarily, and may be changed at will; but at no time — if the feeling of Tonality is to be clear — should there be any doubt or confusion as to its identity. This is the principle of Tonality; and in some form or other it must be operative in any musical system which is logical and consistent. Any sound, therefore, considered with re- ference to the principle of Tonality makes it- self felt in a way conditioned by the relation- ships which exist between it and the Tonal 30 THE FOUNDATIONS OF MUSICAL ESTHETICS centre. Conversely, the change in the Tonal centre implies a corresponding change in the manner in which any sound impresses the mind. In a succession of musical sounds each mem- ber of the succession in turn comes into and moves out of the focus of attention, but the unifying of such a succession from the point of view of pitch is accomplished by the fact that each sound is referred to some fixation point or tonal centre, and is realised according to the relations subsisting between it and this centre. Thus, if we take a succession of different sounds : — we can produce a distinct number of different impressions, according as we regard each different sound in turn as the fixation point or tonal centre of the whole. For example, by loading any one of these sounds with extra emphasis or tone, we can strongly direct the attention towards the sound so emphasised, and the whole succession tends to form one individual group centred round this strongly TONALITY AND SCALES 31 accented sound. By changing the sound em- phasised the succession can be made to suggest a series of different tonalities. As another illustration of the same principle take the sound: — i and refer it in turn to a succession of different keys or tonalities, C, B, A, etc., etc. In each case the single sound C is accompanied by a specific feeling which is extra to the sensation of definite pitch, and which is different in each case. This specific feeling is caused by the different relations exhibited between this sound C and the central sound of each new tonality. A point of considerable importance is that this feeling of Tonality and the manner in which it appeals to the musical sense are not fixed and definite for all time, but are subject to the process of evolution and development. If we examine music composed in the course of the last 600 years we cannot fail to observe signs of this process of evolution. From the earliest times, even in the dim ages of which we have no record, some such unifying prin- ciple must have been at work, and in the 32 THE FOUNDATIONS OF MUSICAL ESTHETICS musical system which immediately, preceded ours and from which our modern system de- veloped we can trace the active influence of some such principle of tonality, although it was felt and expressed in a direction differing from that in which we now realise it. In the music of the early Middle Ages the principle of tonality manifests itself under a form purely melodic. That is, the relation of the component sounds of a work to the appre- hended centre of gravity is always successive, never simultaneous. From the operation of this 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 individuality to the reference of a fixed series of sounds to various members of this series, in turn, as the tonal centre. The monochord, which was em- ployed for the purpose of training singers, served to " standardise " the intervals which were used in artistic music, and the sounds which formed these intervals collected into a consecutive series constituted a scale which could appear successively in the different modes by the simple expedient of taking a different member of the series as the centre of gravity of the system. TONALITY AND SCALES 33 It is possible even for us who have our minds saturated with harmonic conceptions to realise something of the operations of this principle. Thus, if we arrange the white notes of the pianoforte in such a way that each is successively realised as the centre of gravity of the whole series, we can group the other sounds so that their mutual relations are under- stood by reference to that particular sound which for the time being is regarded as the tonal centre. Naturally, the chosen centre must be insisted upon and confirmed, other- wise the more usual arrangements of our modern system will tend to re-assert them- selves. The ignorance of this principle and the vicious tendency to regard tonality through the limitations of the major and minor scales are responsible for the maltreatment of much of the old folk-music which was invented by a people ignorant of these essentially harmonic schemes. The following setting of an old Scottish tune which the arranger has made to end outside of its proper tonality is a shocking example of this musical "Procrustes' bed": — 34 THE FOUNDATIONS OF MUSICAL ^ESTHETICS m ^3Q ^ e ? -^ Sh r^^ ( ■ ^:-i / g r"r" -— ^ »-^ 4 ^ ^ » ^ T rf ^s=? ^^ imtead r f f F ^ Tonality, according to mediaeval music, and music which is invented or composed by people without harmonic prepossessions, must be real- TONALITY AND SCALES 35 ised as stated melodically. The very first be- ginnings of harmony were not the result of con- scious or directed endeavour, but arose accidentally as a by-product of operations di- rected to quite other ends — and it is doubtful if the human ear, at this period, could ade- quately realise the harmonic effect of even the simple common chord. In the earliest har- monic music there was not so much an attempt to harmonise a melody as to perform the same or different melodies at different pitches. In all probability, at first, the performers were for the most part unconscious of any harmonic ef- fect at all. Eventually, with the development of the art of 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 on what may be described as negative harmonic principles. That is, the conscious effort of the composer was that these parts should combine in such a way that dissonant combinations were either avoided altogether, or that such discords as did occur should have a purely ornamental function, and be capable of solution by melodic movement. In the best examples of these works the oper- 36 THE FOUNDATIONS OF MUSICAL /ESTHETICS ations of the principle of Tonality are still feh melodically. Each part or voice conforms to a tonal scheme which, centring round a particu- lar sound, in the series, is realised as a definite mode. It was even possible for more than one mode to be employed simultaneously. However, with the development of the har- monic sense which followed the perfecting of the contrapuntal method, the composer eventu- ally reached a point where it is obvious that there was an embryonic realisation of the rela- tions between chords as chords. The first ef- fect of this new power of realisation was to lead to harmonic experiments, which often appear crude and tentative, but the modern realisation of Tonality, which binds into a consistent and proportioned whole both the successions and combinations used in music, is not apparent. On the other hand the composer had evolved some realisation of harmonic relations, although the fact that this is confined to the relations of only such combinations as appear in immediate succession makes these works sound to our ears somewhat vague and incoherent. The principle of Tonality in modern music is chiefly realised in connection with harmonic relationships which it controls and defines. It serves not only to connect up the constituent TONALITY AND SCALES 37 notes of individual chords, but to control the relationships 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 as founded on something more authoritative than mere custom and convention. It is a fact, as has already been pointed out in Chapter II, that most musical sounds are not simple and single, but when they occur are almost invariably associated with other sounds of different pitch. These subordinate sounds, or harmonics, or upper partials, form what is termed the Harmonic Series of the fundament- al sound from which they are generated. Refer- ence to p. 12, where the complete Harmonic Series of C is given, will show that the first two subordinate sounds in the series, excluding the octave and double octave of the generator, are the fifth and third from C. The summation of these three sounds gives us what is called the Major Common Chord. In the formation of this chord the three individuals, C, E and G, " fuse " into and form an entity which is felt as single and individual, not merely as the aggre-' gate of these three sounds. Similarly, the other sounds which occur in the Harmonic Series may be combined to form chords, and 38 THE FOUNDATIONS OF MUSICAL ^ESTHETICS practically all the characteristic combinatiens of modern music can be obtained in this way. The Harmonic Series presents a whole sys- tem of sounds which is based on the generator and in which the determining factor with re- gard to any one sound is the relationship it bears to this one fundamental sound. From this point of view, therefore, Tonality is implied in every single sound. However, when we come to consider this principle of Tonality from the point of view of harmonic successions we find it is strengthened by association with a further important princi- ple, viz., that of Progression. This principle, stated briefly, is that every sound in the limits of a definite tonality is naturally attracted to and tends to progress either directly or indi- rectly to the centre of the tonal system — the key-note and its derived harmony. Musical confirmation of a tonal centre necessitates progression to that centre, and the degree of relationship between any sound in the system and the centre of that system is measured by the tendency of this sound to proceed to the tonal centre. Now, every sound most naturally tends to proceed to that other sound in the Harmonic Series of which it is the first " foreign " upper TONALITY AND SCALES 39 partial, viz., the fifth'. So, any chord tends most naturally to proceed to that chord which is derived from the note a fifth below the root of the first. Thus, the harmony derived from the note G tends most naturally to proceed directly to the harmony derived from the note C; 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 to which 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 sequence present the note C as the centre point of the tonality, which is thus seen to be a structure in 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 element into the series. 40 THE FOUNDATIONS OF MUSICAL ^ESTHETICS balance being maintained by the equal distri- bution of sharper and flatter sounds on either side of the centre. The last sharp, F sharp, and the last flat, G flat, have the same pitch in the system of equal temperament. This sound is on the extreme limits of the key, and its tendency of progres- sion to the key centre is very slight. Its chief function is to assist in defining change of ton- ality ; appearing as F sharp when the change is to the sharp side, and as G flat when the change is to the flat side. Although the B on the sharp side and the D flat on the other are near the limits of the ton- ality, yet the melodic connection between these notes and the key-centre (to which they act as leading notes— the one upwards, the other, downwards) is very pronounced. The choice of any other sound as key-centre will show a corresponding re-arrangement in the functions of the constituent notes. The following is the scheme arranged round the centre F sharp : — I o '^ ^ ItfV go l^'^ '^^ XTTSI ^^ ^ — ^ TONALITY AND SCALES 4 1 While the sounds in the key have the natural relations just indicated, the notes efeployed in that scheme which we call a scale are simply a selection from the twelve notes of the key. This selection may be made according to any desired system; some seem to be more natural than others. The Major scale, for example, seems to most of us moderns to be derived from a peculiar necessity of the musical sense. But this is certainly not the case; only our harmonic prepossessions contrive to make us think this. In fact, the making of scales seems to be almost entirely a matter of taste, and the only difficulty for the modern composer which limits his choice is the solution of the nice problems in harmony raised by the use of these unusual scales. Even that difficulty is fast vanishing with the general loosening of har- monic necessity which is characteristic of modern practice. In fact, one of the most popular of these new scale forms is just that in which no single sound in the whole selection can progress to its nearest relative, because that relative is omitted. If the student will look again at the notes of the key of C as written out on p. 39, he will notice that the omission of every alternate note will produce that fa- vourite scheme of the modern composer — the 42 THE FOUNDATIONS OF MUSICAL /ESTHETICS Whole-tone scale. Of course, such omission at the same time eliminates that note to which every note of this scale would most naturally tend to progress in accordance with its acous- tical relationship. However, this peculiarity suits the characteristic fluidity — if it is not the cause of it — of most music written in this formula. or 7i ^ ^ CHAPTER V HARMONY In the preceding chapter it has been stated that the feeling of tonality, or key, in modern music is a realisation of relationships between the twelve sounds with which our system of tuning provides us. These twelve sounds are unified into one whole by the relationships which they severally bear to one central sound. This whole is organised so that each sound fills a place and function relative to this tonal centre different from that occupied by any other sound. The tonality, therefore, may be likened to a constellation in which we find a definite centre sound with eleven other subordinate sounds grouped round this centre, each oc- cupying its own particular place in the system and filling its own particular function. Be- tween this central sound and the others, and between each of these others, there are definite degrees of relationship, and the order of the ♦3 44 THE FOUNDATIONS OF MUSICAL .ESTHETICS relationships is indicated by the arrangement of the sounds grouped round the central sound. The key, therefore, is realised as a structure in equilibrium which is stable as long as the special relationships of the subordinate sounds to the tonal centre are maintained. If these special relationships are interfered with the whole tends to break up and re-crystallize round some fresh centre. Just as, in the limits of the tonality, there are degrees of relationship between individual sounds, so there exist similar degrees of re- lationship between the harmonies derived from these individual sounds. As the closest pos- sible relationship exists between two sounds next together in the above series, i.e., between two sounds which are a fourth or a fifth apart, so the closest possible harmonic relationship exists between the harmonies built up on two such sounds. This fact is independent of the particular quality of the harmonies involved, or of the simplicity or complexity of the par- ticular combinations. HARMONY 45 To 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. A first chord progresses when it is immediately followed by another chord, and although in most 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 fact that the relationships which exist between consecutive harmonies must be realisable if the progression is to sound logical. If the relationship is so obscure that it cannot be realised, or realised only with great difficulty, the progression will tend to sound illogical, until familiarity has established and confirmed the relationship. For this reason new pro- gressions take time to be understood generally before 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 always find the commonplaces of expression adequate for their needs; and the mind which is indi- 46 THE FOUNDATIONS OF MUSICAL ^ESTHETICS vidually perceptive will always light on hidden treasure in the shape of undiscovered harmonic truth. It must, however, be borne in mind that re- lationships between sounds are felt not only harmonically but also melodically. Certain individual constituents of a harmony may pos- sess certain melodic tendencies, in virtue of the relationships existing between them and the rest of the combination. This is the case with all kinds of discords, but particularly with those discords which we call unessential. The nature of these unessential discords is such that they form unstable constituents of what are otherwise stable combinations. They were in- vented and chiefly used in the days when the only relationships distinctly apprehended were melodic relationships; before tonality in the modern sense, as conditioned by harmonic re- lationships, was developed and realised. J3l -^ J J ,1 2Z S ^^ -e- In the above progression, the chief deter- mining factor is the necessity for simplifying HARMONY 47 and clarifying the complex harmonic relations by melodic movement. Thus at + the G which appears and adds complication to the harmony finds its solution in the melodic progression to F, one of the simple constituents of the har- mony. Such extraneous notes — the first discords to be consistently used by the early composers — filled the purpose of decoration or melodic embellishment, supplying that element of "pro- gression" which in the earliest music was lacjiing in the harmony as a whole. In fact, this feeling of logical and necessary progres- sion is mostly lacking in old music, in which harmony was an accidental circumstance re- sulting from the endeavour to perform two or more melodies simultaneously; or, if it is pres- ent, is only realised and stated melodically; i.e., the relations of single sound to single sound are present, but no feeling for harmonic relation, as we understand it, is traceable. The conception of key or tonality as a con- nected system of related sounds revolving round a definite centre, and permeated by this principle of progression to that centre was ab- sent from the minds of the early composers, who regarded music from quite another stand point. 48 THE FOUNDATIONS OF MUSICAL /ESTHETICS Such are the fundamental features of the early contrapuntal style as compared with modern idiom, and these conceptions are still maintained to some degree in the exercises in strict counterpoint which the student is called upon to perform. Strict counterpoint is an attempt to construct music from which the two modern principles of rhythmic balance and harmonic differentiation are excluded. The advantage of such exercise is often not obvious to the student who is apt to rebel at what he considers the artificial dullness of counterpoint. But in principle the practice of counterpoint is of considerable value, especially in modem times when the musical idiom in vogue owes so much to, and is so much influenced by the all-pervading pianoforte, in that the task set is, roughly speaking, to "melodize" a succes- sion of harmonies without the complication which is added by the necessity of observing the 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 giving a general presentation of the main facts on which modern musical art Is based, no endea- vour need be made to indicate the complex HARMONY 49 and elaborate theory of harmony which we owe to 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 tonality is the first principle of harmonic discrimination. All the elaborate and highly complex details of treatment which are embalmed in the text- books can be reduced to one or two very simple and general principles. The first of these is that no combination of sounds — no chord, as we call such — ^has any musical significance in itself. Such musical significance as it possesses depends entirely on the fact that ii either initiates, continues or completes a movement. This is emphatically the case in rhythmically conceived music, in which harmonic progression occupies a com- paratively secondary place. In the second place, this harmonic move- ment is executed with general reference to the tonality as a whole, and with specific reference to the place or function in the tonality of the particular harmony concerned. In other words, the progression of any harmony is con- ditioned by (i) the relationship existing be- tween it and the centre of the key system; and 50 THE FOUNDATIONS OF MUSICAL ESTHETICS (2) by the fact that it is concerned either with the initiation, the continuation or the comple- tion of progression. This is a matter which for the most part has been ignored by the text-books, which as a rule are content to isolate a number of com- binations, freeze them into immobility, and then proceed to lay down laws according to which they are supposed to be treated. It is rather curious and instructive that this dogmatic statement of the so-called "rules of harmony " is made most authoritatively in the case of the more complex dissonant combina- tions. The treatment of the simple common chords is mostly dealt with vaguely and the formulation of precise rule is reserved for the complex dissonances. But, as a matter of musical fact, the more complex combinations are in reality only decorated and ornamented forms of the simple chord, and the implicit function and relations of the former with re- gard to the tonality are identical with the func- tion and relations of the simple chord on which they are based. To illustrate this point: the Dominant triad in the key has the special function of suggest- ing immediate progression to the key-centre, towards which it stands in the closest relation- HARMONY 51 ship. 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 order of relationships which exist between the indi- vidual notes of the tonality illustrated and dealt with in the preceding chapter. The connection between two harmonies is direct and immediate when they are derived from notes the one of which is a fourth below or a fifth above the other. Thus, the harmony derived from G is immediately connected to that derived from C, and also to that derived from D. The tendency of progression towards C is stronger than towards D, because the note G is the first foreign upper partial of C. Such progression may be termed Centripetal, be- cause the feeling is progression towards the centre. Progression from the harmony of G to that of D, however, is Centrifugal and is away from the key-centre. The former of these is the more natural because of the attraction towards the key-centre. In the case of the latter the progression is maintained against this attraction, and therefore, this type of progression requires a definite output of 52 THE FOUNDATIONS OF MUSICAL /ESTHETICS musical energy which prevents it from sound- ing so natural or necessary as the other. Harmonies derived from sounds separated by other intervals than these are less directly related and their juxta-position tends either to produce an effect somewhat inconclusive: — $ 2r ^ or to create an implicit — if not an explicit- feeling of contradiction. i 231 In this latter case care must be taken to counter- act this feeling of key contradiction by special manipulation of the melodic progressions. # S However, even in the case of such a progres- sion as the last, harmonies not directly related can be forced into a kind of direct connection HARMONY 53 by the use of what may be called chord-fusion. By this term is meant the simultaneous em- ployment of more than one simple chord. Such simple chords then blend into a more complex combination which may take on itself the char- acter and relationships of either of the original simple chords. Thus, the chord of G is the nearest relative to that of C, while the chord of D is related only indirectly to that of C; if we fuse the chord of D with that of G we produce a complex dissonant combination which in virtue of the presence in it of the harmony of G is directly related to the har- mony of C : — $ 1 This fact of chord-fusion renders possible the logical use of any combination of the notes of the key. As the chief fact in the idea of Tonality is the implicit and explicit tendency to progress to the key-centre and as the direct progression to this key-centre takes place only from the Dominant harmony, such chord fu- sion is mostly carried out on the basis of Dominant harmony. But it is equally possible 54 THE FOUNDATIONS OF MUSICAL /ESTHETICS on Other basses, and so long as the dissonant combinations so formed receive an appropriate solution, and so long as the relationships in the tonality are clearly observed and attended to 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 another special feature of modern music — modulation. Just as the single notes of our system enter into definite and consistent relations with one another, and just as the harmonies derived from these notes form specific relationships which define and fix tonality or key; so corresponding degrees of relationship exist be- tween the various aggregations of single notes and harmonies which have been co-ordinated into a series of keys or tonalities. These degrees of relationship are strictly parallel to those established between the single sounds and harmonies of any one key. Just as the closest relationship exists between a note and those other notes from which it is separated by the intervals of a fifth and a fourth re- spectively, so the closest relationship between keys are these in which the tonal centres of each key are separated by the above intervals. Similarly, as in the case of single notes the HARMONY 55 degree of relationship gradually diminishes as. we proceed from the key centre outwards in both directions; so, a precisely parallel and analogous modification of relationship proceeds as we move from the key whose central point is C to the keys whose tonics are successively the other notes in the scale of relationship. At this point it is necessary to interpolate a caution to the reader to avoid confusing the terms key and scale. There is only one key or tonality associated with each tonal centre but there are possible a very large number of scales. The scale is only 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 general principles of relationship formulated above. The term key is a comprehensive term which includes the whole material of the system; the term scale is a term applied to a particular mode of selection of this material. The two modes in common use at present are the Major and Minor scales; but the only reason for the prevalence of these in modern music is the fact that the solution of harmonic problem is easier and more apparent in these two modes than in any other. 56 THE FOUNDATIONS OF MUSICAL /ESTHETICS Modulation in the proper sense of the term, takes place, therefore, between keys, not be- tween scales. To go from one mode of a key to another mode of the same key, is like chang- ing from one room to another of the same house ; to go from one key to another key is, on the contrary, a radical change involving a fresh scene and a fresh outlook. This fact of key relationship is used by the modern composer for the purpose of giving shape or " form " — as it is called — to his work. According to the practice of the early classical composers only changes involving very simple relationships were commonly used. But the modern composer allows himself — as in the use of harmony — ^practically any change he likes. This side of the matter will be dealt with more fully in the later parts of the book under the consideration of the principles of musical fotm. CHAPTER VI THE RHYTHM OF CONTRAPUNTAL MUSIC So far, the matters dealt with in the preceding chapters have been concerned with those princi- ples of musical thinking which refer to rela- tionships between musical sounds from the point of view of pitch. But the relationships which exist between sounds, considered from the point of view of Time or Duration, are of at least equal potency and significance in the scheme of modern musical art. ^Esthetic principles concerned with time re- lationships between sounds are the basis of what is called Rhythm in music; and the sys- tematic combination of these with principles dealing with Pitch relationships constitutes the essentials of that side of musical construction which is termed musical Form. Modern musical art is practically the result of the com- bined and simultaneous operation of these t\io contrasted " codes " — as they may be called — the one relating to sounds as they occur in 57 58 THE FOUNDATIONS OF MUSICAL /ESTHETICS pitch, the other to sounds as they occur in time. The discovery and full formulation of these " codes " of aesthetic principles were long and tentative processes, during which the musical sense of mankind developed from a condition that can only be described as primitive into one capable of appreciating the subtleties of a very complex art. Without going into the details of this process of development — a matter somewhat outside the scope of this book — it is proposed in this chapter to give a general sketch of the course which this development has taken, chiefly with reference to the foundation principles of rhythm. There is no doubt that the chief factor which conditioned the earliest development of music- al art was the fact that it was essentially a vocal art. Instrumental music of a primitive kind probably existed from very early times, but it is doubtful if it was ever self-sufficient or inde- pendent until comparatively modern times. Such as it was in the earliest times, it was in all 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 THE RHYTHM OF CONTRAPUNTAL MUSIC 59 liberty or variety in performance; in fact, the only instrument which was sufficiently under control and sufficiently responsive to be used for artistic purposes was the human voice. So far, then, as the artistic development of music was concerned, it is fairly obvious that the direction in which this extended and the rate at 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 was composed for and performed by voices. The time outline of the earliest vocal music was determined by the syllabic quantities of the words which were sung. So long as the musical outline was a simple setting of the words, and so long as the performance was strictly in unison, or by different voices moving strictly in some consecutive or parallel interval such as the fourth or fifth, no special time no- tation would be necessary. But when the musical outline became more complicated, and when musicians learned the art of combining two or more melodies characterised by con- trasted directions or rates of motion, some method of regulating and indicating the relative time values of the sounds had to be used in order to maintain the music in its proper pro portions. 6o THE FOUNDATIONS OF MUSICAL /ESTHETICS The first efforts of the musicians who invent- ed our notation were, from this point of view, confined to the production of such symbols as would indicate clearly very simple quantitative relations; and the music they composed, for which this notation was required, was built up entirely of successive sounds which were ren- dered continuous and unified into a series by the . simplicity of ratio in time value which existed between them. Sounds exactly the same length stand to one another in a relationship immediately appre- hended. Sounds the time values of which are in simple ratio, e.g., 1:2 or 1:3, present rela- tionships comparatively easily apprehended; and successions of such sounds can be summed up into a continuous unity when some further co-ordinating principle relating to pitch is operative. The early musicians were so influenced in the choice of the time outlines of their compositions by their realisation of verbal quantities, that some of them of set purpose attempted to formulate regulations for musical rhythm based on the syllabic quantities of the words sung. A certain Jean Antoine de Baif (1532- 1589) wrote some " Chansons Mesur6es " which were set to music by contemporary composers In THE RHYTHM OF CONTRAPUNTAL MUSIC 6 1 these verses de Baif indicated with the signs - yj the " longs " and " shorts " of each of his lines, and the composers chose such musical values as corresponded to these quantitative signs. 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 veflt £116 v6le mducheletes, elle v6le mduchgrons. The musical setting is: — i q: ZL 32 ^ Ja bdiS roTtde mesa-^- rede la ^ i/e JizS^-zon 1S>- 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 Musiciens de la Renaissance francais>*). 62 THE FOUNDATIONS OF MUSICAL /ESTHETICS The fundamental principles on which this systematization of musical value is based are operative even at the present day, although the strict proportions insisted on by theory are not always observed in practice, being modi- fied by the operation of the modern feeling for balance in structure and determinative pro- gression. We find, therefore, at the date when coun- terpoint was the natural and indeed the only means of expression at the command of the artistic composer, that the time outline of music was regulated by a system the chief ad- vantage of which was that it co-ordinated the various melodic lines which combined to form the structure. The sounds in this time outline were related to one another in the very simplest arithmetical proportions, and although these values 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 of length, but all lengths related in very simple proportions. It was, therefore, regulated as regards extent by the number of words sung; THE RHYTHM OF CONTRAPUNTAL MUSIC 63 as regards outline or syllabic pattern, by the values of the syllables of these words. Be- tween the lengths of the component phrases of a contrapuntal work, there was, consequent- ly, no necessary relation: some might be long, some short. The chief factor in performance was the necessity for the due and proper allot- ment of time value to each syllable, so that the requirements of harmonic combination might be complied with. Latterly, no doubt, some greater freedom was used, both in the modelling of the music to the words, and probably in actual perform- ance. Thus, instead of building up the phrase from a series of elementary "longs" and "shorts" each corresponding to one particu- lar syllable, the later contrapuntists showed often a fine sense of melodic decoration and feeling for contrast in the construction of the phrase. Thus the following outline shows a very high development of this feeling for beauty in line: — i k 64 THE FOUNDATIONS OF MUSICAL /ESTHETICS With regard to the composition of such con- trapuntal works, as a whole, the main principle observed was what may be described as the consistent maintenance of continuity. It must be remembered that the artistic problem to be solved at that time was the combination of simultaneous melodic lines, differing, it is true, as to the time values of their constituent sounds, but all characterised by a similar fluidity and by an equal absence of definite and regular articulation. Each musical phrase conformed to the outline of the verbal phrase which it illustrated. More or fewer words did not matter; the elasticity of the musical outline enabled it to expand or to contract accordingly. The problem of unifying the whole work and of reducing the feeling of discursiveness en- tailed by the peculiarities of the style, was solved by a self-sacrificing adherence to certain melodic formulae, and by the more or less per- sistent recurrence of a limited number of phrases. The principle of Imitation which is inherent in a vocal style of composition was freely used; at first, in a manner somewhat casual and restricted, but latterly, subject to certain definite and characteristic regulations. The full systematization of the contrapuntal idiom was reached in the Fugue, a form which THE RHYTHM OF CONTRAPUNTAL MUSIC 65 has persisted right down to modern times, and which, though mostly associated now with an instrumental medium, was in its origin based on and derived from the conditions and ne- cessities of vocal music. Even in works of this type which were written for instruments, in the details of which the technical character of the instruments exercised a very important determining function, the principle which oper- ated was essentially the principle underlying early vocal music. That is, continuous state- ment and amplification of statement, with no regular articulation indicating balance and symmetrical design as a whole and co-ordinat- ing all the separate parts. The absence of any definite feeling for tonality based on the co- ordination of the relations in pitch between simultaneous sounds, and the ignorance of the great modern principle of key relationship emphasised the same features in this early music. These features and the peculiarities of de- sign which they connote are still to be seen in the more modern contrapuntal music. But they are, in such modern music, supplemented by other features of which the early examples were entirely innocent. The radical changes in the outlook of the musician occasioned by 66 THE FOUNDATIONS OF MUSICAL /ESTHETICS the development of the feeling for key and key relationship and by the adoption for artistic purposes of the principle of rhythmic balance, effected considerable modifications in the con- trapuntal practice without absolutely obliterat- ing its idiomatic features. In a modern fugue, for example, the whole work is knit together and unified by the in- fluence of the principle of Tonality and all that it implies. Variety is provided and maintained by a judicious choice and contrasting use of key changes, or modulation. The subject matter is in many cases rendered definite by being conceived as a rhythmically balanced phrase — a feature unknown in early contra- puntal music — and is often of strongly marked pattern characterised by idioms which are dis- tinctly non-vocal. However, even in such works the main principles controlling develop- ment are essentially the principles operative in early contrapuntal vocal music. These are, as previously stated, continuous statement and amplification of statement, imitation by one voice or part of phrases previously sung by another, fluidity of outline, and an almost en- tire lack of balanced and definite articulation. Similar characteristics are to be found in much modern music which is not avowedlv THE RHYTHM OF CONTRAPUNTAL MUSIC 67 fug-al. Such works as the Preludes to the English Suites of Bach, and a good deal written by even the most modern composers, are based on structural principles identical with those which underlie the fugal form. Fluidity of outline, the lack of balanced ar- ticulation, and the assiduous maintenance of continuity proclaim the near kinship of such pieces to the Fugue, and indicate their descent from the original vocal music of the early con- trapuntists. The problem presented to the performer by such pieces is fairly complicated and admits of no very definite solution. In the next chapter it will be shown how the "elocution" of the rhythmically balanced work is a matter of phrase identification, and how the application of the broad principles of rhythm renders pos- sible this identification of phrase. In this contrapuntal music, however, there are no direct means by which we can always authori- tatively decide this important question of phrase outline. Built on vocal idioms which originally owed their phrase outline to the de- finition of words, modern instrumental music in this idiom has no verbal associations which can serve as a guide to the performer. But, if the performance of such works is to convey 68 THE FOUNDATIONS OF MUSICAL .ESTHETICS any meaning, there must be present in every case 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 the dislike which the unsophisticated have towards contrapuntal music is traceable to the fact that many performers imagine a fugue is to be "rattled" through from beginning to end without colour or contrast; excepting perhaps an 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 illustrations may help to make this point clear. If a certain voice or part consists entirely of repetitions of the same sound identical in pitch and in value »l»j»# •»*»»*M »Mm* we would have an undifferentiated succession which we might divide up in any way, and in no one way rather than in any other. Just as there is no particular reason if we wish to di- vide up a straight line why we should divide it into any particular number of parts rather than into any other. THE RHYTHM OF CONTRAPUNTAL MUSIC 69 But suppose that in the series of sounds there are some sounds which are differentiated from the others by time value : — i or by pitch : — & • f T m m £ or by both time value and pitch : — % rxrur,' r P y P "n*" then such differences, especially if they occur regularly, produce points in the succession which can be regarded as indicative of some shape. Just as if the straight line referred to above should now become curved: — Now, although continuity is maintained m the curved line just as much as in the straight. 70 THE ^ OUNDATIONS OF MUSICAL iESTHETICS there are features — chiefly associated with change of direction — in the curved line which lend themselves to the indication of possible articulations. The parts into which this curved line then articulates need not be balanced either in themselves or with reference to each other, but the important point is that by taking advantage of the differences in direction, etc., the line can be reasonably regarded as an ag- gregate of the several parts so obtained, and can so acquire a character and an individuality of its own. According to the same principle the char- acteristic features of any melodic succession can afford indications as to how that succession may be articulated and so acquire an aesthetic individuality, although the parts so articulated may neither be internally balanced nor present any balance with reference to each other. The fact that, in much modern music which is composed in the contrapuntal idiom, the subject matter is conceived on the basis of rhythmic balance, predisposes the mind of the composer to a development in which this char- acteristic feature of modern musical thought is more or less prominent. The regular employ- ment of sequential imitation in such works is THE RHYTHM OF CONTRAPUNTAL MUSIC 7 1 also ascribable to the desire of the composer to present this development under conditions which, in their formal aspect, convey this feel- ing of balance, while at the same time main- taining the continuity of progression. The following examples illustrate these points. The first four are subjects of fugues by Bach, and it will be felt that the natural ar- ticulations which they display are such that the feeling of a balanced statement com- pounded of distinct and individual balanced units is maintained in each expression. — m m* m * ^ m ♦-JH^ ^ — ■ 72 THE FOUNDATIONS OF MUSICAL iESTHETICS ''^i'UisjiOL The bar-lines in the above have been arranged so that they occui only before the rhythmic climanes of the several units. In the examples with which this chapter closes the reader will be able to trace the strong influence which the sequential idea is able to exercise on a development which, although not foreign to contrapuntal idiom, is characterised by a feeling of balanced state- ment and re-statement; a feature added to purely contrapuntal methods by modem prac- tice. The general principles upon which this rhythmic balance is maintained will be dealt with in the following chapter. THE RHYTHM OF CONTRAPIfNTAL MUSIC 73 Bach: Fugue in A minor 74 THE FOUNDATIONS OF MUSICAL /ESTHETICS Bach : Forty-eight Preludes and Fugues. Book IL, No. I. mh i=ri ^ =r^ ^ ^ ^ *f I J^ l ,- ' i ^ i^ ^ ^^ ^^ ^^ I J J- m ^^ efc ^ 55 CHAPTER VII THE PRINCIPLE OF RHYTHMIC BALANCE The artistic music of the Middle Ages — by which is meant music other than folk-music — was a sophisticated form of expression de- veloped wholly and solely from the vocal side. Whatever may have been the case in the tunes and " chansons k danser " sung by the people, the feeling for rhythmic balance — arising out of the symmetrically balanced physical move- ment — was rigorously tabooed by the eccle- siastics who were the professional musicians of these times. The associations of the dance with the profane and ordinary common life of the people disposed the ecclesiastical musician to 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 76 THE FOUNDATIONS OF MUSICAL ESTHETICS solved was the combination of simultaneous melodic lines, varied, it is true, as to the values of their constituent sounds, but all alike dis- tinguished by fluidity of outline, the absence of definite and regular articulation, and the simi- larity of texture which results from the use of common melodic formulae. The musical art of this period resembles in its lack of definite design the oriental decorative "arabesques" in which the eye is confused and the attention hypnotised by the multiplicity of interlacing lines, now convergent, now divergent, but without any subordination to a general prin- ciple of shape or perspective. The rise and development of instrumental music, however, were the means of introducing a new and important factor into the situation. As vocal music had attained to a very con- siderable development before the composer thought of writing for instruments, the natural result was that the earliest compositions for instruments were based solely on the matured vocal idiom. In other words, they were the exact counterpart of the prevalent vocal com- positions, only without word*. Divested of the words which gave the shape to the music, the effect of such compositions was soon realised to be far from satisfactory; and, after some THE PRINCIPLE OF RHYTHMIC BALANCE "J "J considerable time during which composers of instrumental pieces experimented more or less blindly in the endeavour to dig out some prin- ciple of design from the technical effects pecu- liar to each instrument, the eventual solution of the problem was found in the performance of musical pieces types of which had been in existence all along, but which had been un- recognised by the professional composers. These were found in the dance tunes sung and played by the people. A dance tune, unlike the vocal type of melody, 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, as performed by an assemblage of people either in the course of some mystic or sacred rite, or purely as a social diversion, consisted of the regular and periodic repetition of some series of movements. The simplest of all dances is the March, in which the body of the dancer moves in cycles each of which contains two simple movements. With more complex dances the series of movements is more com- plex, but all possess this feature in common, that after the series is completed the body of the dancer is in the same relative attitude as it 78 THE FOUNDATIONS OF MUSICAL ESTHETICS was at the beginning of the series. In the case of dances performed by one individual the cyclic character of the movements need not be so apparent nor so necessary, but in dances in which a number of individuals take part this cyclic arrangement is a necessary condition. When an assemblage of people performed the same dance at the same time, the task of co-ordinating the movements of the different individuals was probably accomplished by shouts and cries; just as the drill-serjeant co- ordinates the step of the recruits with " Left — Left — Left." These primitive shouts natural- ly developed into some kind of simple sym- laetrically balanced song, which derived its symmetry 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 natural and obvious thing for him to do was to fall back on that kind of music probably already associated in some measure with instrumental performance, and write dance music; i.e., music which is constructed on the basis of regularity and balance of rhythmic statement. The combination of this new principle with THE PRINCIPLE OF RHYTHMIC BALANCE 79 the paraphernalia of the contrapuntal style produced a species of composition in which sometimes the one idiom seems to be para- mount, sometimes the other : where certain sec- tions or divisions of the work are conceived on the basis of regular rhythmic articulation, and where in other divisions the natural fluidity of the contrapuntal style re-asserts itself. In many cases the dance shape was adopted in its entirety but by sophisticating the treatment the composer concealed the somewhat obvious origin from which it derived. In order that a rhythmic progression may be felt as balanced it is necessary, in the first place, that the mind should attend to the pro- gression in a peculiar way; and, secondly, that there should be inherent in the progression certain natural arrangements and proportions which can intuitively be realised as balanced and symmetrical. Before proceeding to the consideration of the purely musical side of such a progression it is necessary to consider briefly what is implied in both these conditions. A rhythmic progression is a succession oi sounds which unfolds itself in time, and which, in virtue of the definiteness and simplicity of the relations of value existing between these 60 THE FOUNDATIONS OF MUSICAL /ESTHETICS sounds, serves as a measure of the extent and rate at which time passes. This extent and rate are, however, relative rather than abso- lute. In such a progression two things are essential: first, the existence of sounds in suc- cession; second, the existence of definite and simple relations of value between these suc- cessive sounds. If the sounds of a succession present amongst themselves relations of value which are not definite nor simple the succession ceases to be realised as rhythmical. In European music the relations of value which must exist in order that a progression may be felt as rhythmical are of a very simple nature; viz., representing ratios of i: 2, 1:3, 1:4, etc' The consideration of a series of sounds in succession may be associated with two different forms of mental activity. In the one case the direction in which this activity is chiefly exer- ' In oriental music, the development of which has been on lines divergent from those followed by European music, the relative values of successive sounds are frequently very complex, and the oriental musician seems to be able to apprehend the complex proportions implied by such values, and to feel as rhythmical pro- gressions which we at present cannot so realise. (Of. The Thought in Music, Appendix A). Even in our European music these com- plex relationships in value are met with in what is called " Tempo Rubato," but there the apprehension is assisted by the operation of this very principle of rhythmic balance. THE PRINCIPLE OF RHYTHMIC BALANCE 8 1 cised may be described as backwards; the out- look is retrospective. That is, each sound as it comes into and passes out of the focus of perception has its value and place in the pro- gression assigned to it according to the re- lations which exist between it and those sounds which have preceded it. No definite attempt is made to forecast to any extent the outline of what is to follow it. To illustrate figura- tively: the attention of the listener is like that of a person who is proceeding through a country with his back to the direction of pro- gression. As each object comes in its turn into his field of vision he realises it in its rela- tions to that part of the landscape which he has already seen, but forms little or no idea of its relations to that which is still to come. The simplest musical example of this kind of attention is in the apprehension of the fluid progression typical of counterpoint: — 82 THE FOUNDATIONS OF MUSICAL /ESTHETICS $ Cj ^ '^ ~J Jl j^T-J ^^^ ^=B^ r r etc m -jr. t TT The apprehension of progressions like the above is almost entirely of the type described. So long as each sound entering the focus of attention stands in easily understood relations of quantity to its predecessors, so long this re- trospective attention is satisfied, and the pro- gression can — from this point of view — come to rest at any point. Contrasted with this is that type of activity in which the attention is directed chiefly for- wards. The act of attention is now projected so that it extends to and culminates at a point THE PRINCIPLE OF RHYTHMIC BALANCE 83 in the progression which lies in the future. Each sound entering the mental focus, besides being stored up in the memory in its relations to what has preceded it, is realised chiefly in the relations which exist between it and this point of culmination or crisis. The musician, in this case, is aware of the point of crisis in a way analogous to that in which the person who aims and throws a missile at any object is aware of the object at which he aims and also of the trajectory which his missile will de- scribe. This type of mental activity is that which chiefly characterises the apprehension of modem music in which the basis of design is this prin- ciple of Rhythmic Balance. In this the co-or- dinating factor is supplied by the fact that the musical intuition grasps in one act of thought a progression embracing a number of sounds arranged so as to convey the feeling of sym- metry and balance. The following are examples of such balanced groups, each ar- ranged round and culminating at its definite point of crisis: — 84 1HE FOUNDATIONS OF MUSICAL /ESTHETICS Such groups are felt as balanced because they are symmetrically arranged around a nucleus. This nucleus is generally called the Accent. As this nucleus or culminating point is felt to be the climax of the group, and as it is natural that such should be the most force- ful point in the group, the word accent has come to be understood as mainly indicating extra emphasis or loudness. In connection with rhythmic progression, however, accent re- fers to the fosition of this nucleus, which may or may not be the loudest point in the group. Such balanced groups are compounded of two equal but contrasting elements, the one preceding the nucleus, the other succeeding it. THE PRINCIPLE OF RHYTHMIC BALANCE 85 These elements are called beats or pulses, and while they are identical as regards quantity or value, they differ in quality, which difference is indicated by calling the one strong, the other weak. The weak beat is that which precedes and leads to the accent; the strong beat bears the accent. It must be realised that what we call accent is a special quality which characterises a cer- tain "place" in the progression. Rhythmic progression is essentially continuous and does not dwell on or delay at this "place" which is no sooner reached than it is quitted. The accented place, like -die mathematical point, has position but no magnitude. In the balanced group which coheres round the ac- cent, thereiore, some value must always pre- cede and some value must always succeed the accent. This balanced group is the unit of musical thought; it may vary infinitely as regards out- line, and in one and the same piece to a limited degree as regards dimension. In the simplest primitive form of unit the value which precedes the accent is exactly equal to that which fol- lows it. > 1 > _ 1 > o err, r r I p p ""' r r r i ° 86 THE FOUNDATIONS OF MUSICAL /ESTHETICS But, SO long as the total value remains the same, any value can be transferred from the one side of the accent to the other. A musical work in which this principle of rhythmic regularity and balance is the basis of design, consists of a chain of such units or phrases, so arranged and of such dimensions as to give the effect of continuity with more or less regular articulations. Each unit is identic fied with its own accent, and these accents are so arranged that they occur either at regular intervals or at intervals which present simple relations of value. The distinction between the rhythm of modern music and that of the contrapuntal idiom is, therefore, twofold ; in the first place, in rhythmically balanced music every accent is associated with a symmetrically balanced group or unit ; secondly, the occurrence of these accents is either regular or in accordance with a scheme based on simple relative values. If two successive accents are separated by a cer- tain interval of time, any change in the dimen- sion of the interval of separation will be such THE PRINCIPLE OF RHYTHMIC BALANCE 87 that the new interval presents, relative to the old, the simplest possible proportion : e.g., I : 2, 2 : I, I : 4, etc. It is, therefore, possible to indicate graphic- ally the rhythmic outline of modern music in some such manner as the following : — f^U. f^dnh S^ttm *'~U»i> s'rumt The figures on the curve show the points which correspond to the accents of the five units which make up this example. The essential nature of rhythmic progression is best exemplified by the following illustration, which I quote from my Principles of Phrasing and Articulation in Mttsic. Suppose A and B are two jetties in a river which flows in the direction of the arrow, from A to B. A person floating down the river with the current from A to B, will have a feeling of departing from A so long as he keeps his eye and attention fixed on A. 88 THE FOUNDATIONS OF MUSICAL ^ESTHETICS But if he shifts his attention to B, his feeling with reference to his progression will be one of af-proach to B. Substitute, for the flowing river and the jet- ties A and B, the continuous flow of rhythmic progression between two consecutive accents. The change in the direction of the attention from a preceding to a succeeding accent may take place anywhere between the two. Usu- ally this change takes place at a point con- ditioned by what has preceded the first accent. But the composer can, by manipulation of the musical outline, so arrange that this change can take place practically anywhere after the first accent is quitted. In this way, even if a piece is composed of units of the same dimension, variety can be secured and the monotony of mechanical change can be avoided. The rhythmically balanced unit or group is the ultimate fact in the analysis of design in modern music. From a practical point of view this analysis is of the utmost importance, because these units are the ultimate " phrases " of a work, and the correct " phrasing " in per- formance is simply the indication, by means of tone and time-inflexions, of the points of articulation which join the component units of a piece. The indication of these does not THE PRINCIPLE OF RHYTHMIC BALANCE 89 necessarily break up the continuity of progres- sion, but only serves to explain the meaning of the music by insisting on the outlines of the structure. Just as it is not necessary to lop off the hand in order to use the articulation or joint at the wrist. In the case of the early composers who em- ployed this characteristic idiom, the units which compose their works are generally simple in outline rather than complex, and variations in size, while not infrequent, are mostly confined to such as are comparatively simple. The following example illustrates this point : — Haydn: Sonata in F. The bar-lines are arranged in the above to indicate the rhythmic accents. The course of development, however, which has led to modern music has affected this factor of musical effect as much as the others. go THE FOUNDATIONS OF MUSICAL ^ESTHETICS The internal arrangement of the component units of a work has tended to become more highly organised and more complex; and the contrasting variations in dimension between the individual units in one and the same work have become more pronounced. In place of the simple Augmentation to double the dimension, or Diminution to half the dimension, variations in size of a kind very much more complex have become a frequent characteristic of the modern rhythmically conceived work. As an example of the possibilities of such variations in the hands of the modern com poser, the following Prelude of Chopin is ap- pended. The notation and barring employed by the composer have been modified in order to show the grouping and arrangement of the units. The barline in this transcription of the Prelude is used only where these rhythmical ac- cents occur. There are, therefore, just as many barlines as there are phrases or units. The slurs are employed to show the exact dimen- sions of each unit, and where two units of dif- ferent dimensions occur simultaneously each is designated by its own appropriate slur. THE PRINCIPLE OF RHYTHMIC BALANCE 9 1 O c/e/tcatissirno. =2- a ZZ- f 92 THE FOUNDATIONS OF MUSICAL ESTHETICS B. i ^ THE PRINCIPLE OF RHYTHMIC BALANCE 93 ■.2 ■5 ^^ ^ i ^^^^ i iifmCi f fr i jjjlljlj/ 94 THE FOUNDATIONS OF MUSICAL ESTHETICS rirf i- l | ifnf^ THE PRINCIPLE OF RHYTHMIC BALANCE 95 A. Tempo. %fti# ^^^^^ ,.r^ J^ %r 'Jy 96 THE FOUNDATIONS OF MUSICAL iESTHETICS 8v... ^ ^^=^ The two points in the above marked respect- ively A and B would probably in actual per- formance receive an interpretation in which the simple schemes indicated would be some- what modified. The feeling of the largely conceived progression in the left hand part at A would probably obliterate the small articu- lations of the right hand progression, and the whole passage would be swept along under the impetus of the larger rhythmic oscillation to- wards the climax at the "A Tempo." In the indication of this largely conceived rhythmic oscillation the most important factor is that balanced inflexion of time which is termed Tempo Rubato. By means of this necessary element of artistic performance the progression from and to accent can be indicated, and the shape and meaning of the phrase made clear. THE PRINCIPLE OF RHYTHMIC BALANCE 97 At B it is possible and, perhaps, preferable, to regard the whole concluding passage as leading up to an accent which has no sound as- sociated with it. This view certainly finds corroboration in the pregnant dissonance which never receives any overt resolution. CHAPTER VIII MUSICAL FORM The expression " Musical Form " has to a cer- tain type of musician all the sacred associa- tions of "that blessed word Mesopotamia." As too often used, the generalisations which constitute it are employed as a kind of musical decalogue invested with some kind of sacro- sanct authority, and the final verdict of a damning criticism is reached by reference to its laws and ordinances. However, a little consideration of historical process will show that like every other element in artistic production, this so-called Musical Form, in so far as it is vital and effective, has been, and is in a continual state of evolution and development. Briefly put, the Form of any musical work is that principle or method employed in ar- ranging the component parts of that work in virtue of which the work becomes a vital and 38 MUSICAL FOKM 99 organic unity. In the very earliest period of musical history, before self-sufficient instru- mental music existed, the Form of a work was primarily dependent on the words which were the basis of the structure. Roughly speaking, the scheme employed by the composer of that period was as follows : — ^A musical phrase, arranged as regards outline to fit the verbal phrase, was invented — or, as often as not, bor- rowed — due attention being paid to such matters as quantity and pitch. As the work progressed and the words of the text changed, new musical outlines moulded on new words appeared, and this principle continued until the piece came to an end. As Key, in our sense of the word, was not at this time realised by musicians, there is, in such works, neither modulation nor key-develop- ment. The unity of the work from the point of view of pitch is secured by the general pre- dominance of certain melodic relationships, im- plied by consistent use of one so-called mode throughout. The chief place with regard to design was taken by the principle of melodic Imitation. Just as the discovery and inven- tion of harmony arose from the endeavour on the part of different voices to sing the same tune at the same time, so the chief character- lOO THE FOUNDATIONS OF MUSICAL ESTHETICS istic of the mediaeval composer's scheme from the point of view of design was the consistent performance by different voices of the same melody at different times. As time went on the development of the technical skill of the composer in the direction of harmonic combination was accompanied by a fuller and clearer systematization of this principle of melodic Imitation. Just as the casual and fortuitous combinations of melodies which formed the crude and primitive Dia- phony and Descant became systematized into a supple and expressive art of Counterpoint, so the casual imitations which were the earliest attempts at design became systematized and regulated into the art-forms which are known as Canon and Fugue. The Canon was a piece of music in which the principle of Imitation was rigorously and consistently maintained throughout; as can easily be understood, it was therefore in capable of much artistic development. The very rigour and strictness which operated in Canon prevented it from ever assuming much importance as an artistic structure, because along with all the limitations imposed by any one principle of design there must exist a pos- sible freedom for development, else that prin- MUSICAL FORM lOI ciple will become reduced to a barren and mechanical formula. The developments possible within the limi- tations of canonic form are concerned rather with the management of the mechanism of imitation than with the intrinsic musicality of the idea or mood expressed. Consequently, the enumeration of the different ways in which this rigorous imitation may take place prac- tically summarizes all there is to be said about Canon as a principle of musical design. The chief of these were: — (a) Canon direct at various intervals, (b) Canon inverted, or by contrary move ment, (c) Canon by augmentation, (d) Canon by diminution, (e) Canon by retrograde movement, &c., &c. Besides the above there were what might be called " Puzzle Canons," the solution of which had to be sought for. These last were termed Ricercare — from the Italian verb, to search into, to investigate — a term which even- tually came to be applied to a species of com- position which stands midway between the Canon proper and the Fugue. The stringency I02 THE FOUNDATIONS OF MUSICAL /ESTHETICS of the Canon, tjie difficulties attending its composition, and the comparative poverty of the musical result, led composers to vary the strict imitations by the use of contrasting counterpoints and other effects. The result was a loose style of composition free, it is true, from the more mechanical restrictions of the Canon, but without any special or distinctive feature which might serve as a general prin- ciple of design. This type, however, was es- sentially a form of transition and its chief in- terest is that it indicates the course of develop- ment which led from the strict Canon to the more highly organised and more elastic Fugue. To enter into the technical details which characterise Fugal form would be beyond the scope of this book; the reader who is desirous of studying these will find them fully classified and tabulated in the text-books. It is neces- sary, however, to indicate the manner in which Fugal form and the idioms associated with it which originated in the principle of melodic imitation, are connected to and influenced by the great principles of design which are oper- ative in modern music. The origin of the two great conditioning principles of design in modern music — definite- ness of Tonality, and rhythmic balance in MUSICAL FORM IO3 Statement — dates from the period when the characteristic features of Fugue were in the process of becoming systematized and regu- lated. To the operations of these two prin- ciples is due the difference between the highly developed Fugue of the later composer and the invertebrate imitative discursiveness of the work of the earlier composers. Under the operation of the principle of Tonality, the Fugue, as a whole, acquired a unity and a symmetry which were unknown to the loosely constructed pieces in the modal idiom. The change from a central tonality to contrasting and subordinate keys, the identi- fication of whole sections of the work with one such key, and the final convincing reassertion of the central tonality, provided a shape in which the compromise between unity of idea and mood and diversity of detail and interest was effectually maintained. In place of the mechanical application of the principle of imitation which was a necessary result of the rigorous methods of Canon, there was substituted a scheme in which this imita- tion alternated with passages designed to af- ford relief, in which the fancy and aesthetic feeling of the composer found scope for their exercise. While the changes of Tonality, and I04 THE FOUNDATIONS OF MUSICAL /ESTHETICS the Statement of the subject matter in these various tonalities, served to supply the main supporting pillars of the musical structure, decorative passages, mostly of relevant mat- ter, provide relief and variety and maintain interest. Although the more modern composers allow themselves considerable freedom in this re- spect, these key changes were, in the case of the classical Fugue, almost invariably con- fined to tonalities which stand to the centre key in some very close relationship. As the essential basis of musical form with reference to the broader lines of design de- pends on this principle of Sequence of Ton- ality, it may be useful here to re-state the facts underlying this principle. The basis of relationship between sounds rests on acoustical fact, and just as individual sounds are felt in certain relationships in con- formity with these facts, so harmonies derived from such individual sounds, and the complex centralised systems (which we call keys) grouped round such individual sounds, stand to one another in similar relationships. In the case of Fugue, a form which attained its highest development at a time when this realisation of musical relationship was at a MUSICAL FORM I05 comparatively early stage of its evolution, the key relationships which outline the design of the whole work were at first of a nature com- paratively simple. The influence of the other principle of de- sign which characterises modern music — rhyth- mic balance of statement — is to be seen mainly in the organisation of the subject matter of Fugue. As has already been pointed out, the contrapuntal idiom which pervades this class of composition is, in a sense, antagonistic to this principle of rhythmic balance. Where the necessities of the contrapuntal idiom regulate the structure, this principle is therefore in abeyance; but in the organisation and elabora- tion of the subject matter its influence is par- ticularly noticeable. Also, in these decorative and unessential passages termed Episodes, the prevalence of the sequential method is a tribute to the desire on the part of the composer for symmetry and balance. The development of instrumental music re- sulted in the adoption for artistic purposes of the rhythmic outlines and idioms of the Dance tune. These became the basis of a type of instrumental music which eventually developed into the Suite. In its artistic form, however, the original Dance tune was moulded and de- I06 THE FOUNDATIONS OF MUSICAL ESTHETICS veloped so that although in each case the char- acteristic idiom and title was preserved, yet the whole movement departed from the primi- tive simplicity of the tune which was actually danced to, and became a sophisticated and distinctive piece for independent performance. The Suite consisted of a group of such in- strumental pieces generally based on dance idioms. The members of this group were bound up together by the fact that each is in one and the same key, and they follow one another in such a way that there is a more or less gradual transition of mood and movement, affording artistically calculated contrasts. Each of these pieces or dances is built on the same design or form. They differ amongst themselves not in regard to their shapes con- sidered as wholes, but in the patterns and out- lines of the units out of which they are con- structed. These idiomatic patterns give each dance its individuality, and the reader will find details of each in any text-book or dictionary of music. The principles of construction exemplif.ed in the general design or shape of these dance movements are very simple. The question of shape from the larger point of view is essential- ly a question of Key relationship and pro- MUSICAL FORM 107 gression ; i.g., movement out from a tonaf centre and movement back to that tonal centre. The manner in which this progression is accom- plished gives rise to all the variety of the so- called Forms. The very simplest solution of the problem is that in which the musical statement moves from the tonal centre to a contrasting subor- dinate key, and having reached this point of contrast moves back more or less directly to the original centre. Such a progression evi- dently divides into two parts, in the first of which movement is centrifugal, i.e., away from the key centre; and in the second of which movement is centripetal, i.e., back to the key centre. This is essentially the scheme under- lying what is called Binary or Two-Part Form. The following little piece is a neat example of this scheme: — Bach No. 10 of Twelve Little Preludes. 108 THE FOUNDATIONS OF MUSICAL /ESTHETICS ^m -jOT^ m i: US ^ ^ m i irr m W ¥^ M » rrf » £ I fc^ ^ ^ ^^ P=^^ ^s se sS ^ OT ^ 3 =f ^ s=^ :t H f f s MUSICAL FORM 109 Obviously, the very simplicity of this scheme prevents its employment on a very large scale without considerable modification. Conse- quently, when composers came to construct pieces on a larger scale the primitive simplicity of this Binary Form was modified and de- veloped. The process of development even- tually culminated in that Form which is called the Sonata, and the nature and character of the subordinate forms can perhaps be best realised by consideration of the process which ultimately led to the Sonata. The term Sonata and the collateral terms Cantata and Toccata were originally employed as descriptive not of the form or shape of a musical composition, but of the particular method of performance which it required. Cantata was something sung — ^performed by the human voice; no THE FOUNDATIONS OF MUSICAL ^ESTHETICS Sonata was something played by a violin or bowed instrument as opposed to Toccata, which was something played on an instrument with keys or "touches." The modern use of the term Sonata, on the other hand, connotes a certain form or shape of composition, and has little reference to the type of instrument on which such composition is performed. With the exception that the presence of the word Sonata in the title or de- scription of a work almost always implies the use of a keyed instrument; e.g., pianoforte or organ. This keyed instrument may be solo or may be used in conjunction with some other single instrument; violin, flute, etc. The term Sonata is not applied to composi- tions written for more than two instruments, although in form or design such compositions may be precisely similar to such works as usually are associated with this title. Such works are termed Trios, Quartets, Quintets, etc., according to the number of individual instruments required for performance. This numerical nomenclature has been extended as far as nine; when a piece requires more than nine single instruments some vague and inde- finite term, such as. Serenade, would probably be used. MUSICAL FORM III Historically, the Sonata derives from the same origins as the Suite; i.e., it had its root in the dance tunes and songs which, transcribed for instruments, formed the first and earliest self-sufficient instrumental music. While, however, in the Suite the dance origin is never lost sight of, but is preserved both in the titles of the movements and in their shapes and characters, in the very earliest examples of the Sonata these dance titles are abandoned, being replaced by a simple indication of Mood or Tempo — ^Allegro, Adagio, etc., and the outlines of the shape are altered and modified so that the original squareness of the dance tune is obliterated, and the music moves in cycles which at one and the same time are freer and more susceptible of development. In these primitive Sonatas, also, the germ of a more highly organised and developed out- line begins to appear. The invariable type of movement found in the dance form was that outline which has been described under the name of Binary Form, in which two equal parts are united, similar in idiom and contrast- ing only, or chiefly, in tonal progression. From this simple Binary Form the more highly organised Ternary or Three-part Form de- veloped, and on the basis of this latter wa? 112 THE FOUNDATIONS OF MUSICAL ESTHETICS constructed that type of fully developed move- ment which in modern music is associated with the term Sonata. The origin of this Ternary Type is to be found in certain movements of the Suite in which the initial idea or subject is reintroduced in the tonic key just before the end of the move- ment. Sometimes this "rudimentary recapit- ulation" is so imperceptible as to be scarcely noticeable; and it is further concealed by the fact that the subjects of these movements are often so indefinite as hardly to merit that name. The characteristic outlines of this " Sonata on one subject" (as this variety of Ternary Form may be called) are displayed in the fol- lowing scheme: — (i) Exposition beginning in the Tonic key modulating to a related key. (2) Middle Section consisting of modu- lations and developments based on the initial idea, with a progressive return to the tonic key, (3) Recapitulation of the initial idea, without modulation; concluding ca- dences or Coda confirming the tonic key. MUSICAL FORM II3 The foregoing outline subjected to certain developments produced what may be termed "Ternary or Sonata Form with two subjects." The second subject, at first tentatively intro- duced, eventually became systematised and fixed as an essential feature in this design. In the Exposition of the " Sonata on one sub- ject," as the music approached the related key in which this first part closes, the composer got into the habit of introducing a secondary idea or figure. The introduction of such an idea was no doubt suggested by the fact that the change of key could be made more definite and more distinctly perceptible when stated in terms of a new musical phrase or subject. This idea, which at first was quite secondary and little more than cadential emphasis, even- tually developed into a real second subject of distinct character and pronounced dimensions. The general scheme of the design so pro- duced may be summarised as follows: — (i) Exposition, consisting of (a) Prin- cipal Subject modulating towards a related key by means of a transitional passage; (b) Second Subject in re- lated key, generally composed of three distinct elements. 114 THE FOUNDATIONS OF MUSICAL /ESTHETICS (2) Middle Section made up of fragments of the Subjects arranged in a very variable order with regard to modu- lation and constituents. (3) Recapitulation, without modulation to the relative key, consisting of (a) Principal Subject in tonic key with transitional passage directed towards the Tonic; (b) Second Subject with all its elements transposed to the Tonic key. As far as the lines of definition are concerned the above scheme is essentially the design of the modern Sonata Form, but these early Works differ from the modern examples in two chief points. These are: first, the poverty and indefinitoness of the subjects; and, second, the fact that the middle section lacked organisation and was based more on the effect of contrasting modulations than on development of subject matter in the if*l sense of the term. The Tiodpfn composer, with few exceptions, is not content to base his work on the first subject which comes into his head — or under his fingers — but will spend much time experiment- ing and looking for subjects of a distinctive MUSICAL FORM 1 1 5 nature. Such striking and impressive subjects do not come by chance and in this connection there is nothing more instructive than to examine the careful and laboriously calculated touches and alterations by means of which Beethoven moulded his subject matter into that form which satisfied his artistic sense as the best possible. The highest invention is really a kind of divinely ordered criticism, and those musical ideas which often seem most spontaneous and most "natural" have reached that "naturalness" by the unremitting exer- cise of a nice criticism which has chosen only the suitable and rejected remorselessly the un- suitable elements. The term "Development" as used generally in music means the orderly and logical growth and transformation which a musical idea un- dergoes when it is employed to outline pro- gression. In this sense the process of building up the complete musical statement from the original unit is a development of that unit — a development which may take place in two different directions, indicated by the fact that a thing will suggest either its like or its op- posite. In connection with the Sonata and that par- ticular section of it with which this term is Il6 THE FOUNDATIONS OF MUSICAL ^ESTHETICS associated, the ward development generally has the first of these two meanings. Some- times an idea is developed by being contrasted with an entirely new idea — in which case we say that the development is, or contains, an Episode; but the general signification of the word is that an idea progresses to something which is obviously related to itself, but which as obviously differs from it in some particular. As the musical idea is stated in terms of Rhythm, Melody and Harmony, there are three directions in which development can take place; besides which any two or all three of these may be affected. The three factors of effect can each be treated in three different ways : (a) By Amplification, or Augmentation, (b) By Elimination, or Diminution, (c) By Supeiposition. An important factor in development which is contingent on the work as a whole and not on its separate ideas is the main pro- gression of the tonality inside of which these other factors take their place. This is, perhaps, the particular feature of the so-called Develop- ment Section which is most apparent and MUSICAL FORM II7 noticeable in the majority of works. Practically, the whole of the Exposition is stated in the limits of two tonalities — the tonic and the con- trasting related key in which the second subject appears. In the Development Section of the modern Sonata, however, there is always a more or less logical progression through a number of different tonalities, not necessarily in any close relationship to the main key of the movement, along with which proceed the developments, properly so-called, of the subject matter. In this direction is manifested the real aesthetic value of the development, and in this the form shows itself most fertile and affords most scope for the artistic sense and feeling of the composer. The tonal movement which characterises the Exposition and the Recapitu- lation of the Sonata Form is on the whole of a direct nature; but that which is found in the Development is what might be called " oscil- latory " — progression now to a sharper key, now to a flatter, with the emotional results which follow such fluctuations. In fact, it is usually at this part of the work that the approach to the real climax of the whole is realised. With the re-entry of the Tonic key after this series of tonal oscillations, the composer reaches a point where he generally has said all there is to say. Il8 THE FOUNDATIONS OF MUSICAL ESTHETICS and his main business, in most cases, from this point, is to get back to the emotional level at which the work started and complete the circle by finishing there. Besides differing from the more primitive So- nata in these two main directions — interest of subject matter and organisation of development — the modern Sonata shows other results of the evolutionary process to which it has been sub- jected. These chiefly concern the details of structure, such as the transitional passages uniting the salient subject matter, and the con- cluding passages or cadences which at first served mainly the purpose of key definition. Just as the establishment of the Fugal Form means Bach, so the systematization of the So- nata Form on modern lines is associated with the name of Beethoven. In his hands these subordinate and secondary features of design, which previous composers had been accustomed to regard as comparatively unimportant, and which they had frequently treated in a very perfunctory fashion, became integral parts of the structure, and not infrequently present an interest, both technical and musical, second to no other part of the work. The transitional passages, besides effecting change of key, usually contrive to link up or- MUSICAL FORM II9 ganically the two contrasting subjects, so that the continuity of progression is unbroken and the diversity of key and subject matter are not obtained by the sacrifice of the unity of the movement. The Recapitulation, which, so far as subject matter is concerned, is a repetition of the Ex- position, in the hands of Beethoven was made the vehicle for modifications of manner, which materially improved the old " necessary form- ality " of repetition, of which one is so conscious in the earlier Sonatas. By the introduction of various kinds of alterations in the outline and treatment of the subjects, curtailing here, ex- panding there, he contrived to maintain interest and to invest the re-statement of previously heard matter with a new significance. Finally, with that insight into musical possibilities which was his distinguishing characteristic, he ele- vated the Coda — originally a comparatively uninteresting and unimportant featiu^e — into what is sometimes a section of the movement equalling in dimensions and as interesting structurally as any of the other sections. In many cases this Coda became what may be called a second or " terminal development," differing from the central development chiefly in the direction or trend of the key movements. I20 THE FOUNDATIONS OF MUSICAL iESTHETICS This trend, in the case of the Coda, is con- trolled by the fact that the whole of this section is realised as focussed on, and moving to the final close, and the evolution of musical idea and mood is determined by this main fact. The direction of development in Sonata Form since the time of Beethoven has been two- fold : (i) In the broadening of the basis of the tonal arrangements and contrasts, which supply the skeleton of the structure ; (2) In the further elaboration and accumu- lation of material or subject matter. The modern composer has evolved a sense of key relationship which permits him to use and to appreciate key successions and contrasts which would have sounded strange and uncon- vincing to the musician of one hundred years ago. At the same time diversity and com- plexity of subject matter to a degree unknown at that time is the usual feature of all modern works which are written in Sonata Form. What remains intact, however, and what must so remain, except in the case of music which is MUSICAL FORM 121 purely impressionistic, is the threefold basis on which Sonata Form is established.^ (i) Statement, (2) Development, (3) Re-Statement. In the preceding pages the term Sonata Form has been employed consistently as in- dicative of the shape or design of one particular kind of movement. In modern practice, how- ever, the word Sonata is almost always associ- ated with a work which contains more than one distinct movement. In some cases these movements are connected (occasionally on the basis of subject matter common to all) ; but the plan generally followed is one in which each movement is complete in itself and based on subject matter peculiar to itself. The shape or design, however, of each movement is nearly always modelled on lines which approximate more or less to those which characterise the forms described in the preceding part of this chapter. There are, however, many cases of individual movements which are of an amorphous nature, deriving their special features of design from indefinite origins, of emotional rather than 122 THE FOUNDATIONS OF MUSICAL ^ESTHETICS formal significance. In some cases the relics of the old contrapuntal idiom are to be met with, either in the shape of regular and formal Fugal writing, or in some design which essays to com- bine the characteristic features of both the con- trapuntal and the modern method. For details of the less important shapes the reader is referred to the text-books which are devoted to this subject. In every case, however, the shape which characterises any and every movement is the result of a solution of the artistic problem which the composition of each work presents to the composer. That is, how to combine into an organic unity the separate components of any one work ; and how at the same time to maintain continual variety and interest with regard to both matter and manner : in short, how to com- bine unity and multiplicity. While the prob- lem remains ever the same, the solutions become more and more difficult. As the Art develops the materials increase in complexity and heterogeneousness, and the conventional formulae which served as a basis for the artistic aspirations of an earlier age become less and less adequate for those of later times. BIBLIOGRAPHY Helmholtz. — The Sensations of Tone. Trans- lated by Alex. J. Ellis. London, 1912. Taylor, Sedley. — Sound and Music. London, 1896. Wood, Alex. — The Physical Basis of Music. Cambridge, 19 13. DTndy, Vincent. — Cours de Composition Musicale. Paris, 1909. Lalo, Charles. — Esquisse d'une Esthetique Musicale Scientiflque. Paris, 1908. Matthay, Tobias. — Musical Interpretation. London, 19 13. Macpherson, Stewart. — Musical Form. Lon- don, 1908. Music and its Apprecia- tion. London, 19 10. McEwen, J. B. The Thought in Music — an Enquiry into the Principles of Musical Rhythm, Phrasing and Expression. London, 19 12. The Principles of Phrasing and Articulation in Music. London, 1914. Parry, C. Hubert H. — The Evolution of the Art of Music. London, 1909. Style in Musical Art. London, 191 1. "3 124 THE FOUNDATIONS OF MUSICAL /ESTHETICS Prout, E. — Fugue. London, 1891. Musical Form. London, 1893. Affiled Forms. London, 1895. Stanford, C. Villiers and Cecil Forsyth. — A History of Music. London, 1916. Wallace, W\\X\asQ..—The Threshold of Music An Inquiry into the Develofment of the Musical Faculty. London, 1908. The Musical Faculty, its Origins and Pro- cesses. London, 19 14. There is a very large number of text-books of various sorts dealing with the special sub- jects of Harmony and Counterpoint, but with few exceptions they are only part of the apparatus of Pedagogy, and are distinguished neither by a philosophical nor scientific outlook. Amongst the most important exceptions are: — Day, Alfred. — A Treatise on Harmony. Edited by G. A. Macfarren. London, 1885.^ Stainer, J. — A Theory of Harmony. London, 1871. Hull, A. Eaglefield. — Modern Harmony, its Exflanation and Afflication. Lon- don, 191 5. 1'irjqi^iMiW . P