Aristotle · a new plain-English translation from the original language
1| Book 19: Problems Concerning Musical Harmony Why do both those who are toiling and those who are enjoying themselves play the pipe? Is it so that the former may be less pained, and the latter more pleased? Why does the same person, with the same voice, carry farther when singing and shouting with others than alone? Is it because doing something, or pressing, or pushing all together does not amount to merely as many times as the number of people, but just as a line two feet long does not mark out double but something like four times as much, so things combined are more powerful in proportion than when they are divided. So when people are all together, the strength of the voice becomes one and pushes the air all at once, so that it travels many times as far; for the voice from all of them together is many times that of each single one.
2| Why is it that singers most often break their voice when singing the parhypate, no less than when singing the nete and the notes above it, and with a bigger leap? Is it because this note is the hardest of all to sing, and it is a starting-point? The difficulty is due to the tension and pressure put on the voice; and in these notes there is exertion; and what is exerting itself is more easily damaged. But why is this note difficult, while the hypate is easy, even though each involves a quarter-tone? Is it because the hypate comes with relaxation, and at the same time, after the strain of tension, it is easy to throw the voice upward again? For the same reason, it seems, the phrases said 'in relation to one note' apply to this note or to the paranete. For they require concentration and a disposition most proper to the character, directed toward the intention. But then what is the cause of doing this together with a concord? Why do people take more pleasure in hearing songs whose melodies they happen to know beforehand, than ones they do not know? Is it because the one who hits the mark is more evident, as if at a target, when they recognize what is being sung? And this is pleasant to observe. Or is it because learning is pleasant? The reason for this is that the one activity is acquiring knowledge, while the other is using it and recognizing it again. Further, the familiar is more pleasant than the unfamiliar.
3| Why is the parakataloge in songs tragic? Is it because of its unevenness? For the uneven is emotional, both in greatness of fortune and of grief. The even is less mournful. Why did the ancients, in making seven-stringed scales, retain the hypate but not the nete? Is this false (for they retained both, and removed the third string instead) or not? But rather it is because the lower string holds the force of the higher note's sound, so that the hypate rendered the answering note more than the nete would, since the high pitch is more a sign of power, while the low is easier to sound. Why does the low note hold the force of the high note's sound? Is it because the low is greater? For it resembles an obtuse angle, while the high resembles an acute angle. Why do we hear a solo song more pleasantly, if someone sings it to the accompaniment of a pipe or a lyre? And yet, sung to strings, it is the same melody in both cases. For if sameness were the reason, it ought to be even more pleasant with many pipers, being still more of the same thing. Or is it because the one hitting the mark is more evident, when singing to a pipe or a lyre? But singing to many pipers or many lyres is not more pleasant, because it obscures the song.
4| Why, if the human voice singing without words is more pleasant, is it not more pleasant when, say, humming wordlessly, but rather the pipe or the lyre is more pleasant? Or is it that even there, unless it imitates something, it is not equally pleasant? Yet nonetheless it is also on account of the function itself. For the human voice is more pleasant, but instruments are more incisive in striking a note than the mouth is. That is why it is more pleasant to listen to them than to hum. Why is an echo higher in pitch? Is it because it is diminished, becoming weaker? Why does the lower-pitched of the strings always take the melody? For if it is necessary to sing the paramese together with the mese alone, the mese still results none the less; but if one sings the mese, when both notes are needed, they do not come out bare and distinct. Is it because the low is large, and so is dominant? And the small is contained within the large; and by division, two netai arise within the hypate. Why, in the octave, does the low note become the answering note of the high, but not the high of the low? Is it because the melody belonging to both is present chiefly when it is in both, but failing that, it is in the low note, since that is the greater?
5| Why does the octave pass unnoticed, and seem to be a unison, as for instance in the phoinikion and in the human voice? For the notes that lie in the high register are not unisons with each other, but stand in proportion to one another across the octave. Is it because, just as the same note seems to be the same note, equality by proportion produces this among notes? And the equal belongs to the one. This same thing is also what deceives people in the case of pan-pipes. Why were the nomes not composed in strophes, while the other choral songs were? Is it because the nomes belonged to competitors, and since these were by then capable of imitation and of extending themselves, the song became long and manifold? For just as the words did, so too the melodies followed the imitation, always becoming different. For it is more necessary to imitate by the melody than by the words. That is why the dithyrambs too, once they became imitative, no longer have strophes, though earlier they did. The cause is that in ancient times free men themselves danced in the chorus; so it was difficult for a crowd to sing in the manner of a competitor, and so they sang set, harmonious melodies instead. For it is easier for one person to undergo many changes than for many people to do so, and easier for the competitor than for those who are preserving a fixed character. That is why they made the melodies simpler for them. And the strophic form is simple; for it is a number, and is measured by a single unit. The same cause also explains why the parts sung from the stage are not strophic, while those of the chorus are strophic; for the actor is a competitor and an imitator, but the chorus imitates less.
6| Why is the answering note more pleasant than a concord generally? Is it because it becomes more evident that the notes are in concord, than when a voice sings in accord with the concord itself? For in that case one note must necessarily merge into unison with the other, so that the two, becoming directed toward a single sound, make the other one imperceptible. Why do people not sing answering notes at the interval of a fifth? Is it because the concordant note within that concord is not the same as it is in the octave? For in the octave, the low note stands in the same proportion within the low register as the high note does within the high register; so it is, in a way, at once the same note and another note. But the notes in the fifth and the fourth do not stand this way, so that the sound of the answering note is not made apparent in them; for it is not the same note. Why is the concord of the octave alone sung together with the instrument playing the same interval? For this is the one they double at the octave, and no other. Is it because it alone is composed of answering strings, and among answering strings, if one sings the other as well, it produces the same effect? For the one string in a way carries the sound of both, so that even when only one is sung, the concord is sung within this consonance, as though both were singing; or, with one being sung and the other played on the pipe, the two are sung as though they were one. That is why it alone is turned into melody, because in it the answering strings carry the sound of a single string. (The source text is disordered at this point, interleaving the end of this sentence with the opening words of the next chapter; the sense has been reconstructed above and the next chapter's question follows in the next block.)
7| Why does this belong only to the answering strings? Is it because they alone are equally distant from the mese? This middle position, then, produces a certain likeness among the notes, and the ear seems to say both that it is the same note and that both are outermost notes. Why is it that, if someone moves the mese, after tuning the other strings, and then uses the instrument, it causes distress and sounds out of tune not only when the note struck is that of the mese, but throughout the rest of the melody as well; whereas if someone moves the lichanos or some other note, the difference is apparent only when that note itself is used? Is this reasonable? For all good melodies use the mese frequently, and all good poets return to the mese often, and if they depart from it, they quickly come back to it, but they do nothing like this with any other note. Just as, in speech, if certain connectives are removed the resulting speech is not Greek — for instance the word 'and' (te) and the word 'and' (kai) — while removing certain others causes no distress, because some words must necessarily be used often if there is to be coherent speech, while others need not be, so too, among the notes, the mese is like a connective, and especially so among fine melodies, because its note occurs within them most often of all.
8| Why is it that among singers, those who sing lower are more obviously detected than those who sing higher, if they sing off pitch? And likewise in rhythm, those who go wrong in the slower tempo are more obviously detected. Is it because the time taken by the low note is greater, and this is more perceptible? Or is it because in a greater time it affords more perception, while the low and high notes escape notice because of their speed? Why do the many, when singing, preserve the rhythm better than the few? Is it because they look more to one person, a leader, and start more slowly, so that they more easily hit the same mark? For in speed there is more room for error. Why is the highest string double the lowest? Is it first because a string plucked from its half-point and plucked whole are consonant through the octave? The same holds for pipes too: the note produced through the hole at the middle of the pipe is consonant with the note through the whole pipe, an octave apart. Further, in flutes the octave is obtained at the interval of a double ratio, and pipe-borers take it this way. [And likewise the fifth corresponds to the ratio of one and a half.] Further, those who tune panpipes stop up the wax right at the top for the lowest note, but fill the highest pipe up to its half-point. Likewise they get the fifth by the ratio of one and a half, and the fourth by the ratio of four to three. Further, in triangular harps, when the tension is made equal, the strings are consonant through the octave, one string being double the other, the other half, in length.
9| Why is it that if someone plucks the highest string and then stops it, the lowest string alone seems to echo back? Is it because the sound arising from that string is most closely akin to the note, since it is consonant with it? So because it is increased along with what is similar to it, it alone appears to sound, while the others are inaudible because of their smallness. Why is the middle note called "middle" in scales, when among eight notes there is no exact middle? Is it because in ancient times scales had seven strings, and seven has a middle? Why do most people sing sharp, off pitch toward the high side? Is it because it is easier to sing high than low? Or is it because it is worse than the low? For error is the doing of the worse thing. Why is it that hearing alone, of the objects of perception, has character? For even if a melody is without words, it still has character; but color does not, nor smell, nor flavor. Is it because hearing has, virtually, motion, which the sound sets going in us? For such motion belongs to the other senses too — color also moves sight — but it is the motion that follows upon this kind of sound that we perceive. And this motion has a resemblance both in the rhythms and in the ordering of high and low notes, though not in their blending. But a concord has no character. In the other objects of perception this is not so. And these motions are motions of action, and actions are a sign of character.
10| Why are the songs called "nomoi," that is, laws? Is it because before people knew how to write, they sang the laws, so as not to forget them, as is still the custom among the Agathyrsi? And so they gave the same name to the first of the later songs as to the first laws. Why is it that rhythms and melodies, being voice, resemble character, while flavors do not, nor colors nor smells either? Is it because they are motions, just as actions are? For the activity is already something ethical and produces character, while flavors and colors do not produce it in the same way. Why is there no choral song in tragedy in the hypodorian or hypophrygian mode? Is it because it has no antistrophe? Rather it is sung from the stage, for it is imitative. Why were the followers of Phrynichus more given to composing melodies? Is it because at that time the melodies in tragedies were many times more numerous than the metrical passages? Why is it called "through all," that is, the octave, and not, in accordance with the number, "through eight," as with "through four" and "through five"? Is it because there were seven strings anciently? Then Terpander, removing the third, added the highest string, and after this it was called "through all," not "through eight"; for there were seven.
11| Why is it more harmonious to go from the high note down to the low than from the low up to the high? Is it because the one comes to be beginning from a starting-point? For the middle note is both leader and highest of the tetrachord. But the other does not begin from a starting-point, but from an end. Or is it because the low note coming after the high is nobler and more euphonious? Why do a double octave-plus-fifth and a double fourth not make a concord, but a double octave does? Is it because it is not... (text breaks off) nor a double fourth... is, but the fourth and the fifth...
12| Why is the octave the finest concord? Is it because its ratios lie in whole terms, while the ratios of the others do not lie in whole terms? For since the highest string is double the lowest, as the highest is two, the lowest is one, and as the lowest is two, the highest is four, and so on always. But the middle note stands in the ratio of one and a half to it. For the fifth, being in the ratio of one and a half, is not in whole numbers: for as the lesser is one, the greater is that much and also half again. So that whole is not compared with whole, but a fractional part is added on. The same holds likewise in the fourth: for the ratio of four to three is such that one must cut off a portion and add on one further third of the three [it is in the ratio of four to three]. Or is it because the octave, being composed of both, is most complete, and because it is the measure of melody... throughout everything in motion the motion at the middle point is most intense, but at the beginning and the end it is gentler? And when the motion is most intense, the pitch too is higher than that of the moving thing. That is also why strings, when stretched tighter, sound a higher note: for the motion becomes quicker. But if voice is a movement of air or of something else, the pitch must become highest at the midpoint of its passage. So that if this does not happen, there could be no movement of anything.
13| Why is it that if the middle string is set in motion, the other strings too resound and sound out, but if the middle string stays still and one of the others is moved, only the one moved sounds? Is it because being in tune belongs to all of them together, and standing in a certain relation to the middle note belongs to all of them, and the ordering of each is already through that relation? So when the cause of their being in tune, the thing that holds them together, is removed, they no longer appear to hold in the same way. But when only one string is out of tune while the middle one remains, it is reasonable that the failure should be confined to that one string, since being in tune belongs to the others still. Why is it that, although the high note in voice depends on smallness and the low note on largeness (for the low, because of its bulk, is slow, while the high, because of its smallness, is quick), it is more of a task to sing high notes than low, and few can sing the upper range, and the high nomes and sharp notes are hard to sing because they are stretched taut? And yet it is less work to move a small quantity than a large one, and so too with air. Is it not the same thing to be naturally high-voiced and to sing high by effort? Rather, all things are naturally high-voiced through weakness, through being unable to move much air but only a little, and a little air travels quickly; whereas in singing high by effort, the high note is a sign of power. For what is carried forcefully is carried quickly, and so the high note is a sign of power; that is also why people in good condition are high-voiced. And it is a task to sing the upper notes; the low notes belong below.
14| Why do all people delight in rhythm and melody and, generally, in concords? Is it because we delight, in accordance with nature, in motions that accord with nature? A sign of this is that children delight in them as soon as they are born. And it is through habit that we delight in particular styles of melody. We delight in rhythm because it has a recognizable and ordered number and moves us in an ordered way; for ordered motion is by nature more akin to us than disordered motion, so that it is also more in accordance with nature. Here is a sign: by laboring and drinking and eating in an ordered way we preserve and increase our nature and our power, but by doing these things in a disordered way we destroy it and drive it out of its own state; for diseases are motions of the body that are not in accordance with its natural order. And we delight in concord because it is a blending of things standing in a ratio to one another as opposites. Now the ratio is order, and order was by nature pleasant. And everything blended is more pleasant than the unblended, especially, if it is something perceptible, when the ratio in the concord gives both extremes an equal power.
15| Why is the concordant more pleasant than the unisonous? Or is it that the antiphonal too is concordant, through the whole octave? For the antiphonal arises out of boys and young men and grown men, who stand apart in pitch as the highest string does from the lowest. Now every concord is more pleasant than a single note (why has been stated), and of these the octave is most pleasant; but the unisonous has a single note. They sing an octave apart in the octave concord because, just as in meters the feet stand to one another in a ratio, equal to equal or two to one or some other ratio, so too the notes in a concord have a ratio of motion to one another. Now in the other concords the closes of one of the two parts are incomplete, ending at the half; hence they are not equal in power. And being unequal, the difference is perceptible, as in choruses, in that at the close some sing more loudly than others. Further, it happens that the highest note has the same ending as the periods among the notes. For the second stroke of the air from the lowest note is the highest note. And though they end at the same point without producing the same effect, one common and joint result comes about, just as with those who play an accompaniment under a song; for these, even though for the rest they do not follow the pipe closely, if they end together at the same point, they please more by the ending than they distress by the differences before the ending, because what is common out of things that differ is most pleasant when it arises out of the octave. Now singing an octave apart is out of opposite voices. For these reasons they sing an octave apart in the octave concord.
16| Why is it more pleasant to listen to singers singing songs which one happens to know beforehand than if one does not know them? Is it because the one who hits the mark is more clearly recognized, as at a target, when people recognize what is being sung? And it is pleasant to observe when one recognizes. Or is it because the listener feels a kind of fellow-feeling with the one singing something familiar? For he sings along with him. And everyone sings gladly who is not doing it under some compulsion. Why does a double octave make a concord, but a double fifth or a double fourth does not? Is it because the fifth is in the ratio of three to two, and the fourth in the ratio of four to three? Now when there are two successive numbers in the ratio three to two, or two in the ratio four to three, the extremes will have no ratio to one another at all; for they will be neither superparticular numbers nor multiples of one another. But the octave, since it is in the ratio two to one — when this ratio occurs twice, the extremes will be to one another in the ratio four to one. So then, since concord belongs to notes that have a rational ratio to one another, and the notes that are a double octave apart have such a ratio to one another, while those a double fifth or double fourth apart do not, the notes a double octave apart would be concordant, but the others would not, for the reasons stated.
17| Why, if someone plucks the highest string and then damps it, does only the lowest string seem to sound on in response? Is it because the highest note, as it dies away and fades, becomes the lowest? A sign of this is that one can sing the highest note starting from the lowest; for, taking it as though this itself were the song of the highest note, they get the resemblance to it from the lowest note. And since an echo too is a kind of song, being a contact with the voice of the highest note as it dies away, and being a sound the same as the note of the lowest string, it reasonably seems, because of this resemblance, that the plucked highest string is what sets the lowest string sounding. For we know where the highest string moves when it is damped; but seeing that the lowest string itself is, in its own motion, imperceptible, and hearing a note coming from that region, we suppose that this is the string sounding — which happens to us in many cases, where we can know the exact truth neither by reasoning nor by perception. Further, if it happens that when the highest string is struck, being most taut, the bridge is set moving, there would be nothing surprising in that. And once the bridge is moved, it is not unreasonable that all the strings should be moved together and produce some sound. Now to the other strings the note of the highest string is foreign, both as it dies away and as it begins; but to the lowest string, the dying note is the same note. When this is added to the lowest string's own proper motion, it is not at all strange that the whole should seem to belong to the lowest string. And it will be a greater sound than the one common to the rest of the strings, because the others sounded as though gently pushed by the highest string, whereas the highest string sounds with the whole of its own power, being the most vigorous of them all. So it is reasonable that its secondary effect too should be stronger than that of the others, so that even small motions are stirred up, as though the lowest string itself had come to sound.
18| Why is it more pleasant than solo singing if someone sings to the accompaniment of the pipe or the lyre? Is it because everything more pleasant, when mixed with something more pleasant, becomes one thing? The pipe is more pleasant than the lyre, so that the song mixed with the pipe would be more pleasant than the song mixed with the lyre, since the blended is more pleasant than the unblended, provided one takes in the perception of both together. For wine is more pleasant than a mixture of vinegar and honey, because things blended by nature are more thoroughly blended with one another than things blended by us. For wine too is a blend of a sharp and a sweet flavor. And the so-called wine-like pomegranate juices show this as well. Now song and the pipe blend with each other because of their likeness, for both come about by breath; but the note of the lyre, since it does not come about by breath, or is less perceptible than that of the pipes, is less able to blend with the voice; and since it produces a difference perceptible to sense, it gives less pleasure, just as was said in the case of flavors. Further, the pipe conceals many of the singer's mistakes by its own sound and its resemblance to the voice, whereas the notes of the lyre, being bare and less able to blend with the voice, when observed by themselves and being clearly perceptible in their own right, make the fault of the song evident, standing over it like a straightedge. And since many faults occur in singing, the combination of both must necessarily turn out worse.
19| Why is the middle string in an octave of eight strings called the "middle," while in another set of eight there is no middle? Is it because in ancient times the modes had seven strings, and seven has a middle? Further, since among the intervals lying between the extremes only the middle is in a sense a starting point (for in any system whose parts incline toward one or the other extreme, the point lying midway is a starting point), this will be the middle. And since the extremes of a mode are the lowest note and the highest note, and midway between them lie the remaining notes, of which the one called the "middle" is the sole starting point of the other tetrachord, it is rightly called the middle. For of things lying between certain extremes, the middle alone was a starting point. Why do the many, when singing, keep the rhythm better than the few? Is it because they look more toward the one leader, and begin more slowly, so that they more easily hit the same mark together? For error becomes greater in speed. And it happens that the many attend to the leader; for if any one of them stood apart and sang on his own, standing out above the crowd, he would not shine. But among the few they stand out more; hence among themselves they compete more on their own account than in relation to the leader.
20| Why do most people sing off-key toward the sharp side? Is it because it is easier to sing sharp than flat? At any rate they sing sharper more often, and it is in this that they go wrong. Why did the ancients, when they made their scales seven-stringed, keep the hypate but not the nete? Or is it not the nete they took away, but rather the string now called paramese, along with the interval of a tone? They used the topmost note of the close-packed cluster on the sharp side as a middle note; that is why they called it the mese, the "middle." Or was it because it was the endpoint of the upper tetrachord and the starting point of the lower one, and stood in a middle position, a tone away from either extreme?
21| Why do the choruses in tragedy sing neither in the hypodorian nor in the hypophrygian mode? Is it because these harmonies have the least melody of all, and melody is what the chorus needs most? The hypophrygian has a character suited to action, which is why in the Geryone [and] the exit and the arming-scene were composed in it, while the hypodorian is grand and stately, which is why it is the most suited to lyre-song of all the harmonies. Both of these are ill-suited to a chorus, but more proper to the actors on stage. For those actors are imitators of heroes, whereas among the ancients only the leaders were heroes, and the common people were ordinary men, and it is of these that the chorus consists. That is why a mournful and quiet character and melody suits it: for the other harmonies have this human quality, but the phrygian least of all of them, since it is inspired and Bacchic. So under this mode we are acted upon in some way; and the weak are more subject to being acted upon than the capable are, which is why this mode suits choruses. But under the hypodorian and hypophrygian we act, and acting is not proper to a chorus. For the chorus is a concerned bystander who does not act: it offers only goodwill to those it is present with. Why, among the notes that make up a concord, is the softer one the lower one? Is it because melody, by its own nature, is soft and calm, but by its mixture with rhythm becomes rough and full of movement? Since the low note is soft and calm, while the high note is full of movement, then among notes carrying the same melody, the lower one would be the softer, more so within that same melody — since the melody was soft for it.
22| Why, with jars that are equal and alike, if one is empty and the other is filled to half, does the echo make a concord at the octave? Is it because the sound coming from the half-full jar becomes double that from the empty one? For how does this differ from the case of pan-pipes? The faster motion seems to be the sharper one, and in the larger vessels the air meets resistance more slowly, and in vessels of double size, by that much more, and proportionately in the others. And a wineskin of double size likewise makes a concord at the octave with the half-size one.