time-measure possesses its definite _standard_ according to which it is divided and co-ordinated. From this we arrive, in the _third_ place, at distinct _kinds_ of _time-measure._ The first thing of importance to notice in this connection is the division of time according to either an _even_ or an _uneven_ number of equally divided parts. Of the first kind we have, for example, the two-four and the four-four time. In these even number is predominant. Of the opposite kind is the three-four time, in which the co-ordinate divisions constitute a unity of equal parts, of course, but in a number that is uneven. Both types are to be found united in six-eight time, to take an example, which no doubt numerically appears to be similar to the four-four time, but as a fact, however, does not fall into three but into two divisions, of which, however, the one no less than the other, relatively to its closer aspect of division, accepts three, that is an uneven number, as its principle.
A particularization of this kind constitutes the constantly repeated principle of every particular measure of time. However much notwithstanding the definite time-measure is bound to control the _variety_ of the time-duration and its longer or shorter sections, we must not therefore extend its effective power to the length that it places this variety in subjection in a wholly abstract way, that in short, for example, in the four-four measure only four notes of equal length as fourths can appear, in the three-four time only three, and so forth. The regularity restricts itself to this, that as, for instance, in the four-four time the sum of the separate notes are only equal to four equal parts, which may not only be divided into eighths and sixteenths, but conversely may again contract into less divisions, and indeed are capable moreover of more diffuse division.
(_γ_) The further, however, this elastic mode of differentiation is carried the more necessary it is that the essential divisions of the time should be asserted as predominant and also should be indicated in an effective way as an illustration of the fundamental principle of their co-ordination. This is carried out by the _rhythm_, which first gives vital significance to time-measure and the beat. With respect to this vitalization[436] we may distinguish the following points.
(_αα_) In the first place we have _accent_, which to a greater or less degree attaches in an audible way to definite divisions of time, while others pass by on the other hand without an accent. By virtue of such emphasis, or lack of emphasis, which is itself of various kinds, every particular measure of time possesses its particular rhythm, which is placed in exact association with the specific mode of division to which its rhythm applies. The four-four time, for instance, in which an even number is the principle of division, has a twofold arsis; on the other hand there is that on the first note or fourth division, and then, though in weaker power, on the third. The first is called on account of its stronger accentuation, the _strong_ accent, the second in contrast to it the _weak_ one. In the three-four time the accent rests entirely on the first fourth, in six-eight time on the contrary it is on the first of the eight divisions and the fourth, so that in this case the twofold accent asserts a division of equal length in two halves.
(_ββ_) In so far as music is an accompaniment rhythm is brought into essential relation with _poetry._ In the most general way I will on this merely venture the observation that the accents of the musical beat ought not to directly contradict those of the metre. If, for example, one of the unaccentuated syllables, relatively to the rhythm of the verse, is placed in a strong accent of the beat, while the arsis, or it may be the caesura, falls in one of the weak accents of the music, then we get a false opposition between the rhythm of the poetry and that of the music which it is better to avoid. We may affirm the same thing with regard to the long and short syllables. These also ought in general to fall into harmony with the duration of the tones, so that the longer syllables are coincident with the longer notes, the shorter with the shorter, albeit this accordance is not to be pressed with absolute precision, inasmuch as music is frequently permitted greater play for the duration of its long notes, no less than for the exuberant subdivision of the same.
(_γγ_) In the _third_ place we may at once in anticipation observe that we have to distinguish the animated _rhythm of melody_ from the abstractly considered and severely regular return of the beat rhythm.
In this respect music possesses a similar and, in fact, yet greater freedom than poetry. In poetry the beginning and termination of _words_[437] need not necessarily coincide with the beginning and end of the verse feet; rather a thoroughgoing coincidence of this nature gives us a verse that halts and is without caesura. And, furthermore, the beginning and ending of the sentences and periods ought not throughout to mark the beginning and conclusion of a verse. On the contrary, a period will terminate more satisfactorily in the beginning or even in the middle and near the last feet of the verse. From which point we begin with a new one which carries the first verse into the one that follows. The same thing holds good in the case of music relatively to its time-beat and rhythm. The melody and its different phrases[438] need not absolutely commence with the fall of a beat and close with the conclusion of another: such may in a general way move freely to this extent that the main-arsis of the melody may be incident to that portion of a musical beat, on which, relatively to its ordinary rhythm, no such emphasis applies; whereas, conversely, a tone, which in the natural process of the melody would necessarily receive no accentuated prominence, may quite conceivably be placed in the strong accent of the time-measure, which requires an arsis, so that consequently such a tone, relatively to the time-rhythm, has a different effect from that which the same tone claims to assert as distinct from that rhythm and purely in the melody. This opposition, however, asserts itself most strongly in so-called syncopations. If, on the other hand, the melody absolutely adheres in its rhythms and divisions to the time rhythm it tends to drag, and lacks warmth and invention. In short, what is required is a freedom from the pedantry of metre and the barbarism of a uniform rhythm. A deficiency in more free movement readily increases the limpness and sluggishness to the point of actual gloom and depression; and in this way, too, many of our popular melodies possess aspects of mournfulness, drag and burden, in so far as the soul merely possesses a means of advance as its expression more monotonous than itself, and in virtue of such is constrained to consign to it also the doleful emotions of a broken heart. The speech of Southern peoples, on the other hand, more especially the Italian, offers a rich field for a rhythm and flow of melody which is more notable for its variety and movement. And it is precisely here that we mark an essential distinction between German and Italian music. The uniform coldness of the Iambic mode of scansion, which recurs in so many German songs, kills the free and jubilant impulse of the melody, and restrains any further rise and devolution[439]. In more recent times Reichard and others, owing to this very fact that they have said goodbye to this iambic drone, have imported into their lyrical compositions a new and rhythmical life, although we still find traces of the former type in some of their songs. However, we do not only mark the influence of the iambic rhythm in songs, but also in many of our most important musical compositions.
Even in the Messiah of Handel the composition does not only in many arias and choruses follow the meaning of the words with declamatory truth, but also adheres to the fall of the iambic rhythm, partly in the distinction simply that it makes between its long and short duration, partly in the fact that the protraction of the iambic rhythm requires a more elevated tone than the corresponding short syllable in the metre.
I have no doubt this is one of the characteristic features of Handelian music, owing to which we Germans feel so much at home with the same, quite apart from its excellences in other respects, its majestic swing, its victorious onward movement, the wealth it discloses of profoundly religious no less than more simple idyllic emotions. This rhythmical substance of the melody comes more directly to our sense of hearing than that of the Italians, who are inclined to find in it a want of freedom, as something, too, that strikes the ear as strange and alien.
(_β_) _Harmony_ The further aspect, in virtue of which alone the abstract basis of time-beat and rhythm receives its fulfilment, and thereby is enabled to become actually concrete music is the kingdom of tones regarded as such. This more essential domain of music is dominated by the laws of _harmony._ We have here a further elementary fact to deal with.
In other words, a material substance[440] does not only through its oscillation for art emerge from the mere visible reproduction of its _spatial_ form, and is carried further into the elaboration of its configuration _in Time_[441], but it produces _distinct_ sounds according to its particular physical constitution no less than its different length and brevity and number of vibrations through which it passes in a given period of time, and consequently in this respect, too, Art is compelled to take account of it and give it form agreeably to its own nature.
With regard, then, to this second element we have to emphasize with more accuracy three main points.
The _first_ one presented to our consideration is the difference between the various _instruments_, whose invention and elaboration has been found essential to create that totality of musical sound, which in respect to musical sound constitutes a sphere of different tones independently of all distinction of the relation of pitch whether it be a high or a low one.
_Secondly_, however, musical tone is, quite apart from the different peculiarities of either instruments or the human voice, itself an articulated totality of different tones, tone-series, and scales, which in the first instance repose on quantitative relations, and in the determination of these relations are tones which it is the function of every instrument and the human voice, according to its specific quality, to produce in less or greater completeness.
_Thirdly_, music neither consists in single intervals nor in purely abstract series of tones, that is, keys unrelated to each other, but is a concrete interfusion of opposed or mediating sound, which necessitates a forward progression and a passage from one point to another. This juxtaposition and change does not depend on mere contingency and caprice, but is subject to definite rules, which constitute the necessary foundation of all true music.
In passing now to the more detailed consideration of these several points of view I am forced, as already stated, to limit myself for the most part to the most general observations.
(_α_) Sculpture and painting discover their sensuous material, such as wood, stone, metals, and the like, or colours and other media of that type more or less straight to hand, or, at least, they are only compelled to elaborate the same in a subordinate degree, in order to adapt them to the uses of art.
(_αα_) Music, on the contrary, which throughout is set in motion through a medium artificially prepared for the purposes of art from the first, must necessarily pass through a distinctly more difficult preparation before the production of musical tones is secured. With the exception of the human voice, which returns us Nature in her immediacy, Music is compelled itself to create all its other instruments of genuine musical tone throughout before it can exist as an art.
(_ββ_) With regard to these means as such we have already above formed our conception of the _timbre_ proper to them in the sense that it is the result of a vibration of the spatial medium, is the first excitation thereof of ideal import, which enforces itself as such in contradistinction to the purely sensuous juxtaposition, and, by virtue of this negation of spatial reality, asserts itself as the ideal unity of all the physical qualities of specific gravity and the purely sensuous type of corporeal coalescence. If we inquire further as to the qualitative peculiarities of the medium thus made to emit musical sound we shall find that in its character as material substance no less than as artificially constructed, it varies greatly. We may have a longitudinal or oscillating[442] column of air, which is limited by a fixed channel of wood or metal, or we may have a longitudinally stretched string of gut or metal, or in other cases a stretched surface of parchment or a bell of glass or metal. In this connection we may draw attention to the following distinguishing features. In the _first_ place it is the _lineal_ direction[443] which is mainly predominant, and produces the instruments most effective in musical employment; and this is so whether, as in the case of wind-instruments, the main principle is represented by a column of air which is relatively more deficient in cohesion or by a material line adapted to tension, but of sufficient elasticity to be made to vibrate, as is the case with stringed instruments.
_Secondly_, we have the principle of surface rather than line represented in instruments of inferior significance, such as the kettle-drum, bell, and harmonica. There is, in fact, a subtle sympathy between the self-audible principle of ideality and that type of rectilinear tone[444], which, by virtue of its essentially simple subjectivity, demands the resonant vibration of simple line extension rather than that of the broad and round surface. In other words, ideality is as subject this spiritual point, which is made audible in tone as its _mode of expression._ But the closest approach to the exposition and expression of the mere _punctum_ is not the surface, but the simple linear direction. From this point of view broad or round surfaces are not adapted to the requirements and enforcement of such audibility. In the case of the kettle-drum we have a skin stretched over a kettle or basin, which by being struck at a single point sets the entire surface vibrating with a muffled sound. Though a musical sound, it is one which from its very nature, as belonging to such an instrument, it is impossible to bring either to clear definition or any considerable degree of variety. We find a difficulty of an opposite type in the case of the harmonica and the bells of glass which are set in vibration in it. In this case it is the concentrated intensity of tone which fails to project itself, and which is of such an affecting character that not a few, when hearing it, receive actual nervous pain. But, despite this specific effect, this instrument is unable to give permanent pleasure and is with difficulty combined with other instruments on the rare occasions such an attempt is made. We find the same defect on the side of differentiation of tone in the bell and a similar punctually repeated stroke as in the case of the kettle-drum.
The ring of a bell, however, is not so muffled as in the latter; it rings out clearly, although its persistent reverberation is more the mere echo of the single beat as struck at regular intervals.
_Thirdly_, the human voice may be regarded in respect to the tones emitted as the most complete instrument of all. It unites in itself the characteristics of both the wind instrument and the string. That is to say we have here in one aspect of it a column of air which vibrates, and, further, by virtue of the muscles, the principle of a string under tension. Just as we saw in the case of the colour inherent in the human skin, we had what was in its aspect of ideal unity, the most essentially perfect presentment of colour, so, too, we may affirm of the human voice that it contains the ideal compass of sound, all that in other instruments is differentiated in its several composite parts. We have here the perfect tone, which is capable of blending in the most facile and beautiful way with all other instruments. Add to this that the human voice is to be apprehended as the essential tone of the soul itself, as the concordant sound which by virtue of its nature expresses the ideal character of the inner life, and most immediately directs such expression. In the case of all other instruments on the contrary we find that a material thing is set in vibration, which, in the use that is made of it, is placed in a relation of indifference to and outside of the soul and its emotion.
In the human song, however, it is the human body itself from which the soul breaks into utterance. For this reason, too, the human voice is unfolded, in accord with the subjective temperament and emotion, in a vast manifold of particularity. And this variety, if we consider its distinguishing features sufficiently generalized, is based on national or other natural relations. Thus, for example, we find that the Italians are pre-eminently the people among whom we meet with the most beautiful voices. An important feature of this beauty is to start with the content of the sound simply as sound, its pure metallic quality, which neither fines away in mere keenness or vitreous attenuation, nor maintains a persistent muffled and hollow character, but, at the same time, though never carried to the point of tremolo in its tone, preserves in the compact body of its tone something of the vital vibration of the soul itself. Above all else the purity of voice-production is most essential, or in other words we must have no foreign element of sound asserted alongside of the freest expression of essential tone.
(_γγ_) Such a totality of instruments the art of music can employ, either in separation or complete combination. In the latter case of late years we may note an exceptional artistic development. The difficulty of such artistic collaboration is enormous. Every instrument possesses a character of its own, which is not directly congenial to the peculiarity of some other instrument. It follows from this that whether we are considering the harmonious co-operation of various instruments of different type, or the effective production of some particular quality of sound such as that of wind or strings, or the sudden blast of trombones, or the successive alternations of change that are inseparable from the music of a large choir, in all such cases knowledge, circumspection, experience, and imaginative endowment are indispensable, in order that, in every example of the kind, whether of tonal quality, transition, opposition, progression, or mediation, we do not lose sight of an ideal significance, the soul and emotional value of the music. For example, I find in the symphonies of Mozart, who was a great master of instrumentation and its sense-appealing, that is its vital no less than luminous variety, a sort of alternation between the different instruments which frequently resembles in its dramatic interplay a kind of dialogue. In one aspect of this the character of some particular type of instrument is carried to a point, which anticipates and prepares the way for that of another; looked at in another way, one kind of instrument replies to another; or asserts some typical mode of expression which is denied to the instrument it follows, so that in the most graceful fashion we thus get a kind of conversation of appeal and response, which has its beginning, advance and consummation.
(_β_) The _second_ material which enlists our attention is no longer the physical quality asserted in the sound, but the essential definition of the tone itself, and its relation to other tones. This objective relation, whereby musical tone in the first instance, not merely in its essential and emphatically defined singularity, but also in its fundamental relation to simultaneously persistent tones, expatiates, constitutes the actual _harmonious_ element of music, and is based, regarded under its own original physical conditions, upon _quantitative differences_ and numerical proportions. A closer examination of the contents of this system of harmony presents, as understood to-day, the following points of importance.
_First_, we have _separate_ tones in their definite metrical relation, and associated with other tones. This is the theory of particular _intervals._ _Secondly_, there is the connected series of tones or notes in their simplest form of succession, in which one tone immediately leads up to another; such are the _scales._ _Thirdly_, we have the distinctive characteristics of these scales, which, in so far as each starts from a different tone, as its fundamental tone, is thereby differentiated into the particular _keys_ distinct from each other, and into the system of keys which they constitute.
(_αα_) The particular notes do not only receive their tone, but also the more inclusively positive[445] determination of such sound by virtue of a corporeal substance in vibration. In order to get at this determinacy we have to define the type of vibration itself not in any chance or capricious manner, but once for all as it essentially is. The column of air, for example, or the string or surface under tension, which produces sound possesses invariably a certain length or extension. If we take a string, for instance, and fasten it between two points, and set the part of it thus stretched in vibration, the points of initial importance to discover are the thickness of the string, and the degree of tension. If we have these two aspects identical in the case of two strings then the all-important question follows, as was first noticed by Pythagoras, what is the string's length, the reason being that strings, in other respects identical, if of different lengths give a different number of vibrations in the same interval of time. The difference of one of these numbers from another and the relation of any one to another constitutes the fundamental ground for the distinction and relation between different tones in their degrees of pitch as high or low. Doubtless when we listen to notes thus related our perception carries little resemblance to one of numerical relations. It is not necessary for us to know anything of numbers and arithmetical proportions; and indeed when we do actually perceive a string vibrating, such vibration passes away without our being able to apprehend the numerical relation, while of course it is equally unnecessary for us to glance at the body in vibration at all, in order to receive the impression of its tone. An association, therefore, between the tone and its numerical relations may very possibly at first sight strike us, not merely as incredible, but we may receive the impression that its acceptance implies that our sense of hearing and ideal apprehension of harmonies suffer even depreciation when we look for their cause in that which is purely quantitative. However this may be, it is an undoubted fact that the numerical relation of vibrations in identical periods of time is the foundation of the specific definition of tones. The fact that our sense of hearing is essentially simple is no valid objection. The apparently simple impression, no less than the complex may, in respect to its essential character and existence, carry within its compass other aspects essentially multifold and related fundamentally to something different. When we perceive, for example, blue or yellow, green or red, in the specific purity of these colours, we receive in like manner the appearance of a perfectly simple determinacy, whereas violet readily is decomposed into its constituent colours of blue and red. Despite this fact the pure blue is not a simple fact, but a distinct correlation and fusion of light and shadow[446]. Religious emotions, a sense of right in any particular case, appear to us in the same way as simple; nevertheless all religious feeling, every impression that partakes of this sense of right, is related to ourselves in entirely different ways, though producing this simple feeling as its point of unity.
In just such a manner, then, tone is based upon a manifold, however much we hear and perceive it as something entirely ultimate; a varied nature, which, for the reason that musical tone comes into being by means of the vibration of a body, and thereby together with its vibrations is subject to temporal condition, is deducible from the numerical relation of this oscillation in _time_, in other words from the _determinate number_ of vibrations in a given period. I propose to draw attention merely to the following points in respect to this deduction.
_Tones that accord_ in the fullest sense, and on hearing which a distinction is not perceptible as opposition, are those in the case of which the numerical relation of their vibrations is of the _simplest_ character; those on the contrary which are not so out and out accordant possess proportionate numbers more _complex._ As an example of the first kind we have _octaves._ In other words, if we tune a string, where we shall have the keynote given us by a definite number of vibrations, and then halve the same; in that case this second half will give us in the same time precisely the same number of vibrations as the previous entire string[447]. Similarly in the case of _fifths_ we have _three_ vibrations to two of the keynote; in the case of _thirds_ we have _five_ to _four_ of the keynote. In the case of seconds and sevenths we have a different kind of proportion; here to _eight_ vibrations of the keynote we have in the former case _nine_ and in the latter _fifteen._ (_ββ_) Inasmuch then--we have already referred to this--as these relations cannot be posited as we like, but disclose an ideal necessity for their particular aspects[448], no less than the totality they together constitute, for the like reason the particular intervals, which are fixed by such numerical relations, do not persist in their relation of indifference to each other, but are inevitably comprised together in and as a whole. The first form of this totality of notes thus created is, however, as yet no _concrete_ concord of different notes, but an entirely abstract series of a system, a series of notes related under the most elementary mode to each other, and their position within the totality thus comprised. This is no other than the simple series of notes known as scales. The fundamental basis of this is the tonic, which repeats itself in its octave, and is extended through the remaining six notes placed between these limits, which by virtue of the fact that the keynote directly falls into unison with its octave makes a return upon itself. The remaining notes of the scale either harmonize completely[449] with the keynote, as is the case with the fifth and the third, or possess a more fundamental distinction of sound in conflict with it, as is the case with seconds and sevenths, and take their place consequently in a definite series, which, however, I do not now propose to discuss or explain further.
(_γγ_) _Thirdly_, in these scales we find the source of different _keys._ In other words, every note of the scale can, in its turn, be posited as the keynote of a fresh series of notes, which is co-ordinated precisely as the first is. With the development of the scale through an increase of notes the number of keys has correspondingly increased. Modern music avails itself of a larger variety of keys than that of the ancients. Further, inasmuch as generally the different notes of the scales, as already observed, are related to one another in unobstructed harmony, or a relation that deviates from such immediacy in a more fundamental way, it follows that the different series which arise from these notes, taken severally as keynotes, either display a closer relation of affinity, and consequently permit of a passage readily from one to another, or, on account of their alien character, do not so admit of this. Add to this that the keys are divided from each other by the distinction of hardness and softness, that is, as major or minor tonality; in conclusion they possess, in virtue of their key-note, from which they are generated, a definite character, which of itself responds to a particular kind of emotion, such as lamentation, joy, mourning, and so forth. In this particular even writers in ancient times have anticipated much on the subject of distinction between the keys, and applied their theory in many ways to actual composition.
(_γ_) The _third_ important matter, with the discussion of which we may conclude our brief remarks upon the theory of harmony, is concerned with the simultaneous concord of the notes themselves, in other words, the _system of chords._ (_αα_) We have no doubt already seen that the intervals constitute a whole; this totality, however, is in the first instance comprised in the scales and the keys merely in the form of an associated series, in the succession whereof each note is asserted separately in isolation.
In consequence the tonal sound remained abstract, because we find here that it is only one particular and determinate tone that is asserted.
In so far, however, as the notes in fact are what they are[450] merely in virtue of their relation to one another, it follows necessarily that their tonal modality should attain also an existence as this concrete body of tone itself, in other words different notes will have to coalesce in one and the same body of tone. In this conjoint fusion, in the composition of which, however, the mere number of notes capable of such coalescence is not the essential point, for we may have a unity of this kind with merely two[451], we possess our definition of _chords._ For inasmuch as the different notes are not definable for what they are as a result of caprice or chance, but are necessarily regulated by virtue of an ideal principle and co-ordinated in their actual succession, it follows that a regularity of similar character will have to declare itself in the chords, in order that we may determine what kind of associations will be adapted to musical composition, and what on the contrary must be excluded. It is these rules which first give us the theory of harmony in the full sense; and it is according to this we find again that the chords are embraced in an essentially regulated system.
(_ββ_) In this system chords are particularized and distinguished in their passage from one to another, inasmuch as it is clearly _defined_ notes which thus sound together. We have consequently to consider as an immediate fact a totality of separately distinguishable chords. In attempting the most general classification of these we shall find that the original distinctions we cursorily alluded to in our discussion of intervals, scales, and keys will once again serve us.
In other words the _first_ kind of chords are those in which notes come together, which are completely consonant. In the musical effect of these consequently there is no opposition, no contradiction perceptible; the consonance remains completely undisturbed. Such is the case in the so-called _consonant_ chords, the foundation of which is supplied by the _triad._ This confessedly is generated from the key-note, the third, the mediant[452] and the fifth or dominant. In these we find the notion of harmony expressed in its simplest form, or rather the intrinsic idea of harmony generally. For we have a totality of distinct notes under consideration, which assert this distinction while they also declare an undisturbed unity.
We have here an immediate identity, which moreover is not without the element of separation and mediation, albeit this mediation is not at the same time limited by the self-subsistency of different tones[453], satisfied with the mere transitional passage from one note to another in the relation of a series, but the unity is here an actual one and a return in immediacy upon itself.
But in the _second_ place we may observe as a further incident of distinct types of the triad, which I cannot now examine in more detail, the deliberate appearance of a deeper mode of opposition. We have, however, already at an earlier stage seen that the scales contain over and above those notes, which coalesce without opposition, others which annul such consonance. Examples of these are the diminished and augmented seventh. Inasmuch as these notes equally belong to the totality of tones, they too will necessarily find an entrance into the triad form. And when this happens it follows that the immediate unity and consonance above mentioned is disturbed, to the extent that we have added a tone essentially of another character, by means of which for the first time we meet with a _genuine difference_ which actually asserts itself as contradiction. In this way we have the true depth of musical tone really asserted. It proceeds to contradictions that are fundamental and does not flinch from the acerbity[454] or fracture they involve. And, in fact, the notion in its truth is no doubt essential unity; but it is not only immediate unity, but one which ideally is disrupt, which falls into contradictions. In this sense I have for example in my Logic developed the notion as subjectivity, but at the same time disclosed how this subjectivity, as ideal transparent unity, is resolved in that which confronts it in opposition, namely, objectivity. And further such subjectivity regarded as itself wholly ideal is nothing more than a one-sided and abstract presentment of it, which as such retains a something else, an opposed other over against it, namely, objectivity, and only becomes subjectivity in the profounder significance of its truth, in so far as it enters into this opposing other-than-itself, overcomes it and resolves it. And for this reason in the world of reality it is to the higher natures that power is given to endure the pain of that fundamental contradiction of conscious life and to overcome it. In order that music therefore may as an art express the ideal significance no less than purely subjective emotion of the profoundest content, that of religion for example, and above all that of the Christian religion, in which the profoundest depth of suffering is an essential constituent, it must possess the means within its empire of tone to depict such a conflict of opposing forces. And a means of this kind it does possess in the so-called dissonant chords of the seventh and ninth[455]. The function of these, however, I cannot venture further to discuss here.
Looking, however, from a general point of view at the nature of these chords I would draw attention to the _further_ important point, that they hold what is contradictory, under the mode of contradiction already explained, in one and the same unity. That, however, what is contradictory as such should remain in unity is a contradiction in