by Aristotle
11 · Why is the voice higher when it echoes back? Is it because it is smaller, [35] having become weaker?
12 · Why does the lower of two strings sounded together always give the tune? For if one omits paranete, when one should sound it with mese, the tune is given none the less; but if one omits mese, when one should sound both, the tune is lost.7 Is it because the low note is large and therefore strong, and the less is contained in the greater? So too if hypate is stopped down in the centre, two netes [918b1] are produced.
13 · Why is it that the low note in the octave gives the effect of unison with the high, but not vice versa? Is it because, if possible, the sound of both notes is in both notes, but, failing that, in the low note, since it is greater? [5]
14 · Why does the accord in the octave escape notice, and why does there appear to be a simple unison, as for example in the Phoenician lyre and in the human voice? For the upper and lower notes do not give the same sound but are analogous to one another at the octave. Is it because their sound appears to be [10] practically the same because analogy is equality in sounds, and equality is of the one? The same deception occurs also in the pipes.
15 · Why were ‘nomes’ not composed in antistrophes like all other songs, that is, choric songs? Is it because the ‘nomes’ were assigned to virtuosi, and as these were already able to imitate different characters and sustain their parts, the songs [15] composed for them became long and elaborate? Like the words, therefore, the music conformed to the imitation, becoming constantly different; for it was more essential for the music to be imitative than the words. (For this reason too dithyrambs, since they have become imitative, no longer have antistrophes, as they had formerly.) The reason is that in old days free citizens themselves formed the [20] choruses; it was difficult, therefore, for a large number to sing together like virtuosi, so they sang enharmonic songs. For it is easier for a single person to make many changes than for a large chorus, and for a professional than for those who are preserving the character of the music. And so they made the music more simple for [25] them. Now the antistrophic song is simple; for there is one rhythm8 and one unit of metre. For the same reason songs executed from the stage are not antistrophic, but those sung by the chorus are so; for the actor is a virtuoso and an imitator, but the chorus is less imitative.
[30] 16 · Why is antiphonal accompaniment more pleasing than symphonic accompaniment? Is it because in the former the consonance is more obvious than when the accompaniment of the singing is symphonic? For of the two notes played by the instrument one must be in unison with the note sung, and so two notes contending against one drown the other note.
17 · Why is it that singing in fifths does not give the effect of antiphony? Is [35] it because the symphonic notes are not the same as are the notes which are an octave apart? For in the octave the deep note in the lower part of the scale is analogous to the high note in the upper part; it is, therefore, as it were at once the same and different. But this does not occur in fifths and fourths so that the sound of the antiphonal note does not appear, for it is not identical.
18 · Why is it that the accord in the octave alone is used in singing? For in [919a1] ‘magadizing’, this and no other accord is used. Is it because it alone is made up of antiphonal notes, and with antiphonal notes, if but one be sung, the same effect is produced as if both were sung? For the one note in a way contains the sounds of both, so that, when one is sung, the concordant note at this interval is also sung; and [5] when they sing both, or when one note is sung and the other played on the flute, they both as it were sing one note. Therefore the accord in the octave alone is sung, because the antiphonal notes have the sound of one note.
19 · But why does the power of producing the effect of a single note belong [10] only to antiphonal notes? Is it because they alone are equidistant from mese? The presence then of this mean creates a certain similarity in their sounds, and the ear seems to tell us that it is the same note and that they are both extremes.
20 · Why is it that, if after tuning the other strings, one alters mese and uses the instrument, the ear is offended and an unmusical effect is produced not only [15] when mese is used, but in the rest of the piece as well, whereas, if lichanos or any other string is altered, it only seems to make a difference when that particular string is used? Surely this is only natural; for in all good music mese occurs frequently, and all good composers have frequent recourse to mese, and, if they leave it, they [20] soon return to it, as they do to no other note. Similarly in language, if certain connecting particles are removed, such as τε and καί, the language is no longer Greek; whereas the omission of some particles does not offend the ear, because certain particles must be frequently used, if there is to be language, but others not. [25] So mese is as it were a connective among sounds, and particularly in good music, because its sound occurs more often.
21 · Why is it that of singers those who are singing low notes are more conspicuous if they sing out of tune than those who are singing high? So too those [30] who make mistakes in time in the lower notes9 are more conspicuous. Is it because the period of time occupied by the low note is longer, and this longer period is more perceptible (for,10 lasting for a greater time, it creates a deeper sense-impression), whereas a quick,11 high note escapes notice owing to its swiftness? [35]
22 · Why does a large choir keep better time than a small one? Is it because they look more to one man, their leader, and begin more slowly and so more easily achieve unity? For mistakes occur more frequently in quick singing.
23 · Why is nete double hypate? Is it because in the first place, when half [919b1] the string is struck and when the whole string is struck an accord in the octave is produced? So too with wind instruments, the sound produced through the middle hole and that produced through the whole flute give an accord in the octave. Again, [5] in the flutes an accord in the octave is obtained by doubling the length, and this is how flute-makers produce it. Similarly they obtain a fifth by means of a length in the ratio of 3 to 2.12 Again, those who construct Pan-pipes stuff wax into the extreme end of the hypate-reed, but fill up the nete-reed to the middle. Similarly [10] they obtain a fifth by means of a length in the ratio of 3 to 2, and a fourth by means of a length in the ratio of 4 to 3. Further, hypate and nete on triangular stringed instruments, when they are equally stretched, give an accord in the octave when one is double the other in length.
24 · Why, if one strikes nete and then stops it down, does hypate alone seem [15] to resound? Is it because the vibration produced from hypate is very much of the same nature as the sound of nete, because it is in accord with it? When it is increased by the addition of its like, it alone is audible, the other sounds being imperceptible owing to their smallness.
25 · Why is mese so called in the scale, though there is no middle of eight [20] notes? Is it because in the old days scales had seven notes, and seven has a middle?
26 · Why do most men sing high when they sing out of tune? Is it because it is easier to sing high than low? Or is it because singing high is worse than singing [25] low, and a mistake is doing what is worse?
27 · Why is it that of all things which are perceived by the senses that which is heard alone possesses character? For music, even if it is unaccompanied by words, yet has character; whereas a colour and an odour and a savour have not. Is it because that which is heard alone has movement, not, however,13 the movement in us to which the sound gives rise (for such movement exists also in the other things [30] which affect our senses, for colour also moves our sight), but we perceive the movement which follows such and such a sound? This movement resembles character both in the rhythms and in the melodic disposition of the high and low notes, but not in their commingling; for symphony does possess character. This does [35] not occur in the other objects of sense-perception. Now these movements are connected with action, and actions are indicative of character.
28 · Why are the ‘nomes’ which are sung so called? Is it because before men knew
the art of writing they used to sing their laws in order not to forget them, as [920a1] they are still accustomed to do among the Agathyrsi? They, therefore, called the earliest of their subsequent songs by the name as their earliest songs.
29 · Why do rhythms and tunes, which after all are only voice, resemble characters, whereas savours do not, nor yet colours and odours? Is it because they [5] are movements, as actions also are? Now activity possesses and instils character, but savours and colours have no similar effect.
30 · Why is neither the Hypodorian nor the Hypophrygian mode suitable for use by the chorus in tragedy? Is it because they do not admit of antistrophic [10] melody? They are used, however, from the stage, because they are imitative.14
31 · Why were Phrynichus and his contemporaries primarily musicians? Is it because in those days the lyrical portions of tragedies were many times longer than the purely metrical?
32 · Why is the diapason so called and not named after the number of notes [15] an octave, like the fourth and the fifth? Is it because the notes were originally seven in number, and then Terpander took away trite and added nete, and in his time it was called diapason and not octave, since there were seven?
33 · Why is it more satisfactory to pass from a high to a low note than from a [20] low to a high note? Is it because the former amounts to beginning at the beginning, for the mese, or leader,15 is the highest note in the tetrachord? But in passing from a low to a high note one begins not at the beginning but at the end. Or is it because a low note is nobler and more euphonious after a high note?
34 · Why are a double fifth and a double fourth not concordant, whereas a double octave is? Is it because neither a double fifth nor a double fourth is . . .16 [25] though a fourth and a fifth are so?
35 · Why is the accord in the octave the most beautiful of all? Is it because its ratios are contained within integral terms, while those of the others are not so contained? For since nete is double hypate, as nete is two, so hypate is one; and as [30] hypate is two, nete is four; and so on. But nete is to mese in ratio of 3 to 2 (for a fifth is in this ratio), and that which is in the ratio of 3 to 217 is not contained within integral terms; for as the lesser number is one, so the greater number is one with the addition of a half, so that it is no longer a comparison of whole numbers, but parts are left over. The like happens also with the fourth; for the ratio of 4 to 3 gives the [35] lesser18 plus a third of it. Or is it because the accord which is made up of both the other two is the most perfect, and because it is the measure of the melody?
. . .19 in any body which is displaced the movement is most violent in the middle and gentler at the beginning and end, and when the movement is most violent the [920b1] sound of that which is displaced is shriller? For this reason also strings which are tightly stretched give a shriller note, for their movement is quicker. Now if a sound is the displacement of air or of something else, a sound which is in the middle of its [5] course must be shrillest. If this were not so, there would be no displacement of anything.
36 · Why is it that if mese is altered, the sound of the other strings also is spoilt,20 but if on the other hand mese is left alone and one of the other strings altered, the note which is altered alone is spoilt?21 Is it because for all strings being in tune means standing in a certain relation to mese,22 and the arrangement of each [10] is already determined by mese? If, therefore, that which is the cause of their being in tune and which holds them together is taken away, their proper relationship appears to be no longer maintained. But if one string is out of tune but mese is not altered, naturally the defect lies in that string only;23 for all the others are in tune. [15]
37 · Why is it that, though height in a voice is in accordance with smallness and lowness in accordance with largeness (for a low note is slow owing to its largeness, and a high note quick owing to its smallness), yet more effort is required to sing a high than a low note, and few can sing the top notes, and the ‘Orthian [20] songs’ and high music are hard to sing owing to the strain which they involve? Yet it requires less effort to set in motion that which is small than that which is large, and this ought to be true also of the air. Is it because the possession of a naturally high voice and the singing of high notes are not the same thing, but naturally high voices are always due to weakness because of the inability to set more than a little air in [25] motion, and the little air thus set in motion is carried quickly along? But height of note in singing is a sign of strength; for that which is carried violently along is carried swiftly—so that height of note in singing is a sign of strength. Hence persons in robust health24 can sing high. And it requires an effort to sing the high notes, but the low notes are easier.25
38 · Why do all men delight in rhythm and melody and concords in general? [30] Is it because we naturally rejoice in natural movements? This is shown by the fact that children rejoice in them as soon as they are born. Now we delight in the various types of melody because of habit; and we delight in rhythm because it contains a familiar and ordered number and moves us in a regular manner; for ordered [35] movement is naturally more akin to us than disordered, and is therefore more in accordance with nature. This is shown by the fact that by working and eating and drinking in an ordered manner we preserve and improve our nature and strength, whereas if we do these things irregularly we destroy and derange our nature; for [921a1] diseases are disturbances of the natural order26 of the body. And we delight in concord because it is the mingling of contraries which stand in proportion to one another. Proportion, then, is order, which, as we have said, is naturally pleasant. Now that which is mingled is always more pleasant than that which is unmingled, [5] especially if, being perceived by the senses, it contains equally the force of both extremes; and in a concord the proportion has this characteristic.27
39 · Why is ‘antiphony’28 more pleasant than ‘homophony’? Is it because ‘antiphony’ is concord in the octave? For ‘antiphony’ is produced by young boys and [10] men whose voices are separated in pitch as nete is from hypate. Now any concord is more pleasing than a simple note for the reasons already stated, and of concords that in the octave is the most pleasing; whereas ‘homophony’ produces only a simple sound. ‘Magadizing’ is in the concord of the octave, because, just as in verses the [15] feet stand to one another in the proportion of equal to equal, or two to one, or some other proportion, so too the sounds in a concord stand in a proportion of movement to one another. In the other concords the termination of one of the two notes is incomplete since it coincides with the end of only a half of the other; and so they are not equal in force, and being unequal they make a different impression on the sense-perception, as happens in a chorus when at the conclusion they are singing [20] louder than others. Furthermore, hypate happens to have the same conclusions to the periods in its sounds; for the second stroke which nete makes upon the air is hypate. As, then, these notes, though they do not do the same thing, terminate together, the result is that they carry out one common task, like those who are playing a stringed accompaniment to a song; for these, though they do not play the [25] same other notes as the singer, yet, if they finish on the same note, give more pleasure by their conclusion than they give pain by the differences which occur earlier in the piece, because after diversity the unity due to the accord in the octave is very pleasing.29 Now ‘magadizing’ is made up of contrary notes, and for this [30] reason it is carried out in the octave.
40 · Why do men take greater pleasure in listening to those who are singing tunes which they already know than if they do not know them? Is it because it is more obvious that the singer is as it were achieving his aim when they recognize what is being sung, and when they recognize it the contemplation of it is pleasant? [35] Or is it because the listener is in sympathy with one who sings what he himself knows? For he sings with him; and every one enjoys singing when he is under no compulsion to sing.
41 · Why are a double fifth and a double fourth not concordant, whereas a [921b1] double octave is? Is it because a fi
fth is in the ratio of 3 to 2, and a fourth in that of 4 to 3? Now in a series of three numbers30 in a ratio of 3 to 2 or 4 to 3, the two extreme numbers will have no ratio to one another; for neither will they be in a superparticular ratio nor will one be a multiple of the other. But, since the octave is in a ratio of 2 [5] to 1, if it be doubled the extreme numbers would be in a fourfold ratio. So, since a concord is a compound of sounds which are in a ratio31 to one another, and sounds which are at an interval of two octaves from one another are in a ratio to one another [10] (while double fourths and double fifths are not), the sounds constituting the double octave would give a concord (while the others would not) for the reasons given above.
42 · Why is it that, if one strikes nete and then stops it down, hypate seems to respond? Is it because nete, as it ceases and dies down, becomes hypate? (This is [15] indicated by the fact that it is possible to sing nete from hypate; for the similarity can be taken from hypate as being a response to nete?32) And since an echo is a response to a note,33 and when nete ceases a sound is set in motion34 which is the same as the note of hypate, it is only natural owing to the similarity that nete should [20] seem to set hypate in motion. For we know that nete is not35 in motion, because it is stopped down, and seeing that hypate itself is not stopped down and hearing its note we think that it is hypate which is giving forth a sound. (This kind of thing is quite [25] common, where we cannot grasp the exact truth either by reasoning or by the senses.) Again, it would be nothing extraordinary if, after nete is struck when it is very tightly stretched, the bridge were set in motion; and it would not be strange if, when the bridge moved, all the strings were set in motion with it and made a sound. [30] Now the sound of nete is alien to the other notes both in its end and in its beginning, but is the same as hypate in its end. This having been added to the movement of hypate itself, it would not be strange that the sound should seem to be entirely that of hypate; and it will be louder than the combined sound of the other notes, because the latter, being as it were impelled by nete, give only a soft sound, whereas nete, [35] being the most violent of notes, sounds with its full force; and so naturally its second sound would be louder than that of the others, especially if only a slight movement has taken place in them.36