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- Herausgeber: Strelbytskyy Multimedia Publishing
- Kategorie: Poesie und Drama
- Sprache: Englisch
Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle. He was the most famous music theorist in antiquity and came to be referred to simply as "the musician." Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony survives incomplete, as well as some fragments concerning rhythm and meter. The Elements is the chief source of our knowledge of ancient Greek music. Contents: The Translation The Elements of Harmony The Greek Texts
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The Complete Works of Aristoxenus
Illustrated
The Elements of Harmony
Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle.
He was the most famous music theorist in antiquity and came to be referred to simply as "the musician."
Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony survives incomplete, as well as some fragments concerning rhythm and meter. The Elements is the chief source of our knowledge of ancient Greek music.
The Translation
The Elements of Harmony
Translated by Henry Stewart Macran, 1902
BOOK I
[The references throughout the translation are to Meibom’s edition.]
[1] THE branch of study which bears the name of Harmonic is to be regarded as one of the several divisions or special sciences embraced by the general science that concerns itself with Melody. Among these special sciences Harmonic occupies a primary and fundamental position; its subject matter consists of the fundamental principles — all that relates to the theory of scales and keys; and this once mastered, our knowledge of the science fulfils every just requirement, because it is in such a mastery that its aim consists. In advancing to the profounder speculations [2] which confront us when scales and keys are enlisted in the service of poetry, we pass from the study under consideration to the all-embracing science of music, of which Harmonic is but one part among many. The possession of this greater science constitutes the musician.
The early students of Harmonic contented themselves, as a matter of fact, with being students of Harmonic in the literal sense of the term; for they investigated the enharmonic scale alone, without devoting any consideration to the other genera. This may be inferred from the fact that the tables of scales presented by them are always of enharmonic scales, never in one solitary instance of diatonic or chromatic; and that too, although these very tables in which they confined themselves to the enumeration of enharmonic octave scales nevertheless exhibited the complete system of musical intervals. Nor is this the sole mark of their imperfect treatment. In addition to ignoring diatonic and chromatic scales they did not even attempt to observe the various magnitudes and figures in the enharmonic as well as in the other genera. Confining themselves to what is but the third part of that complete system, they selected for exclusive treatment a single magnitude in that third part, namely, the Octave. Again, their mode of treating even branches of the study to which they did apply themselves was imperfect. This has been clearly illustrated in a former work in which we examined the views put forward by the students of Harmonic; but it will be brought into a still clearer light by an enumeration of the various subdivisions of this science, and a description of the sphere of each. [3] We shall find that they have been in part ignored, in part inadequately treated; and while substantiating our accusations we shall at the same time acquire a general conception of the nature of our subject.
The preliminary step towards a scientific investigation of music is to adjust our different notions of change of voice, meaning thereby change in the position of the voice. Of this change there are more forms than one, as it is found both in speaking and in singing; for in each of these there is a high and low, and a change that results in the contrast of high and low is a change of position. Yet although this movement between high and low of the voice in speaking differs specifically from the same movement in singing, no authority has hitherto supplied a careful determination of the difference, and that despite the fact that without such a determination the definition of a note becomes a task very difficult of accomplishment. Yet we are bound to accomplish it with some degree of accuracy, if we wish to avoid the blunder of Lasus and some of the school of Epigonus, who attribute breadth to notes. A careful definition will ensure us increased correctness in discussing many of the problems which will afterwards encounter us. Furthermore, it is essential to a clear comprehension of these points that we differentiate distinctly between tension and relaxation, height and depth, and pitch — conceptions not as yet adequately discussed, but either ignored or confused. This done, we shall then be confronted by the question whether distance on [4] the line of pitch can be indefinitely extended or diminished, and if so, from what point of view. Our next task will be a discussion of intervals in general, followed by a classification of them according to every principle of division of which they admit; after which our attention will be engaged by a consideration of the scale in general, and a presentation of the various natural classes of scales. We must then indicate in outline the nature of musical melody — musical because of melody there are several kinds, and tuneful melody — that which is employed in musical expression — is only one class among many. And as the method by which one is led to a true conception of this latter involves the differentiation of it from the other kinds of melody, it will scarcely be possible to avoid touching on these other kinds, to some extent at least. When we have thus defined musical melody as far as it can be done by a general outline before the consideration of details, we must divide the general class, breaking it up into as many species as it may appear to contain. After this division we must consider the nature and origin of continuity or consecution in scales. Our next point will be to set forth the differences of the musical genera which manifest themselves in the variable notes, as well as to give an account of the loci of variation of these variable notes. Hitherto these questions have been absolutely ignored, and in dealing with them we shall be compelled to break new ground, as there is in existence no previous treatment of them worth mentioning.
[5] Intervals, first simple and then compound, will next occupy our attention. In dealing with compound intervals, which as a matter of fact are in a sense scales as well, we shall find it necessary to make some remarks on the synthesis of simple intervals. Most students of Harmonic, as we perceived in a previous work, have failed even to notice that a treatment of this subject was required. Eratocles and his school have contented themselves with remarking that there are two possible melodic progressions starting from the interval of the Fourth, both upwards and downwards. They do not definitely state whether the law holds good from whatever interval of the Fourth the melody starts; they assign no reason for their law; they do not inquire how other intervals are synthesized — whether there is a fixed principle that determines the synthesis of any given interval with any other, and under what circumstances scales do and do not arise from the syntheses, or whether this matter is incapable of determination. On these points we find no statements made by any writer, with or without demonstration; the result being that although as a matter of fact there is a marvellous orderliness in the constitution of melody, music has yet been condemned, through the fault of those who have meddled with the subject, as falling into the opposite defect. The truth is that of all the objects to which the five senses apply not one other is characterized by an orderliness so extensive and so perfect. Abundant evidence for this statement will be forthcoming throughout our investigation of our subject, to the enumeration of the parts of which we must now return.
[6] Our presentation of the various methods in which simple intervals may be collocated will be followed by a discussion of the resulting scales (including the Perfect Scale) in which we will deduce the number and character of the scales from the intervals, and will exhibit the several magnitudes of scales as well as the different figures, collocations, and positions possible in each magnitude; our aim being that no principle of concrete melody, whether magnitude, or figure, or collocation, or position shall lack demonstration. This part of our study has been left untouched by all our predecessors with the exception of Eratocles, who attempted a partial enumeration without demonstration. How worthless his statements are, and how completely he failed even in perception of the facts, we have already dwelt upon, when this very subject was the matter of our inquiry. As we then observed all the scales with the exception of one have been completely passed over; and of that one scale Eratocles merely endeavoured to enumerate the figures of one magnitude, namely the octave, empirically determining their number, without any attempt at demonstration, by the recurrence of the intervals. He failed to observe that unless there be previous demonstration of the figures of the Fifth and Fourth, as well as of the laws of their melodious collocation, such an empirical process will give us not seven figures, but many multiples of seven. Further discussion here is rendered unnecessary by our previous demonstration of these facts; and we may now resume our sketch of the divisions of our subject. [7]
When the scales in each genus have been enumerated in accordance with the several variations just mentioned, we must blend the scales and repeat the process of enumeration. The necessity for this investigation has escaped most students; nay, they have not so much as mastered the true conception of ‘blending.’.
Notes form the next subject for inquiry, inasmuch as intervals do not suffice for their determination.
Again, every scale when sung or played is located in a certain region of the voice; and although this location induces no difference in the scale regarded in itself, it imparts to the melody employing that scale no common — nay rather perhaps its most striking characteristic. Hence he who would deal with the science before us must treat of the ‘region of the voice’ in general and in detail so far as is reasonable; in other words so far as the nature of the scales themselves prescribes. And in dealing with the affinity between scales and regions of the voice, and with keys, we must not follow the Harmonists in their endeavour at compression, but aim rather at the intermodulation of scales, by considering in what keys the various scales must be set so as to admit of intermodulation. We have shown in a previous work that, though as a matter of fact some of the Harmonists have touched on this branch of our subject in a purely accidental way, in connexion with their endeavour to exhibit a close-packed scheme of scales, yet there has been no general treatment of it by a single writer belonging to this [8] school. This position of our subject may broadly be described as the part of the science of modulation concerned with melody.
We have now set forth the nature and number of the parts of Harmonic. Any investigations that would carry us further must, as we remarked at the outset, be regarded as belonging to a more advanced science. Postponing accordingly to the proper occasion the consideration of these, their number, and their several natures, it now devolves upon us to give an account of the primary science itself.
Our first problem consists in ascertaining the various species of motion. Every voice is capable of change of position, and this change may be either continuous or by intervals. In continuous change of position the voice seems to the senses to traverse a certain space in such a manner that it does not become stationary at any point, not even at the extremities of its progress — such at least is the evidence of our sense-perception — but passes on into silence with unbroken continuity. In the other species which we designate motion by intervals, the process seems to be of exactly the opposite nature: the voice in its progress stations itself at a certain pitch, and then again at another, pursuing this process continuously — continuously, that is, in time. As it leaps the distances contained between the successive points of pitch, while it is stationary at, and produces sounds upon, the points themselves, it is said to sing only the latter, and to move by intervals. Both these descriptions must of course be regarded in the [9] light of sensuous cognition. Whether voice can really move or not, and whether it can become stationary at a given point of pitch, are questions beyond the scope of the present inquiry, which does not demand the raising of this problem. For whatever the answer may be, it does not affect the distinction between the melodious motion of the voice and its other motions. Disregarding all such difficulties, we describe the motion of the voice as continuous when it moves in such a way as to seem to the ear not to become stationary at any point of pitch; but when the reverse is the case — when the voice seems to the ear first to come to a standstill on a point of pitch, then to leap over a certain space, and, having done so, to come to a standstill on a second point, and to repeat this alternating process continuously — the motion of the voice under these circumstances we describe as motion by intervals. Continuous motion we call the motion of speech, as in speaking the voice moves without ever seeming to come to a standstill. The reverse is the case with the other motion, which we designate motion by intervals: in that the voice does seem to become stationary, and when employing this motion one is always said not to speak but to sing. Hence in ordinary conversation we avoid bringing the voice to a standstill, unless occasionally forced by strong feeling to resort to such a motion; whereas in singing we act in [10] precisely the opposite way, avoiding continuous motion and making the voice become, as far as possible, absolutely stationary. The more we succeed in rendering each of our voice-utterances one, stationary, and identical, the more correct does the singing appear to the ear. To conclude, enough has been said to show that there are two species of the voice’s motion, and that one is continuous and employed in speaking, while one proceeds by intervals and is employed in singing.
It is evident that the voice must in singing produce the tensions and relaxations inaudibly, and that the points of pitch alone must be audibly enunciated. This is clear from the fact that the voice must pass imperceptibly through the compass of the interval which it traverses in ascending or descending, while the notes that bound the intervals must be audible and stationary. Hence it is needful to discuss tension and relaxation, and in addition height and depth of pitch, and finally pitch in general.
Tension is the continuous transition of the voice from a lower position to a higher, relaxation that from a higher to a lower. Height of pitch is the result of tension, depth the result of relaxation. On a superficial consideration of these questions it might appear surprising that we distinguish four phenomena here instead of two, and in fact it is usual to identify height of pitch with tension, and depth of pitch [11] with relaxation. Hence we may perhaps with advantage observe that the usual view implies a confusion of thought. In doing so we must endeavour to understand, by observing the phenomenon itself, what precisely takes place when in tuning we tighten a string or relax it. All who possess even a slight acquaintance with instruments are aware that in producing tension we raise the string to a higher pitch, and that in relaxing it we lower its pitch. Now, while we are thus raising the pitch of the string, it is obvious that the height of pitch which is to result from the process cannot yet be in existence. Height of pitch will only result when the string becomes stationary and ceases to change, after having been brought by the process of tension to the point of pitch required; in other words, when the tension has ceased and no longer exists. For it is impossible that a string should be at the same moment in motion and at rest; and as we have seen, tension takes place when the string is in motion, height of pitch when it is quiescent and stationary. The same remarks will apply to relaxation and depth of pitch, except that these are concerned with change in the opposite direction and its result. It is evident, then, that relaxation and depth of pitch, tension and height of pitch, must not be identified, but stand to one another in the relation of cause and effect. It remains to show that the term pitch also connotes a quite distinct conception.
[12] By the term pitch we mean to indicate a certain persistence, as it were, or stationary position of the voice. And let us not be alarmed by the theory which reduces notes to motions and asserts sound in general to be a motion, as though our definition involved the proposition ‘that under certain circumstances motion will, instead of moving, be stationary and at rest. The definition of pitch as a certain condition of motion — call it ‘equability’ or ‘identity,’ or by any more enlightening term you can find — will not affect our position. We shall none the less describe the voice as stationary when our senses assure us that it is neither ascending nor descending, simply fixing on this term as descriptive of such a state of the voice without any further implications. To proceed, then, the voice appears to act thus in singing; it moves in making an interval, it is stationary on the note. Now if we use the term ‘motion’ and say ‘the voice moves’ in cases where, according to the physical theory, it undergoes a change in the rate of motion; and if, again, we use the term ‘rest’ and say ‘the voice rests’ in cases where this change in the rate of motion has ceased, and the motion has become uniform, our musical theory is not thereby affected. For it is plain enough that the term ‘motion’ in the physical sense covers both ‘motion’ and ‘rest’ in the sense in which we employ them. Sufficient has been said on this point here; elsewhere it has been treated more fully and clearly.
[13] To resume; it now being clear that pitch is distinct from tension or relaxation, the former being, as we say, a rest of the voice, the latter, as we have seen, motions, our next task is to understand that it is distinct from the remaining phenomena of height and depth of pitch. Now, our previous observations have shown that the voice is, as a matter of fact, in a state of rest after a transition to height or depth; yet the’ following considerations will make it clear that pitch, though a rest of the voice, is a phenomenon distinct from both. We must understand that for the voice to be stationary means its remaining at one pitch; and this will happen equally whether it becomes stationary at a high pitch or a low. If pitch, then, be met in high notes as well as low notes — and the voice, as we have shown, must of necessity be capable of becoming stationary on both alike — it follows that, inasmuch as height and depth are absolutely incompatible, pitch, which is a phenomenon common to both, must be distinct from one and the other alike. Enough has now been said to show that pitch, height and depth of pitch, and tension and relaxation of pitch are five conceptions which do not admit of any identification inter se.
The next point for our consideration is whether distance on the line of pitch admits of infinite extension or diminution. There is no difficulty in seeing that if we refer solely [14] to musical sounds, such infinite extension and diminution are impossible. For every musical instrument and for every human voice there is a maximum compass which they cannot exceed, and a minimum interval, less than which they cannot produce. No organ of sound can indefinitely enlarge its range or indefinitely reduce its intervals: in both cases it reaches a limit. Each of these limits must be determined by a reference to that which produces the sound and to that which discriminates it — the voice, namely, and the ear. What the voice cannot produce and the ear cannot discriminate must be excluded from the available and practically possible range of musical sound. In the progress in parvitatem the voice and the ear seem to fail at the same point. The voice cannot differentiate, nor can the ear discriminate, any interval smaller than the smallest diesis, so as to determine what fraction it is of a diesis or of any other of the known intervals. In the progress in magnitudinem the power of the ear may perhaps be considered to stretch beyond that of the voice, though to no very great distance. In any case, whether we are to assume the same limit for voice and ear in both directions, or whether we are to suppose it to be the same in the progress in parvitatem but different in the progress in the fact remains that there is a maximum and minimum limit of distance on the line of pitch, either common to [15] voice and ear, or peculiar to each. It is clear, then, that distance of high and low on the line of pitch, regarded in relation to voice and ear, is incapable of infinite extension or infinitesimal diminution. Whether, regarding the constitution of melody in the abstract, we are bound to admit such an infinite progress, is a question demanding a different method of reasoning not required for our present purpose, and we shall accordingly reserve its discussion for a later occasion.
The question of distance on the line of pitch being disposed of, we shall proceed to define a note. Briefly, it is the incidence of the voice upon one point of pitch. Whenever the voice is heard to remain stationary on one pitch, we have a note qualified to take a place in a melody.
An interval, on the other hand, is the distance bounded by two notes which have not the same pitch. For, roughly speaking, an interval is a difference between points of pitch, a space potentially admitting notes higher than the lower of the two points of pitch which bound the interval, and lower than the higher of them. A difference between points of pitch depends on degrees of tension.
[16] A scale, again, is to be regarded as the compound of two or more intervals. Here we would ask our hearers to receive these definitions in the right spirit, not with jealous scrutiny of the degree of their exactness. We would ask him to aid us with his intelligent sympathy, and to consider our definition sufficiently instructive when it puts him in the way of understanding the thing defined. To supply a definition which affords an unexceptionable and exhaustive analysis is a difficult task in the case of all fundamental motions, and by no means least difficult in the case of the note, the interval, and the scale.
We must now endeavour to classify first intervals and then scales according to all those principles of division that are of practical use. The first classification of intervals distinguishes them by their compass, the second regards them as concordant or discordant, the third as simple or compound, the fourth divides them according to the musical genus, the fifth as rational or irrational. As all other classifications are of no practical use, let us disregard them for the present.
[17] In scales will be found, with one exception, all the distinctions which we have met in intervals. It is obvious that scales may differ both in compass and owing to the fact that the notes bounding that compass may be either concordant or discordant. The third, however, of the distinctions mentioned in the case of intervals cannot exist in the case of scales. Evidently we cannot have simple and compound scales, at least not in the same way as we had simple and compound intervals. The fourth distinction — that according to genera — must also exist in the case of scales, some of them being diatonic, some chromatic, and some enharmonic. It is obvious that they also admit the fifth principle of division: some are bounded by a rational, and some by an irrational, interval. To these four there must be added three other classifications. First, there is that into the conjunct scales, the disjunct scales, and the scales that are a combination of both; every scale, provided it is of a certain compass, becomes either conjunct or disjunct, or else combines both these qualities — for cases are to be seen where the latter process takes place. There is, secondly, the division into transilient and continuous, every scale belonging to one category or the other; and finally, that into single, double, and multiple, as all without [18] exception admit of classification under these heads. An explanation of each of these terms will be given in the sequel.
Starting from these definitions and classifications we must seek to indicate in outline the nature of melody. We have already observed that here the motion of the voice must be by intervals; herein, then, lies the distinction between the melody of music and of speech — for there is also a kind of melody in speech which depends upon the accents of words, as the voice in speaking rises and sinks by a natural law. Again, melody which accords with the laws of harmony is not constituted by intervals and notes alone. Collocation upon a definite principle is also indispensable, it being obvious that intervals and notes are equally constituents of melody which violates the laws of harmony. It follows that the most important and significant factor in the right constitution of melody is the principle of collocation in general as well as its special laws. We see, then, that musical melody differs from the melody of speech, on the one hand, in employing motion by intervals, and from faulty melody, on the other hand, melody which violates the laws of harmony, by the different [19] manner in which it collocates the simple intervals. What this manner is will be shown in the sequel; for the present it will suffice to insist on the fact that, though melody which accords with the laws of harmony admits of many variations in collocating the intervals, there is yet one invariable attribute that can be predicated of every such melody, of so great importance that with its removal the harmony disappears. A full explanation will be given in the course of the treatise. For the present we content ourselves with this definition of musical melody in contradistinction to the other species, but it must be understood that we have supplied a mere outline without as yet reviewing the details.
