The Complete Works of Aristoxenus. Illustrated (eBook)

[30] IT will be well perhaps to review in anticipation the course of our study; thus a foreknowledge of the road that we must travel will enable us to recognize each stage as we reach it, and so lighten the toil of the journey; nor shall we be harbouring unknown to ourselves a false conception of our subject. Such was the condition, as Aristotle used often to relate, of most of the audience that attended Plato’s lectures on the Good. They came, he used to say, every one of them, in the conviction that they would get from the lectures some one or other of the things that the world calls good; riches or health, or strength, in fine, some extraordinary gift of fortune. But when they found that Plato’s reasonings were of sciences and numbers, and geometry, and astronomy, and of good and unity as predicates of the finite, methinks their disenchantment was complete. [31] The result was that some of them sneered at the thing, while others vilified it. Now to what was all this trouble due?

To the fact that they had not waited to inform themselves of the nature of the subject, but after the manner of the sect of word-catchers had flocked round open-mouthed, attracted by the mere title ‘good’ in itself.

But if a general exposition of the subject had been given in advance, the intending pupil would either have abandoned his intention or if he was pleased with the exposition, would have remained in the said conviction to the end. It was for these very reasons, as he told us, that Aristotle himself used to give his intending pupils a preparatory statement of the subject and method of his course of study. And we agree with him in thinking, as we said at the beginning, that such prior information is desirable. For mistakes are often made in both directions. Some consider Harmonic a sublime science, and expect a course of it to make them musicians; nay some even conceive it will exalt their moral nature. This mistake is due to their having run away with such phrases in our preamble as ‘we aim at the construction of every style of melody,’ and with our general statement ‘one class of musical art is hurtful to the moral character, another improves it’; while they missed completely our qualification of this statement, ‘in so far as musical art can improve the moral character.’ Then on the other hand there are persons who regard Harmonic as quite a thing of no importance, and actually prefer to remain totally unacquainted even with its nature and aim. Neither of these views is correct. On the one hand the science is no proper object of contempt to the man of intelligence — this we shall [32] see as the discussion progresses; nor on the other hand has it the quality of all-sufficiency, as some imagine. To be a musician, as we are always insisting, implies much more than a knowledge of Harmonic, which is only one part of the musician’s equipment, on the same level as the sciences of Rhythm, of Metre, of Instruments.

We shall now proceed to the consideration of Harmonic and its parts. It is to be observed that in general the subject of our study is the question, In melody of every kind what are the natural laws according to which the voice in ascending or descending places the intervals? For we hold that the voice follows a natural law in its motion, and does not place the intervals at random. And of our answers we endeavour to supply proofs that will be in agreement with the phenomena — in this unlike our predecessors. For some of these introduced extraneous reasoning, and rejecting the senses as inaccurate fabricated rational principles, asserting that height and depth of pitch consist in certain numerical ratios and relative rates of vibration — a theory utterly extraneous to the subject and quite at variance with the phenomena; while others, dispensing with reason and demonstration, confined themselves to isolated dogmatic statements, not being successful either in their enumeration of the mere phenomena. It is our endeavour that the principles which we assume shall without exception be evident to those who understand music, and that we [33] shall advance to our conclusions by strict demonstration.

Our subject-matter then being all melody, whether vocal or instrumental, our method rests in the last resort on an appeal to the two faculties of hearing and intellect. By the former we judge the magnitudes of the intervals, by the latter we contemplate the functions of the notes. We must therefore accustom ourselves to an accurate discrimination of particulars. It is usual in geometrical constructions to use such a phrase as ‘Let this be a straight line’; but one must not be content with such language of assumption in the case of intervals. The geometrician makes no use of his faculty of sense-perception. He does not in any degree train his sight to discriminate the straight line, the circle, or any other figure, such training belonging rather to the practice of the carpenter, the turner, or some other such handicraftsman. But for the student of musical science accuracy of sense-perception is a fundamental requirement. For if his sense-perception is deficient, it is impossible for him to deal successfully with those questions that lie outside the sphere of sense-perception altogether. This will become clear in the course of our investigation. And we must bear in mind that musical cognition implies the simultaneous cognition of a permanent and of a changeable element, and that this applies without limitation or qualification to every branch of music. To begin with, our perception of the differences of the genera is dependent on the permanence of the containing, and the variation of the intermediate, [34] notes. Again, while the magnitude remains constant, we distinguish the interval between Hypate and Mese from that between Paramese and Nete; here, then, the magnitude is permanent, while the functions of the notes change; similarly, when there are several figures of the same magnitude, as of the Fourth, or Fifth, or any other; similarly, when the same interval leads or does not lead to modulation, according to its position. Again, in matters of rhythm we find many similar examples. Without any change in the characteristic proportion constituting any one genus of rhythm, the lengths of the feet vary in obedience to the general rate of movement; and while the magnitudes are constant, the quality of the feet undergoes a change; and the same magnitude serves as a foot, and as a combination of feet. Plainly, too, unless there was a permanent quantum to deal with there could be no distinctions as to the methods of dividing it and arranging its parts. And in general, while rhythmical composition employs a rich variety of movements, the movements of the feet by which we note the rhythms are always simple and the same. Such, then, being the nature of music, we must in matters of harmony also accustom both ear and intellect to a correct judgement of the permanent and changeable element alike.

These remarks have exhibited the general character of the science called Harmonic; and of this science there are, [35] as a fact, seven parts. Of these one and the first is to define the genera, and to show what are the permanent and what are the changeable elements presupposed by this distinction. None of our predecessors have drawn this distinction at all; nor is this to be wondered at. For they confined their attention to the Enharmonic genus, to the neglect of the other two. Students of instruments, it is true, could not fail to distinguish each genus by ear, but none of them reflected even on the question, At what point does the Enharmonic begin to pass into the Chromatic? For their ability to discriminate each genus extended not to all the shades, inasmuch as they were not acquainted with all styles of musical composition or trained to exercise a nice discrimination in such distinctions; nor did they even observe that there were certain loci of the notes that alter their position with the change of genus. These reasons sufficiently explain why the genera have not as yet been definitely distinguished; but it is evident that we must supply this deficiency if we are to follow the differences that present themselves in works of musical composition.

Such is the first branch of Harmonic. In the second we shall deal with intervals, omitting, to the best of our ability, none of the distinctions to be found in them. The majority of these, one might say, have as yet escaped observation. But we must bear in mind that wherever we come upon a distinction which has been overlooked, and not scientifically considered, we shall there fail to recognize the distinctions [36] in works of melodic composition.

Again, since intervals are not in themselves sufficient to distinguish notes — for every magnitude, without qualification, that an interval can possess is common to several musical functions — the third part of our science will deal with notes, their number, and the means of recognizing them; and will consider the question whether they are certain points of pitch, as is vulgarly supposed, or whether they are musical functions, and also what is the meaning of a musical ‘function.’ Not one of these questions is clearly conceived by students of the subject.

The fourth part will consider scales, firstly as to their number and nature, secondly as to the manner of their construction from intervals and notes. Our predecessors have not regarded this part of the subject in either of these respects. On the one hand, no attention has been devoted to the questions whether intervals are collocated in any order to produce scales, or whether some collocations may not transgress a...