The Three Dimensions of Music: The Principles of Musical Aesthetics

By
Michael McMullin

I. Music as Medium of Art
Though it is often stated that rhythm, melody and harmony are the "three dimensions" of music, this has the appearance of a casual observation, made without going much below the surface. It is not "scientific", or at least we do not know of a logical demonstration that rhythm, melody and harmony can really be compared with dimensions. They are three elements in music, and at first sight appear to be the three main factors, two of which stand in a kind of horizontal-vertical relation to the other. But are they all equally important, and are they all elements of the same order? If it is meant that melody is horizontal and harmony a vertical dimension, where is the dimension of depth? Rhythm would seem to move horizontally also.

It is the use of the term "dimension" that is open to argument. It is true that a dimension is only a mathematical abstraction and has no objective existence, and it may seem unnecessary to quibble over a loose application of the term to music. But in fact it is important to arrive at clear definitions and the power of thought depends upon the ability to name things consistently. To speak without proper foundation of rhythm, melody and harmony as dimensions is misleading. It sets these three elements in a false relation to one another, and this in turn affects our whole outlook upon the history and theory of music.

Music can exist without harmony, in the form of an unaccompanied melody. A melody must have rhythm, but rhythm by itself, tapped on a piece of wood or sung on a monotone, is not music. Such rhythm is movement in time, and in melody it is varied by movement in pitch. It looks as though this is indeed a combination of movement in two dimensions, but where is the third? If an unharmonised melody is music and music has three dimensions, harmony cannot be a dimension. It might be argued that a single musical tone contains the element of harmony because it can be split up into an harmonic series of partials. The harmonic constitution of sound however determines its "tone-colour", and this is not what is usually understood by harmony.

Musical sound is the fundamental material of which music is made, and its characteristic is that it is itself rhythmic or regular in frequency, as opposed to noise. If rhythm is to be singled out as an element and juxtaposed to melody and harmony, it must first be clearly defined. It is usually associated, both in music and poetry, with the metrical accents, marked in music by barlines. These occur every two or every three beats, and the accents themselves may be marked off rhythmically in pairs, one slightly stronger than the other, as in 4/4 time; or a rhythm of accents may be further elaborated, in various combinations of two or three. The characteristic that makes these groupings rhythmic is the regular recurrence of the accent every two or every three beats, or, in the larger units, every two or every three lesser accents. Rhythm in fact is a regular periodicity, which corresponds with the nature of the living organism, most obviously in the heart-beat and breathing, while ultimately pulsation is in the nature of all manifestation. The fundamental rhythm seems to be alternate. Where we have a rhythm of beats, they are naturally grouped into twos, even where there is no actual grouping and either beat may equally well be imputed with an accent, as in watching the pendulum of a clock. Possibly the rhythm of three is in reality an alternate rhythm, with the second beat split equally into two; or possibly it consists of a rhythm of pairs of first beats or accents only - music in three-time seems naturally to fall into a two-bar or two-beat rhythm.

If the beats are slow, and there is no accent, the alternation may be that between sound and silence, instead of between one beat and another. This would be a simpler rhythm, but there is no reason why the term rhythm should be confined to the bar-period in music. Any appreciable regular periodicity is a rhythm, including that of the sound-waves of a musical tone, or of light-waves, or of any sort of pulsation. The periodicity may be elaborated, as when an alternation of beat and silence becomes an alternation of beats, and then pairs of beats, and so on indefinitely on successive rhythmic planes. This includes the plane of rhythm indicated by the time-signature, but only in passing, and the grouping of bars into four-bar periods is equally a rhythm, as is the grouping of phrases into sentences and sentences into forms. These higher rhythms however, to be appreciable as alternations, have to be defined by changes of pitch. Such changes become rhythmic by a periodic return to the original pitch, or tonal centre, which is further kept in view by varying the pitch only in a simple relation to it. Thus we have scales of tones, the frequencies of which are in certain simple proportions to that of the original, forming a basic pitch-rhythm. In modal music, where the scales are several and less clearly defined that the diatonic scale, and where the tones are not consistently related to a centre by the use of chords, the tonic has to be emphasised at frequent intervals, and we find a continual return to it or its dominant, or 5th.

We can distinguish however three main planes of rhythmic complexity. Firstly, the fundamental rhythm of the vibrations of musical sound of a certain quality. Its rhythmic quality is what distinguishes it from noise, which is irregular. Secondly, the rhythm of the duration of this sound, marked by its division into perceptible beats, and extended by the grouping of beats into larger beats or accents. And thirdly the rhythm of larger groups which has to be marked by the use of sound of different frequency or pitch. It is perhaps permissible to call these three dimensions, or planes, of rhythm. The use of all three together gives us the possibility of a three-dimensional complexity, and the rhythms may be elaborated almost indefinitely in each dimension. When we have a sound-rhythm in three dimensions we have a medium in which artistic expression, in this case music, may exist.

But though this medium of rhythm is the material of music, it is not music itself. When a child produces a tone on a musical instrument it is at once intrigued by the sound, and is attracted to go on experimenting. This rhythmic sound has a peculiar quality in itself, a sympathetic physical effect on the ear. It is not art, but it suggests itself as a medium of artistic expression. It is the actual concrete and physical material, like colours in painting, while the other two dimensions of musical rhythm have to be deliberately produced by the human mind. All art is an expression of values in a rhythmic medium, the medium having a value in itself as a quality of sensation. The next level of rhythm, that of perceptible beats and duration, is imposed upon the first by the artist, which may be only the sounds made by a drum, and in its more basic forms appeals to body-rhythms and can be physically and emotionally stimulating or exciting, and conducive to dance, or other kinds of action. When we add the dimension of pitch we can have melody, which in its simplest rhythmic form may be something like a carillon of bells. But we now have a 3-dimensional medium which lends itself to a full range of expression, not only emotionally, as in speech, in terms of rising and falling, joy or sorrow, loud and soft, slow or fast and light or dark; but also, secondarily, to an unlimited extent in terms of suggestion and association, and this is true in all three dimensions, and means through the mind, memory, and the thinking function. Thus we have the possibility of an integral expression of values in conscious terms, and in terms of the psychological functions of sensation, emotion and thinking.

While a rhythm as such is defined as a regular periodicity, it is made to carry an expression in art only by a distortion of the basic regularity. Thus a fixed rhythm, while it may be stimulating physically, is not art, but art exists through the variations of it, as we express an emotion by a distortion of the regularity of breathing, for instance by holding or catching the breath. Through the irregularities imposed upon the underlying or implied rhythms, and their associations, ideas and meaning can be conveyed in all three dimensions by analogies of effect. If we have the following rhythm of duration:

and enlarge it by the use of notes of different pitch:

this in itself becomes a ground-rhythm which only acquires meaning when it is varied in the following bars:
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This larger unit would in its turn be meaningless as such if it were repeated over and over exactly as it stands. The rhythmic unit is significant only as a variant of the original rhythm:
This variation of the implied regularity of a rhythm gives the significant shape to the idea, or contains the form of the music. Thus the form is not a regular rhytfam but it is defined by the departure from this, and contains the meaning of the music.
4
In the above examples the durational rhythm remains regular from beat to beat, and the form beyond that is defined by the pitch alone. The durational rhythm however varies between the third and fourth examples, while the pitch remains regular over the larger unit. Such a unit is a melody, and the term melody means not only a movement in pitch but implies the existence of form. As soon as we have form in the material we have art, which can only exist in a three-dimensional medium.
When there is melody therefore there is music, and in this sense it is true that "form is melody writ large", for the higher forms are only an elaboration of melody and are defined by melodic units. The simplest kind of music is a plain unadorned melody, and if we consider of what this consists we see that first of all it is, as a whole, rhythmically complete; it can be divided into two corresponding parts, each of Jaduc&u«a&2MLJuliiliudfi
If we speak of a melody, we mean a complete form that is a simple rhythm defined by the melodic line alone. It is the simplest form that may contain a "meaning". In speaking simply of "melody", we are thinking of the curve in pitch or the line of sound that draws the outlines of the forms, whether simple or highly complex The melodic line moves in all the dimensions of rhythm, but by "melodic" we mean mainly the single line which defines the simple formal unit; and since the tone-colour remains constant within this, and the durational rhythm may also do so, as in the fourth example above, the movement in pitch stands out as the most conspicuous attribute of melody. The "melodic line" may therefore be thought of as corresponding to the pitch dimension, and the three elements in music, tone-colour, melody and form may be compared with the three dimensions of musical rhythm: quality, pitch, duration.

We have seen that a monotonous rhythm is not art, but merely the medium of artistic expression, and that form comes into being through an organised alteration in the regularity. This is an intellectual organisation; it is an expression imposed on the rhythm by intervention of the intellect. The pure rhythm has a physical significance, while art has also an intellectual significance. Art is an intellectual expression in terms of an actual physical or sensory effect. This effect, because rhythmic, is sympathetic, or pleasing; it is in accord with the nature of life itself. But when this is organised in the interests of an intellectual expression it is used for more than the immediate sensation of the sound, and acquires, through the indentations made on the rhythm, a secondary effect which acts on the plane of memory-association. Thus when we are discussing artistic expression we are no longer dealing with the physical dimensions of rhythm, nor simply with the factors in music which embody that expression in these dimensions (tone-colour, melody and form), but with the mental or psychological process itself. Here we are on the plane of effects which are brought about indirectly by suggestion and association.
Now these effects of suggestion are conveyed through the sensory medium of the sound. The actual physically perceived effects in this, in all three dimensions, recreates in the mind analogous effects experienced in life. These analogous effects are also sense-effects, and so they appear in terms of some concrete perception. There is therefore, besides the actual experience of the sound-rhythm, a reference in the mind to corresponding rhythms outside of the sound which are no less real experienced effects. These particular experiences become generalised as patterns; in other words they become symbolical.

Suggestion through a rhythm then is a symbolical effect Firstly, it is an active, concrete and objective experience in the present Secondly, because it is rhythmic, it exerts a sympathetic effect upon the subject, or has value. Thirdly, because it contains an intellectual content in the form, it suggests more than the one particular object or experience in which it originates, and therefore is significant It is through the intellectual suggestion that it is related to other things, and any particular experience suggested becomes symbolical in its turn; in fact an ever widening general relationship lies behind the particular form, as when a stone is dropped into water, the circles of ripples radiate out from the centre.
So we see that form is intellectual and that art requires form. This means that there must be a process of intellectual association. But as art acts in all the above three manners at once, and the form exists in terms of actual effects or experiences, the associations will be associations of experiences also. Similarly, as in the first place the concrete perception of the sound-rhythm is the medium, so on the intellectual plane we imagine a particular object or sensation, and this concrete image becomes a medium through which something else is experienced. The important point is that art is throughout concrete, never abstract like reaoning.

In poetry and painting objects in the external world are taken as points of departure and used for their associations of effect. Such objects become symbolic only when certain features with associative properties are selected as forms and expressed through an actual rhythm. The objective experience thus affects the observer as an individual, through a sympathetic rhythm, and acquires a "meaning", through the associative action set up. It becomes a link between the individual on the one hand and the external world or the totality, or God, on the other. This double relationship is what we mean by a symbolic effect

In music the same principle holds, although it is less obvious because music is the least representational of the arts and the most purely symbolic. As it is not the image itself that is important, but the aesthetic experience that takes place in terms of it, we are not concerned with the definite objects of association, but with the type of action or movement set up through these. It is better therefore to speak, not of a symbol, but of a symbolic action, for symbol is the action which sets up a relationship through the object It is the actual effect, experienced fundamentally in the present, and widening in its significance as it is enhanced by more and more experience brought in by association through the intellect, and as each effect is organised as part of a larger whole. The higher the plane of art, the greater the part played by the intellect in terms of form, though the method of effect remains the same, through the medium of sensory experience.
While the image is not important for its own sake, it follows that there must be an image. It may appear superficially that a type of movement may be represented or imagined in the abstract, divorced from any concrete object, but in fact such movement cannot be conceived without thinking of something that executes it. In music it is executed by the instrument of particular tone-colour and associations, but this in turn is symbolical. The sound of a particular kind is the objective experience, but there must be a corresponding experience on the imaginative plane. Exactly what this is depends on the context and may vary, but something must always be visualised to act as a symbol, through which the particular effect can be appreciated. Sometimes the image of the instrument itself suggests ideas directly, as the vertical rows of organ pipes may suggest the dim and vaulted interior of a cathedral, and the emotional line of the melody be conceived in this setting. Sometimes the only image at first suggested may be merely a visualised curve, perhaps no more than a line on paper, or the appearance of the written score. But on further contemplation these become symbols of other things; the curved line may become the motion through the air of something, which may have emotional implications, and/or be associated with particular objects, such as a bird, or wave-motion; and there can be an expansion to an indefinite number of planes of symbol, as the ripples widen from the centre.

It may now be more apparent what are the essential elements in music. These cannot be arrived at by an inspection of the surface, but only by an analysis of the aesthetic process in which each must play a part. If there are "three dimensions" in music, these must correspond to the "three dimensions" of art in general. Art is three-dimensional in the sense that it is an expression of a three-dimensional reality. We can know of things in the physical world only in terms of sensory experience, and while in ordinary language we refer to such experience by a quite arbitrary use of word-formulae, in art we reproduce experiences directly, in terms of real effects. It is non-verbal and direct communication. Any experience is relative, and not only the objective (outer) phenomenon has to be taken into account, but also the subjective and psychological aspects, or how it affects us, and we apprehend it emotionally and mentally as well as in terms of sense-effects. By acting in these three spheres at once, by expressing this triple relationship; art achieves depth, which is impossible to descriptive language. We cannot think rationally in three dimensions at once, and it is impossible to express reality in the neutral and linear terms of reason; at best we can only indicate, but not express, the truth by presenting our subject from various angles in turn. We can only reach reality directly through a symbol.

II. The Aesthetic Process
Though we may speak of art as three-dimensional, this is only a convenient analogy in comparing it with reason. We are not dealing with the dimensions of space, but with a process of action in time, and this is what we really mean by referring to depth, or the inner world. Only space, which is static, and outside, can be reduced to geometrical formulae, and the time element is beyond expression in mechanical terms. Time is change, and art is an expression of the process of change. It is better to refer to the three stages in the aesthetic process as phases of time, analogous to past, present and future, rather than as dimensions with the implied associations of space. Before we attain to a complete relativity there must be three phases of relationship, between (A) the individual observer, (B) the particular object observed, and (C) the totality of experience or the whole. Correspondingly, there are at the same time three phases of effect, involving three psychological functions: a sensory experience (B), an emotional response (A), and a mental significance (C).
Applying this analysis to music, we have in the sphere of rhythm alone the three planes of quality, pitch and duration, while in that of the elements in which musical expression is actually constituted we have the corresponding factors of tone-colour, melody and form. Each set of terms belongs to a particular sphere of discussion and the different spheres may not be confused; but, in order to obtain an organised terminology they may be correlated. In each case the central element (B) is the concrete medium or active material. This is the objective experience. If we require terms to apply to the three phases generally, in whatever sphere of art, we may call this the Dramatic Phase. The subjective, emotional phase (A) we may call Lyrical, and that of the general intellectual relationship (C) Symphonic or Epic: (A) (B) (C)
 LYRICAL DRAMATIC SYMPHONIC
Planes of rhythm: Pitch Quality Duration
Factors in music: Melody Tone-colour Form
Psychological function: Emotional Sensory Intellectual
Phases of symbolism: Subject Object Universal

Once we have the fundamental elements in music, such as are factors in a simple unaccompanied melody, the higher forms can be seen as a greatly increased elaboration of these. The higher the form, the more complex is the texture, and the more intellectual is the plane. This means a higher organisation, and on the higher plane the particular becomes more generalised or inclusive, or more archetypal. The form exists in terms of higher rhythmic units, and if these are to be felt as a coherent whole they have to be grasped and related together more consciously as a development of ideas. In a melody the idea is simple, but when we have the simultaneous occurrence of more than one voice or instrument there is then an interaction of ideas. The ideas stand in a vertical relation to one another as well as in succession, and it is clear that the formal expression may become vastly more complex If the form is an integral whole and all its parts are consistently related, each part must contribute to the idea of the whole and will be incomplete in itself. The melodic line must be strictly related to the context and cannot be developed independently as an end in itself, and the emotional expression must be subservient to the idea. There is therefore a much more formal, as opposed to melodic, intellectual as opposed to purely emotional expression. The idea itself, the symbolic character of each part, becomes more important and more prominent. But as the intellectual content in art must exist in terms of sensory and emotional effects, which means values, and the form in terms of tonal and melodic expression, a highly developed form does not mean that music is less melodic, but that the melody is more highly organised.

It becomes more significant, is on a higher and more intense plane of symbolism, and wider in its implications.
To achieve an integral form, therefore, it is necessary to see that instrument, melody and form each play an essential part. Each line in the score must be "three-dimensional", and logically related to the others in each dimension. The secret of an integral form, as also of an understanding and analysis of music, is an equal development in each dimension, or in each phase of symbolism, so that the whole is completely symbolic or completely organic. There must be meaning and purpose equally in the melodic line, in the instrumentation and in the form, for it is in these three spheres that a positive and creative expression is put into music. It is important that this should be understood, both for criticism and analysis and for teaching. Harmony and counterpoint and instrumentation refer to the technique of combining two or more voices sounding together, in order to achieve this expression, and are something like perspective and draughtmanship, and mixing colours and the technique of pigments in painting. To analyse a composition in terms of keys and chords is like analysing a picture in terms of these factors, and is confusing the means with the end. In so far as "harmony", as a technique, is concerned with tonality, then it is an aspect of melody. The pitch rhythm of melody depends on the establishment of a tonic, and on the relationship of the various notes in the melody to this tonic, or to the intervals from it of an accepted and already known scale. Melody itself is therefore necessarily tonal; it moves in relationship to a scale, and its rhythm depends upon the constant reference to an underlying tonic and its periodic return to this. Where there is modulation, a relationship to a new tonic is implied. When there is "harmony", or several lines of sound, the tonal relationships of the melody are merely stressed or modified. Either the tonic is kept in view by the chords formed on its scale by the lower parts, thus allowing a freer movement to the top part while still retaining an unambiguous tonal relationship; or the tonal relationship is changed by the lower parts, thus throwing the notes of the melody into a different relief from that which might have been implied by it alone. The resources and possible rhythmic scale of melody are in this way greatly increased, but no new element is added. It is solely a question of relative pitch, and key-rhythm is no more than extension of pitch-rhythm. The melody may follow a recognisable rhythm of keys, just as it is based on a scale, but this is not form, any more than a scale is music. The keys and modulations of a piece of music are a function of the melodic line and cannot be separated as something distinct which exists for its own sake.
If harmony is a question of relative pitch, and pitch is the sphere of melodic movement, the distinctive characteristic of harmony may be that several notes of different pitch are sounded together. In this case a chord must be distinct from an arpeggio, for if an arpeggio is "harmonic" then an arpeggio melody must also be harmonic, and it is difficult to see what would constitute "melodic" in opposition to this. It might be argued that the effect of several notes sounded together is something quite different from that of each note sounded separately, on the ground that the whole is more than the sum of its parts. When we are considering the whole however we are considering the effect of each note and line in the score relatively to the others, as they occur both simultaneously and in succession. This is form, which, when there is more than one line, has to be reckoned vertically as well as horizontally. That is, the form does not exist merely in the length, to be measured by the foot or minute, but it is the idea-content or meaning, which depends on the relationship between all the parts. Each line of sound is a melodic line, and has to considered as such in relation to a basic pitch-rhythm, and this pitch-rhythm is determined by the effect of all the parts together. But when the parts pursue independent melodic lines, they are related to one another as separate ideas going on at the same time, each with its own melodic, instrumental and formal character. Each line is related to the others as an individual, and therefore as an element of tone-colour, or as an instrument
When several lines are played on the same instrument they have not of course the same individuality of colour, and do not represent a combination of distinct ideas in this dimension. Nevertheless the lines may conserve a certain character by adhering each to a particular range of pitch, as in a fugue, and otherwise constitute separate strands of the same colour, and may represent a composite idea. For the particular expression of fugue it may even be desirable that the parts should be of the same kind, as human voices, strings, or different ranges on a keyboard instrument. The technique of combining several independent melodic lines is usually known as counterpoint, and we may now ask the question: what is the difference between harmony and counterpoint? In a progression of chords, at least one part, usually the uppermost, must stand out melodically. In "harmonic" music, either the other parts merely emphasise the tonal relationships already implied, or the melody, on a solo voice, is thrown into relief against another tonal background. In either case the other parts form a background and there is really a counterpoint in two parts, the melody against the chordal block. There are two separate ideas, the melodic line or solo part and the general chordal background as a whole, more or less undifferentiated into separate strands.

Now there are two types of chord, concord and discord. The concord consists essentially of a triad, with the third and fifth above the root, the third being either major or minor, corresponding with the two types of scale or mode. The quality of each chord, whether concord or discord, depends upon the nature of the intervals from the root, which thus becomes for immediate purposes a tonic. As the scale is a sequence of certain intervals rhythmically related to a tonic, so is the chord, which is like a scale within a scale. Any note in the chord discordant with the root stands out with a special emphasis as a melodically distorted interval, or as a departure from the rhythm. The minor seventh, for example, occurring in any part, that part becomes temporarily at least melodically conspicuous; a major seventh wants to rise a semitone, while a second at once suggests a suspension, with the lower note eventually falling melodically to form a third. It appears therefore, at least in mainstream music, that discords tend to be contrapuntal in effect They are expected
10 to behave in a certain way, to follow a certain independent melodic movement.

A discord such as a dimished fifth has a special strained effect as a melodic interval from the root, and the presence of such an effect accounts partly for what is referred to as the "colour" of a chord containing it. Similarly chords containing minor sevenths have a slightly clouded or diffused effect But can this strictly be compared with colour? In the case of concords, we have the special rich effect two or more lines sounding in thirds with one another, or sixths (the inversion), and the idea of playing "in harmony" suggests at once the sound of thirds. Any chord must contain thirds, and the third from the root at least, even in another octave, is required to sound in it When a fifth is added, this make another pair of thirds, without producing a discord. In early times the third was regarded as a discord, onty octaves, fifths and fourths being concords. These latter intervals do not produce a clash, but neither do they produce a blend, being too similar or close in the harmonic series. Clearly the third has a peculiar effect which was not desired in the very early church music. Strictly speaking it is a mixed effect, or a lack of unanimity; but, as is not the case with what are later considered discords, two parts may continue indefinitely in thirds with one another without offending the ear. When this happens, and the two parts are equal in colour, there is "harmony", or what sounds harmonious, but no counterpoint, and it seems that thirds provide the essential effect that characterises "harmony". Further, this effect is one of two similar parts mixed or blended, moving in parallel, and is not primarily a pitch effect, but one of instrumentation. Nor does it exist to the same extent, if at all, in the case of two instruments of contrasted tone-colour playing in thirds - or of a large separation in pitch, that is an octave or more apart. In such case the two lines are contrapuntal and distinct Two violins playing in thirds have a peculiar colour effect; there is an enrichment of the tone-colour of one violin, and a suggestion of multiplicity that does not exist in the case of two violins playing in octaves or fifths. In an orchestra, if all the violins play in unison and octaves, we merely get a very loud violin note, but not the idea of numerous voices.

The minor seventh, being another third added to the triad, has a similar effect, but is more disordant with the root and therefore more contrapuntal in character. If "harmonic" music means the presence of similar parts moving in thirds, and thirds are a multiplication of tone-colour, then we have blocks formed by parts of the same or related colouring, which move as blocks, forming a counterpoint against one another, or against a solo voice or instrument. Thus in an orchestra we have strings, brass and woodwind, and these may be again subdivided, or the instruments used individually. When a discord produces a chord of a certain "colour", this colour is instrumental and could not be duplicated in quality with different instrumentation. Discords either emphasise the tone-quality or diffuse it, and the degree of dissonance even is dependent upon the tone-colour. The effect of two flutes clashing in seconds: is quite different from the same played on violins, as far as the colour is concerned. What the two cases have in common is the melodic movement of the two parts in relation to one another, and the tonal clash of the discord. In the same way a diminished seventh chord on the piano has little in common in the way of colour with the same chord on the organ.

When two independent lines are combined, each must be formally intelligible in relation to the other, whether they are single lines or colour blocks. If they are single lines the music is said to be contrapuntal or polyphonic, but when one or both are blocks moving in thirds it is said to be "harmonic", and has its real nature obscured. It is true that any line may move relatively little, or remain stationary for some time, in the form of a chord, pedal note or ostinato figure. In such cases it forms an even more distinct colour block, in contrast to a moving part. It marks a rhythm, both in pitch and time, which is varied by the solo, and forms a background. It has no form of its own until it moves, when it becomes contrapuntal. If "harmonic" means remaining relatively stationary and marking a rhythm, it applies to music which consists of a solo against a background. The music is mainly in the solo part, which is melodic. There is however only one melody at a time, as opposed to polyphony, and it is consequently on a much simpler formal level (hence the coincidence of "harmonic" with "Romantic"). As far as the melody interacts formally with the background, it is chiefly in terms of colour-relationship; if this does not make sense it is less aesthetically developed as music. There is a counterpoint, not of melodic movement so much as of instrumentation. The whole background, in as much as it gives out a rhythm in terms of which the melody takes shape, is comparable to musical sound itself, the rhythmic medium in which music exists, and it is dramatic. An instrument sounding generally in chords, rather than in distinct parts, perhaps over its whole range, is manifesting its potentialities of sonority as an instrument, more than anything else, and this again is in the dramatic phase, or the dimension of tone-colour.

This is of the greatest importance in orchestration, and whether an orchestra is treated contrapuntally in terms of distinct colour-blocks or whether it is treated as though it were an organ or pianoforte, depends on whether "harmony" is regarded as an end in itself, and the important thing the chord produced by all the instruments together, or whether it is regarded merely as the technique of combining several lines of sound. "Harmony" in the former sense is an abstraction. In the latter sense it is concerned as much with instrumentation as with counterpoint It cannot mean anything other than a way of looking at music, that is in cross-sections, on paper, rather than as a living experience. The "harmonic" method, that is the division of the music into certain rhythms of tonality, or "chords", may be useful as a technique or method of procedure, as a rather mechanical way of avoiding incongruities between the parts, and of marking a regular rhythm, but it is no more than a convenient method. If music consists of nothing but chords, it is incoherent, amorphous and deficient in formal organisation to the extent that it is deficient in melody - and one can think of composers to whom this applies. The more it consists of an interaction between melodically and colouristically distinct parts, forming an intelligible whole, or the more polyphonic, the higher the formal level.

The conclusions to be drawn from this lead in many directions and have an important bearing upon the whole of music. So long as rhythm, melody and harmony are thought of as "the three dimensions of music" we cannot have a sound system of aesthetics, and therefore we cannot have a standard of criticism. These are three things of quite different order, and failure to understand what they are and the real part they play may produce confused thought, confused methods of analysis and of teaching, and even confused composition. Thus we have schools which see music as leading towards an unlimited development "harmonic" combinations, or as consisting mainly of accented beats. Instrumentation or tone-colour is the element which emerges as one of primary importance, and corresponds with the rhythmic medium, sensory perception, or the concrete object. "Abstract art" has to be a contradiction in terms, and neither abstraction nor "realism", in the sense of representation or description, have anything to do with aesthetics. Tone-colour is the result of various mixtures of harmonic partials, so the various constituents of chords produce colours in the same way. This is a distribution and diffusion of instrumental colouring that already exists, and that is a fundamental factor, to think of it as something else called "harmony" is misleading, and produces a confusion between this factor and pitch. It has primarily an objective, concrete and symbolic or suggestive function, and this applies equally to arpeggio effects. For example the use of slow-moving diminished seventh chords on the pianoforte can be very suggestive of slowly surging water; this can be compared with rapidly moving water effects of scale or arpeggio passages such as we find in Bach's Chromatic Fantasy, and more explicitly in "impressionistic" works like the "Fountains of the Villa d'Este", "Jeux d'Eaux" and many others.

What is called "impressionism" in painting is precisely a new emphasis upon this objective or directly sensory phase of symbolism, and refers to sense-impression in a general sense. It is achieved largely through colouristic effects, and the term tone-colour has the same implications in music. Ninth chords in Debussy can be compared with impressionistic colouring in painting, and almost any symphonic poem proclaims this principle, while the harp itself has a most conspicuously colouristic effect and not an "harmonic" function. French poetry of the same period is referred to as "symbolist", and this again means the same thing, for this focus upon the sensory medium amounts to a more conscious awareness of the process of symbolism which is the language of all art. If music is to be significant as sensory perception, as well as emotionally and intellectually, it is necessary to understand the nature of symbolism, and how a phase of it is fulfilled in each of these spheres. To relate to the world as a balanced or integrated psychological whole, which means realistically, in the proper sense, we must do so in terms of all four of the psychological functions, sensation, feeling, thinking and intuition. In the arts it is at the high summer or full moon periods in the cycles of cultures or civilisations that the best balance is achieved in this respect, and these are properly speaking the classical periods. In the case of our Western culture this was the sixteenth century, carried over to a large extent into the seventeenth in the form of Baroque. The following sonata period, usually referred to as "classical", is dominated by the development of opera, and the principle of duality, either in the form of hero and heroine, or instrumentally as first and second subjects in sonata form, and their interaction is in this literal sense dramatic. It is in this period too that the form of the concerto is developed, with dramatic interplay between the solo instrument and orchestra. There is a shift in emphasis toward the individual, as standing out from or opposed to the whole, and this is continued further in the following romantic period, where there is a very marked shift in the balance, towards the feeling function and the lyrical. Here a Dramatic period occurs as an intermediate stage between the Classical and Romantic, in a process of decline, in a sense and taken overall, where form becomes less integrated than in the polyphonic period, with a lesser grasp of the whole, and a less developed symbolism. This is obvious in comparing a typical sonata movement with a fugue, especially with something like the great organ Passacaglia and Fugue in C minor by Bach. A loss of a feeling for the unity of creation means a less developed intuition, which is the fourth psychological function, and the one whereby the greater meaning is perceived, entailing the greater spiritual understanding. When we come to the modem and "post-modern" phases, we are in the winter season of the culture and this function, which is associated with the right half of the brain, has fallen into disuse, leaving meaninglessness as the prevailing state of mind. This represents in its typical and overall social manifestation a regressive decline from a feeling for the whole to a sense of separateness, and ultimately from seeing the material world (sensation) as symbolic and meaningful to seeing it as the haphazard detritus from a supposed "big bang", that somehow accidentally became assembled into various "mechanisms", of which we are one kind. This self-contradictory and illogical, not to say unreal state of affairs represents an exact contradiction of the aesthetic process, and of anything that can property be referred to as art, at any time in human history.