From Plato and Aristotle we have learned some elements of what may be called the gamut of sensibility. Between the higher keys which in Greece, as in Oriental countries generally, were the familiar vehicle of passion, especially of the passion of grief, and the lower keys which were regarded, by Plato at least, as the natural language of ease and license, there were keys expressive of calm and balanced states of mind, free from the violent extremes of pain and pleasure. In some later writers on music we find this classification reduced to a more regular form, and clothed in technical language. We find also, what is still more to our purpose, an attempt to define more precisely the musical forms which answered to the several states of temper or emotion.
Among the writers in question the most instructive is Aristides Quintilianus. He discusses the subject of musical ethos under the first of the usual seven heads, that which deals with sounds or notes (peri phthongôn). Among the distinctions to be drawn in regard to notes he reckons that of ethos: the ethos of notes, he says, is different as they are higher or lower, and also as they are in the place of a Parhypatê or in the place of a Lichanos (p. 13 Meib. hetera gar êthê tois oxyterois, hetera tois baryterois epitrechei, kai hetera men parypatoeidesin, hetera de lichanoeidesin). Again, under the seventh head, that of melopoiia or composition, he treats of the 'regions of the voice' (topoi tês phônês). There are three kinds of composition, he tells us (p. 28), viz. that which is akin to Hypatê (hypatoeidês), that which is akin to Mesê (mesoeidês), and that which is akin to Nêtê (nêtoeidês). The first part of the art of composition is the choice (lêpsis) which the musician is able to make of the region of the voice to be employed (lêpsis men di' hês heuriskein tô mousikô perigignetai apo poiou tês phônês to systêma topou poiêteon, poteron hypatoeidous ê tôn loipôn tinos). He then proceeds to connect these regions, or different parts of the musical scale, with different branches of lyrical poetry. 'There are three styles of musical composition (tropoi tês melopoiias), viz. the Nomic, the Dithyrambic, and the Tragic; and of these the Nomic is netoid, the Dithyrambic is mesoid, and the Tragic is hypatoid.... They are called styles (tropoi) because according to the melody adopted they express the ethos of the mind. Thus it happens that composition (melopoiia) may differ in genus, as Enharmonic, Chromatic: in System, as Hypatoid, Mesoid, Netoid: in key, as Dorian, Phrygian: in style, as Nomic, Dithyrambic: in ethos, as we call one kind of composition "contracting" (systaltikê), viz. that by which we move painful feelings; another "expanding" (diastaltikê), that by which we arouse the spirit (thymos); and another "middle" (mesê), that by which we bring round the soul to calmness.'
This passage does not quite explicitly connect the three kinds of ethos—the diastaltic, the systaltic, the intermediate—with the three regions of the voice; but the connexion was evidently implied, and is laid down in express terms in the pseudo-Euclidean Introductio (p. 21 Meib.). According to this Aristoxenean writer, 'the diastaltic ethos of musical composition is that which expresses grandeur and manly elevation of soul (megaloprepeia kai diarma psychês andrôdes), and heroic actions; and these are employed by tragedy and all poetry that approaches the tragic type. The systaltic ethos is that by which the soul is brought down into a humble and unmanly frame; and such a disposition will be fitting for amatory effusions and dirges and lamentations and the like. And the hesychastic or tranquilly disposed ethos (hêsychastikon êthos) of musical composition is that which is followed by calmness of soul and a liberal and peaceful disposition: and this temper will fit hymns, paeans, laudations, didactic poetry and the like.' It appears then that difference in the 'place' (topos) of the notes employed in a composition—difference, that is to say, of pitch—was the element which chiefly determined its ethos, and (by consequence) which distinguished the music appropriate to the several kinds of lyrical poetry.
A slightly different version of this piece of theory is preserved in the anonymous treatise edited by Bellermann (§§ 63, 64), where the 'regions of the voice' are said to be four in number, viz. the three already mentioned, and a fourth which takes its name from the tetrachord Hyperbolaiôn (topos hyperboloeidês). In the same passage the boundaries of the several regions are laid down by reference to the keys. 'The lowest or hypatoid region reaches from the Hypo-dorian Hypatê Mesôn to the Dorian Mesê; the intermediate or mesoid region from the Phrygian Hypatê Mesôn to the Lydian Mesê; the netoid region from the Lydian Mesê to the Nêtê Synemmenôn; the hyperboloid region embracing all above the last point.' The text of this passage is uncertain; but the general character of the topoi or regions of the voice is clearly enough indicated.
The three regions are mentioned in the catechism of Bacchius (p. 11 Meib.): topous (MSS. tropous) de tês phônês posous legomen einai? treis. tinas? toutous; oxyn, meson, baryn. The varieties of ethos also appear (p. 14 Meib.): hê de metabolê kata êthos? hotan ek tapeinou eis megaloprepes; ê ex hêsychou kai synnou eis parakekinêkos. 'What is change of ethos? when a change is made from the humble to the magnificent; or from the tranquil and sober to violent emotion.'
When we compare the doctrine of musical ethos as we find it in these later writers with the indications to be gathered from Plato and Aristotle, the chief difference appears to be that we no longer hear of the ethos of particular modes, but only of that of three or (at the most) four portions of the scale. The principle of the division, it is evident, is simply difference of pitch. But if that was the basis of the ethical effect of music in later times, the circumstance goes far to confirm us in the conclusion that it was the pitch of the music, rather than any difference in the succession of the intervals, that principally determined the ethical character of the older modes.
Although the pitch of a musical composition—as these passages confirm us in believing—was the chief ground of its ethical character, it cannot be said that no other element entered into the case.
In the passage quoted above from Aristides Quintilianus (p. 13 Meib.) it is said that ethos depends first on pitch (hetera êthê tois oxyterois, hetera tois baryterois), and secondly on the moveable notes, that is to say, on the genus. For that is evidently involved in the words that follow: kai hetera men parypatoeidesin, hetera de lichanoeidesin. By parypatoeideis and lichanoeideis he means all the moveable notes (phthongoi pheromenoi): the first are those which hold the place of Parhypatê in their tetrachord, viz. the notes called Parhypatê or Tritê: the second are similarly the notes called Lichanos or Paranêtê. These moveable notes, then, give an ethos to the music because they determine the genus of the scale. Regarding the particular ethos belonging to the different genera, there is a statement of the same author (p. 111) to the effect that the Diatonic is masculine and austere (arrhenôpon d' esti kai austêroteron), the Chromatic sweet and plaintive (hêdiston te kai goeron), the Enharmonic stirring and pleasing (diegertikon d' esti touto kai êpion). The criticism doubtless came from some earlier source.
Do we ever find ethos attributed to this or that species of the Octave? I can find no passage in which this source of ethos is indicated. Even Ptolemy, who is the chief authority (as we shall see) for the value of the species, and who makes least of mere difference of pitch, recognises only two forms of modulation in the course of a melody, viz. change of genus and change of pitch [25].
As the preceding argument turns very much upon the practical importance of the scale which we have been discussing, first as the single octave from the original Hypatê to Nêtê, then in its enlarged form as the Perfect System, it may be worth while to show that some such scale is implied in the history of the Greek musical notation.
The use of written characters (sêmeia) to represent the sounds of music appears to date from a comparatively early period in Greece. In the time of Aristoxenus the art of writing down a melody (parasêmantikê) had come to be considered by some persons identical with the science of music (harmonikê),—an error which Aristoxenus is at some pains to refute. It is true that the authorities from whom we derive our knowledge of the Greek notation are post-classical. But the characters themselves, as we shall presently see, furnish sufficient evidence of their antiquity.
The Greek musical notation is curiously complicated. There is a double set of characters, one for the note assigned to the singer, the other for those of the lyre or other instrument. The notes for the voice are obviously derived from the letters of the ordinary Ionic alphabet, multiplied by the use of accents and other diacritical marks. The instrumental notes were first explained less than thirty years ago by Westphal. In his work Harmonik und Melopöie der Griechen (c. viii Die Semantik) he showed, in a manner as conclusive as it is ingenious, that they were originally taken from the first fourteen letters of an alphabet of archaic type, akin to the alphabets found in certain parts of Peloponnesus. Among the letters which he traces, and which point to this conclusion, the most-significant are the digamma, the primitive crooked iota iota, and two forms of lambda, lambda1 and lambda2, the latter of which is peculiar to the alphabet of Argos. Of the other characters alpha1, which stands for alpha, is best derived from the archaic form archaic_alpha. For beta we find archaic_beta, which may come from an archaic form of the letter[26]. The character delta1, as Westphal shows, is for delta2, or delta with part of one side left out. Similarly the ancient circle_dot, when the circle was incomplete, yielded the character C . The crooked iota (iota) appears as iota2. The two forms of lambda serve for different notes, thus bringing the number of symbols up to fifteen. Besides these there are two characters, reclining_pand epsilon01, which cannot be derived in the same way from any alphabet. As they stand for the lowest notes of the scale, they are probably an addition, later than the rest of the system. At the upper end, again, the scale is extended by the simple device of using the same characters for notes an octave higher, distinguishing them in this use by an accent. The original fifteen characters, with the letters from which they are derived, and the corresponding notes in the modern musical scale, are as follows:
15-characters
These notes, it will be seen, compose two octaves of the Diatonic scale, identical with the two octaves of the Greater Perfect System. They may be regarded as answering to the white notes of the modern keyboard,—those which form the complete scale in the so-called 'natural' key.
The other notes, viz. those which are required not only in different keys of the Diatonic scale, but also in all Enharmonic and Chromatic scales, are represented by the same characters modified in some simple way. Usually a character is turned half round backwards to raise it by one small interval (as from Hypatê to Parhypatê), and reversed to raise it by both (Hypatê to Lichanos). Thus the letter epsilon, epsilon02, stands for our c: and accordingly epsilon04 (epsilon02 anestrammenon or hyption) stands for c*, and epsilon03 (epsilon02 apestrammenon) for c♯ . The Enharmonic scale c-c*-c♯-f is therefore written enharmonicscale, the two modifications of the letter epsilon02 representing the two 'moveable' notes of the tetrachord. Similarly we have the triads triad01, triad02, triad03, triad04, triad05, triad06, triad07. As some letters do not admit of this kind of differentiation, other methods are employed. Thus Δ is made to yield the forms delta1 (for delta2) delta3 Δ: from H (or B) are obtained the forms capalpha1 and capalpha2: and from Z (or I]) the forms lambda3 and lambda4. The modifications of N are / and \: those of alpha1 are alpha2 and alpha3.
The method of writing a Chromatic tetrachord is the same, except that the higher of the two moveable notes is marked by a bar or accent. Thus the tetrachord c c♯ d f is written enharmonicscale.
In the Diatonic genus we should have expected that the original characters would have been used for the tetrachords b c d e and e f g a; and that in other tetrachords the second note, being a semitone above the first, would have been represented by a reversed letter (gramma apestrammenon). In fact, however, the Diatonic Parhypatê and Tritê are written with the same character as the Enharmonic. That is to say, the tetrachord b c d e is not written tetrachord01, but tetrachord02: and d e♭ f g is not tetrachord03, but tetrachord04.
Let us now consider how this scheme of symbols is related to the Systems already described and the Keys in which those Systems may be set (tonoi eph' hôn tithemena ta systêmata melôdeitai).
The fifteen characters, it has been noticed, form two diatonic octaves. It will appear on a little further examination that the scheme must have been constructed with a view to these two octaves. The successive notes are not expressed by the letters of the alphabet in their usual order (as is done in the case of the vocal notes). The highest note is represented by the first letter, A: and then the remaining fourteen notes are taken in pairs, each with its octave: and each of the pairs of notes is represented by two successive letters—the two forms of lambda counting as one such pair of letters. Thus:
The Greek notes
On this plan the alphabetical order of the letters serves as a series of links connecting the highest and lowest notes of every one of the seven octaves that can be taken on the scale. It is evident that the scheme cannot have grown up by degrees, but is the work of an inventor who contrived it for the practical requirements of the music of his time.
Two questions now arise, which it is impossible to separate. What is the scale or System for which the notation was originally devised? And how and when was the notation adapted to exhibit the several keys in which any such System might be set?
The enquiry must start from the remarkable fact that the two octaves represented by the fifteen original letters are in the Hypo-lydian key—the key which down to the time of Aristoxenus was called the Hypo-dorian. Are we to suppose that the scheme was devised in the first instance for that key only? This assumption forms the basis of the ingenious and elaborate theory by which M. Gevaert explains the development of the notation (Musique de l'Antiquité, t. I. pp. 244 ff.). It is open to the obvious objection that the Hypo-lydian (or Hypo-dorian) cannot have been the oldest key. M. Gevaert meets this difficulty by supposing that the original scale was in the Dorian key, and that subsequently, from some cause the nature of which we cannot guess, a change of pitch took place by which the Dorian scale became a semitone higher. It is perhaps simpler to conjecture that the original Dorian became split up, so to speak, into two keys by difference of local usage, and that the lower of the two came to be called Hypo-dorian, but kept the original notation. A more serious difficulty is raised by the high antiquity which M. Gevaert assigns to the Perfect System. He supposes that the inventor of the notation made use of an instrument (the magadis) which 'magadised' or repeated the notes an octave higher. But this would give us a repetition of the primitive octave e-e, rather than an enlargement by the addition of tetrachords at both ends.
M. Gevaert regards the adaptation of the scheme to the other keys as the result of a gradual process of extension. Here we may distinguish between the recourse to the modified characters—which served essentially the same purpose as the 'sharps' and 'flats' in the signature of a modern key—and the additional notes obtained either by means of new characters (reclining_p and epsilon01), or by the use of accents (GammaPrime, &c.). The Hypo-dorian and Hypo-phrygian, which employ the new characters reclining_p and epsilon01, are known to be comparatively recent. The Phrygian and Lydian, it is true, employ the accented notes; but they do so only in the highest tetrachord (Hyperbolaiôn), which may not have been originally used in these high keys. The modified characters doubtless belong to an earlier period. They are needed for the three oldest keys—Dorian, Phrygian, Lydian—and also for the Enharmonic and Chromatic genera. If they are not part of the original scheme, the musician who devised them may fairly be counted as the second inventor of the instrumental notation.
In setting out the scales of the several keys it will be unnecessary to give more than the standing notes (phthongoi hestôtes), which are nearly all represented by original or unmodified letters—the moveable notes being represented by the modified forms described above. The following list includes the standing notes, viz. Proslambanomenos, Hypatê Hypatôn, Hypatê Mesôn, Mesê, Paramesê, Nêtê Diezeugmenôn and Nêtê Hyperbolaiôn in the seven oldest keys: the two lowest are marked as doubtful:—
Greek symbols
It will be evident that this scheme of notation tallies fairly well with what we know of the compass of Greek instruments about the end of the fifth century, and also with the account which Aristoxenus gives of the keys in use up to his time. We need only refer to what has been said above on p. 17 and p. 37.
It would be beyond the scope of this essay to discuss the date of the Greek musical notation. A few remarks, however, may be made, especially with reference to the high antiquity assigned to it by Westphal.
The alphabet from which it was derived was certainly an archaic one. It contained several characters, in particular digamma for digamma, iota for iota, and lambda4 for lambda, which belong to the period before the introduction of the Ionian alphabet. Indeed if we were to judge from these letters alone we should be led to assign the instrumental notation (as Westphal does) to the time of Solon. The three-stroke iota (iota), in particular, does not occur in any alphabet later than the sixth century B.C. On the other hand, when we find that the notation implies the use of a musical System in advance of any scale recognised in Aristotle, or even in Aristoxenus, such a date becomes incredible. We can only suppose either (1) that the use of iota in the fifth century was confined to localities of which we have no complete epigraphic record, or (2) that iota as a form of iota was still known—as archaic forms must have been—from the older public inscriptions, and was adopted by the inventor of the notation as being better suited to his purpose than iota.
With regard to the place of origin of the notation the chief fact which we have to deal with is the use of the character lambda for lambda, which is distinctive of the alphabet of Argos, along with the commoner form lambda. Westphal indeed asserts that both these forms are found in the Argive alphabet. But the inscription (C. I. 1) which he quotes [27] for lambda really contains only lambda in a slightly different form. We cannot therefore say that the inventor of the notation derived it entirely from the alphabet of Argos, but only that he shows an acquaintance with that alphabet. This is confirmed by the fact that the form iota for iota is not found at Argos. Probably therefore the inventor drew upon more than one alphabet for his purpose, the Argive alphabet being one.
The special fitness of the notation for the scales of the Enharmonic genus may be regarded as a further indication of its date. We shall see presently that that genus held a peculiar predominance in the earliest period of musical theory—that, namely, which was brought to an end by Aristoxenus.
If the author of the notation—or the second author, inventor of the modified characters—was one of the musicians whose names have come down to us, it would be difficult to find a more probable one than that of Pronomus of Thebes. One of the most striking features of the notation, at the time when it was framed, must have been the adjustment of the keys. Even in the time of Aristoxenus, as we know from the passage so often quoted, that adjustment was not universal. But it is precisely what Pronomus of Thebes is said to have done for the music of the flute (supra, p. 38). The circumstance that the system was only used for instrumental music is at least in harmony with this conjecture. If it is thought that Thebes is too far from Argos, we may fall back upon the notice that Sacadas of Argos was the chief composer for the flute before the time of Pronomus, [28] and doubtless Argos was one of the first cities to share in the advance which Pronomus made in the technique of his art.
Before leaving this part of the subject it will be well to notice the attempt which Westphal makes to connect the species of the Octave with the form of the musical notation.
The basis of the notation, as has been explained (p. 69), is formed by two Diatonic octaves, denoted by the letters of the alphabet from α to ν, as follows:
| η | ι | ε | λ | γ | μ | Ϝ | θ | κ | δ | λ | β | ν | ζ | α |
| a | b | c | d | e | f | g | a | b | c | d | e | f | g | a |
In this scale, as has been pointed out (p. 71), the notes which are at the distance of an octave from each other are always expressed by two successive letters of the alphabet. Thus we find—
| β | - | γ | is the octave | e - e, | the Dorian species. |
| δ | - | ε | " " | c - c, | the Lydian species. |
| Ϝ | - | ζ | " " | g - g, | the Hypo-phrygian species. |
| η | - | θ | " " | a - a, | the Hypo-dorian species. |
Westphal adopts the theory of Boeckh (as to which see p. 11) that the Hypo-phrygian and Hypo-dorian species answered to the ancient Ionian and Aeolian modes. On this assumption he argues that the order of the pairs of letters representing the species agrees with the order of the Modes in the historical development of Greek music. For the priority of Dorian, Ionian, and Aeolian he appeals to the authority of Heraclides Ponticus, quoted above (p. 9). The Lydian, he supposes, was interposed in the second place on account of its importance in education,—recognised, as we have seen, by Aristotle in the Politics (viii. 7 ad fin.). Hence he regards the notation as confirming his theory of the nature and history of the Modes.
The weakness of this reasoning is manifold. Granting that the Hypo-dorian and Hypo-phrygian answer to the old Aeolian and Ionian respectively, we have to ask what is the nature of the priority which Heraclides Ponticus claims for his three modes, and what is the value of his testimony. What he says is, in substance, that these are the only kinds of music that are truly Hellenic, and worthy of the name of modes (harmoniai). It can hardly be thought that this is a criticism likely to have weighed with the inventor of the notation. But if it did, why did he give an equally prominent place to Lydian, one of the modes which Heraclides condemned? In fact, the introduction of Lydian goes far to show that the coincidence—such as it is—with the views of Heraclides is mere accident. Apart, however, from these difficulties, there are at least two considerations which seem fatal to Westphal's theory:
1. The notation, so far as the original two octaves are concerned, must have been devised and worked out at some one time. No part of these two octaves can have been completed before the rest. Hence the order in which the letters are taken for the several notes has no historical importance.
2. The notation does not represent only the species of a scale, that is to say, the relative pitch of the notes which compose it, but it represents also the absolute pitch of each note. Thus the octaves which are defined by the successive pairs of letters, β-γ, δ-ε, and the rest, are octaves of definite notes. If they were framed with a view to the ancient modes, as Westphal thinks, they must be the actual scales employed in these modes. If so, the modes followed each other, in respect of pitch, in an order exactly the reverse of the order observed in the keys. It need hardly be said that this is quite impossible.
The first writer who takes the Species of the Octave as the basis of the musical scales is the mathematician Claudius Ptolemaeus (fl. 140-160 A.D.). In his Harmonics he virtually sets aside the scheme of keys elaborated by Aristoxenus and his school, and adopts in their place a system of scales answering in their main features to the mediaeval Tones or Modes. The object of difference of key, he says, is not that the music as a whole may be of a higher or lower pitch, but that a melody may be brought within a certain compass. For this purpose it is necessary to vary the succession of intervals (as a modern musician does by changing the signature of the clef). If, for example, we take the Perfect System (systêma ametabolon) in the key of a minor—which is its natural key,—and transpose it to the key of d minor, we do so, according to Ptolemy, not in order to raise the general pitch of our music by a Fourth, but because we wish to have a scale with b flat instead of b natural. The flattening of this note, however, means that the two octaves change their species. They are now of the species e-e. Thus, instead of transposing the Perfect System into different keys, we arrive more directly at the desired result by changing the species of its octaves. And as there are seven possible species of the Octave, we obtain seven different Systems or scales. From these assumptions it follows, as Ptolemy shows in some detail, that any greater number of keys is useless. If a key is an octave higher than another, it is superfluous because it gives us a mere repetition of the same intervals [29].
If we interpose a key between (e.g.) the Hypo-dorian and the Hypo-phrygian, it must give us over again either the Hypo-dorian or the Hypo-phrygian scale [30]. Thus the fifteen keys of the Aristoxeneans are reduced to seven, and these seven are not transpositions of a single scale, but are all of the same pitch. See the table at the end of the book.
With this scheme of Keys Ptolemy combined a new method of naming the individual notes. The old method, by which a note was named from its relative place in the Perfect System, must evidently have become inconvenient. The Lydian Mesê, for example, was two tones higher than the Dorian Mesê, because the Lydian scale as a whole was two tones higher than the Dorian. But when the two scales were reduced to the same compass, the old Lydian Mesê was no longer in the middle of the scale, and the name ceased to have a meaning. It is as though the term 'dominant' when applied to a Minor key were made to mean the dominant of the relative Major key. On Ptolemy's method the notes of each scale were named from their places in it. The old names were used, Proslambanomenos for the lowest, Hypatê Hypatôn for the next, and so on, but without regard to the intervals between the notes. Thus there were two methods of naming, that which had been in use hitherto, termed 'nomenclature according to value' (onomasia kata dynamin), and the new method of naming from the various scales, termed 'nomenclature according to position' (onomasia kata thesin). The former was in effect a retention of the Perfect System and the Keys: the latter put in their place a scheme of seven different standard Systems.
In illustration of his theory Ptolemy gives tables showing in numbers the intervals of the octaves used in the different keys and genera. He shows two octaves in each key, viz. that from Hypatê Mesôn (kata thesin) to Nêtê Diezeugmenôn (called the octave apo nêtês), and that from Proslambanomenos to Mesê (the octave apo mesês). As he also gives the divisions of five different 'colours' or varieties of genus, the whole number of octaves is no less than seventy.
Ptolemy does not exclude difference of pitch altogether. The whole instrument, he says, may be tuned higher or lower at pleasure [31]. Thus the pitch is treated by him as modern notation treats the tempo, viz. as something which is not absolutely given, but has to be supplied by the individual performer.
Although the language of Ptolemy's exposition is studiously impersonal, it may be gathered that his reduction of the number of keys from fifteen to seven was an innovation proposed by himself [32]. If this is so, the rest of the scheme,—the elimination of the element of pitch, and the 'nomenclature by position,'—must also be due to him. Here, however, we find ourselves at issue with Westphal and those who agree with him on the main question of the Modes. According to Westphal the nomenclature by position is mentioned by Aristoxenus, and is implied in at least one important passage of the Aristotelian Problems. We have now to examine the evidence which he adduces to support his contention.
Two passages of Aristoxenus are quoted by Westphal in support of his contention. The first (p. 6 Meib.) is one in which Aristoxenus announces his intention to treat of Systems, their number and nature: 'setting out their differences in respect of compass (megethos), and for each compass the differences in form and composition and position (tas te kata schêma kai kata synthesin kai kata thesin), so that no element of melody,—either compass or form or composition or position,—may be unexplained.' But the word thesis, when applied to Systems, does not mean the 'position' of single notes, but of groups of notes. Elsewhere (p. 54 Meib.) he speaks of the position of tetrachords towards each other (tas tôn tetrachordôn pros allêla theseis), laying it down that any two tetrachords in the same System must be consonant either with each other or with some third tetrachord. The other passage quoted by Westphal (p. 69 Meib.) is also in the discussion of Systems. Aristoxenus is pointing out the necessity of recognising that some elements of melodious succession are fixed and limited, others are unlimited:
kata men oun ta megethê tôn diastêmatôn kai tas tôn phthongôn taseis apeira pôs phainetai einai ta peri melos, kata de tas dynameis kai kata ta eidê kai kata tas theseis peperasmena te kai tetagmena.
'In the size of the intervals and the pitch of the notes the elements of melody seem to be infinite; but in respect of the values (i.e. the relative places of the notes) and in respect of the forms (i.e. the succession of the intervals) and in respect of the positions they are limited and settled.'
Aristoxenus goes on to illustrate this by supposing that we wish to continue a scale downwards from a pyknon or pair of small intervals (Chromatic or Enharmonic). In this case, as the pyknon forms the lower part of a tetrachord, there are two possibilities. If the next lower tetrachord is disjunct, the next interval is a tone; if it is conjunct, the next interval is the large interval of the genus (hê men gar kata tonon eis diazeuxin agei to tou systêmatos eidos, hê de kata thateron diastêma ho ti dêpot' echei megethos eis synaphên). Thus the succession of intervals is determined by the relative position of the two tetrachords, as to which there is a choice between two definite alternatives. This then is evidently what is meant by the words kata tas theseis [33]. On the other hand the thesis of Ptolemy's nomenclature is the absolute pitch (Harm. ii. 5 pote men par' autên tên thesin, to oxyteron haplôs ê baryteron, onomazomen), and this is one of the elements which according to Aristoxenus are indefinite.
Westphal also finds the nomenclature by position implied in the passage of the Aristotelian Problems (xix. 20) which deals with the peculiar relation of the Mesê to the rest of the musical scale. The passage has already been quoted and discussed (supra, p. 43), and it has been pointed out that if the Mesê of the Perfect System (mesê kata dynamin) is the key-note, the scale must have been an octave of the a-species. If octaves of other species were used, as Westphal maintains, it becomes necessary to take the Mesê of this passage to be the mesê kata thesin, or Mesê by position. That is, Westphal is obliged by his theory of the Modes to take the term Mesê in a sense of which there is no other trace before the time of Ptolemy. But—
(1) It is highly improbable that the names of the notes—Mesê, Hypatê, Nêtê and the rest—should have had two distinct meanings. Such an ambiguity would have been intolerable, and only to be compared with the similar ambiguity which Westphal's theory implies in the use of the terms Dorian, &c.
(2) If the different species of the octave were the practically important scales, as Westphal maintains, the position of the notes in these scales must have been correspondingly important. Hence the nomenclature by position must have been the more usual and familiar one. Yet, as we have shown, it is not found in Aristotle, Aristoxenus or Euclid—to say nothing of later writers.
(3) The nomenclature by position is an essential part of the scheme of Keys proposed by Ptolemy. It bears the same relation to Ptolemy's octaves as the nomenclature by 'value' bears to the old standard octave and the Perfect System. It was probably therefore devised about the time of Ptolemy, if not actually by him.
The earliest evidence in practical music of any octaves other than those of the standard System is to be found in the account given by Ptolemy of certain scales employed on the lyre and cithara. According to this account the scales of the lyre (the simpler and commoner instrument) were of two kinds. One was Diatonic, of the 'colour' or variety which Ptolemy recognises as the prevailing one, viz. the 'Middle Soft' or 'Tonic' (diatonon toniaion) [34]. The other was a 'mixture' of this Diatonic with the standard Chromatic (chrôma suntonon): that is to say, the octave consisted of a tetrachord of each genus. These octaves apparently might be of any species, according to the key chosen [35]. On the cithara,—which was a more elaborate form of lyre, confined in practice to professional musicians,—six different octave scales were employed, each of a particular species and key. They are enumerated and described by Ptolemy in two passages (Harm. i. 16 and ii. 16), which in some points serve to correct each other [36]. Of the six scales two are of the Hypo-dorian or Common species (a-a). One of these, called tritai, is purely Diatonic of the Middle Soft variety; the intervals expressed by fractions are as follows:
| a | 9/8 | b | 28/27 | c | 8/7 | d | 9/8 | e | 28/27 | f | 8/7 | g | 9/8 | a |
The other, called tropoi or tropika, is a mixture, Middle Soft Diatonic in the upper tetrachord, and Chromatic in the lower:
| a | 9/8 | b | 22/21 | c | 12/11 | c♯ | 7/6 | e | 28/27 | f | 8/7 | g | 9/8 | a |
Two scales are of the Dorian or e-species, viz. parypatai, a combination of Soft and Middle Soft Diatonic:
| e | 21/20 | f | 10/9 | g | 8/7 | a | 9/8 | b | 28/27 | c | 8/7 | d | 9/8 | e |
and lydia, in which the upper tetrachord is of the strict or 'highly strung' Diatonic (diatonon syntonon—our 'natural' temperament):
| e | 28/27 | f | 8/7 | g | 9/8 | a | 9/8 | b | 16/15 | c | 9/8 | d | 10/9 | e |
Westphal (Harmonik und Melopöie, 1863, p. 255) supposes a much deeper corruption. He would restore ta de lydia [kai iastia hoi tou migmatos tou syntonou diatonou tou ... ta de ...] hoi tou toniaiou diatonou tou Dôriou. This introduces a serious discrepancy between the two passages, as the number of scales in the second list is raised to eight (Westphal making iastia and iastiaioliaia distinct scales, and furthermore inserting a new scale, of unknown name). Moreover the (unknown) scale of unmixed diatonon toniaion is out of its place at the end of the list. Westphal's objection to lydia as the name of a scale of the Dorian species of course only holds good on his theory of the Modes.
The only other differences between the two passages are:
(1) In the scales of the lyre called malaka the admixture, according to i. 16, is one of chrômatikon syntonon, according to ii. 16 of chr. malakon. But, as Westphal shows, Soft Chromatic is not admitted by Ptolemy as in practical use. It would seem that in the second passage the copyist was led astray by the word malaka just before.
(2) The iastia of i. 16 is called astiaioliaia in ii. 16. We need not suppose the text to be faulty, since the two forms may have been both in use.
Another point overlooked in Westphal's treatment is that diatonon syntonon and d. ditoniaion are not really distinguished by Ptolemy. In one passage (i. 16) he gives his lydia and iastia as a mixture with d. syntonon, adding that in practice it was d. ditoniaion. In the other (ii. 16) he speaks at once of d. ditoniaion. This consideration brings the two places into such close agreement that any hypothesis involving discrepancy is most improbable.
In practice it appears that musicians tuned the tetrachord b-e of this scale with the Pythagorean two Major tones and leimma.
Of the remaining scales one, called hypertropa, is Phrygian in species (d-d), and of the standard genus:
| d | 9/8 | e | 28/27 | f | 8/7 | g | 9/8 | a | 9/8 | b | 28/27 | c | 8/7 | d |
One, called iastia, or iastiaioliaia, is of the Hypo-phrygian or g-species, the tetrachord b-e being 'highly strung' Diatonic or (in practice) Pythagorean, viz.:
| g | 9/8 | a | 9/8 | b | 256/243 | c | 9/8 | d | 9/8 | e | 28/27 | f | 8/7 | g |
Regarding the tonality of these scales there is not very much to be said. In the case of the Hypo-dorian and Dorian octaves it will be generally thought probable that the key-note is a (the mesê kata dynamin). If so, the difference between the two species is not one of 'mode,'—in the modern sense,—but consists in the fact that in the Hypo-dorian the compass of the melody is from the key-note upwards, while in the Dorian it extends a Fourth below the key-note. It is possible, however, that the lowest note (e) of the Dorian octave was sometimes the key-note: in which case the mode was properly Dorian. In the Phrygian octave of Ptolemy's description the key-note cannot be the Fourth or Mesê kata thesin (g), since the interval g-c is not consonant (9/8 × 9/8 × 28/27 being less than 4/3). Possibly the lowest note (d) is the key-note; if so the scale is of the Phrygian mode (in the modern sense). In the Hypo-phrygian octave there is a similar objection to regarding the Mesê kata thesin (c) as the key-note, and some probability in favour of the lowest note (g). If the Pythagorean division of the tetrachord g-c were replaced by the natural temperament, which the language used by Ptolemy [37] leads us to regard as the true division, the scale would exhibit the intervals—
| g | 5/4 | b | 6/5 | d | 7/6 | f | 8/7 | g |
which give the natural chord of the Seventh. This however is no more than a hypothesis.
It evidently follows from all this that Ptolemy's octaves do not constitute a system of modes. They are merely the groups of notes, of the compass of an octave, which are most likely to be used in the several keys, and which Ptolemy or some earlier theorist chose to call by the names of those keys.
The extant specimens of Greek music are mostly of the second century A.D., and therefore nearly contemporary with Ptolemy. The most considerable are the melodies of three lyrical pieces or hymns, viz. (1) a hymn to Calliope, (2) a hymn to Apollo (or Helios),—both ascribed to a certain Dionysius,—and (3) a hymn to Nemesis, ascribed to Mesomedes [38]. Besides these there are (4) some short instrumental passages or exercises given by Bellermann's Anonymus (pp. 94-96). And quite recently the list has been increased by (5) an inscription discovered by Mr. W. M. Ramsay, which gives a musical setting of four short gnomic sentences, and (6) a papyrus fragment (now in the collection of the Arch-duke Rainer) of the music of a chorus in the Orestes of Euripides. These two last additions to our scanty stock of Greek music are set out and discussed by Dr. Wessely of Vienna and M. Ruelle in the Revue des Études Grecques (V. 1892, pp. 265-280), also by Dr. Otto Crusius in the Philologus, Vol. LII, pp. 160-200 [39].
The music of the three hymns is noted in the Lydian key (answering to the modern scale with one ♭). The melody of the second hymn is of the compass of an octave, the notes being those of the Perfect System from Parhypatê Hypatôn to Tritê Diezeugmenôn (f-f with one ♭). The first employs the same octave with a lower note added, viz. Hypatê Hypatôn (e): the third adds the next higher note, Paranêtê Diezeugmenôn (g). Thus the Lydian key may be said, in the case of the second hymn, and less exactly in the case of the two others, to give the Lydian or c-species of the octave in the most convenient part of the scale; just as on Ptolemy's system of Modes we should expect it to do.
This octave, however, represents merely the compass (ambitus or tessitura) of the melody: it has nothing to do with its tonality. In the first two hymns, as Bellermann pointed out, the key-note is the Hypatê Mesôn; and the mode—in the modern sense of that word—is that of the octave e-e (the Dorian mode of Helmholtz's theory). In the third hymn the key-note appears to be the Lichanos Mesôn, so that the mode is that of g-g, viz. the Hypo-phrygian.
Of the instrumental passages given by the Anonymus three are clearly in the Hypo-dorian or common mode, the Mesê (a) being the key-note. (See Gevaert, i. p. 141.) A fourth (§ 104) also ends on the Mesê, but the key-note appears to be the Parhypatê Mesôn (f). Accordingly Westphal and Gevaert assign it to the Hypo-lydian species (f-f). In Westphal's view the circumstance of the end of the melody falling, not on the key-note, but on the Third or Mediant of the octave, was characteristic of the Modes distinguished by the prefix syntono-, and accordingly the passage in question is pronounced by him to be Syntono-lydian. All those passages, however, are mere fragments of two or three bars each, and are quoted as examples of certain peculiarities of rhythm. They can hardly be made to lend much support to any theory of the Modes.
The music of Mr. Ramsay's inscription labours under the same defect of excessive shortness. If, however, we regard the four brief sentences as set to a continuous melody, we obtain a passage consisting of thirty-six notes in all, with a compass of less than an octave, and ending on the lowest note of that compass. Unlike the other extant specimens of Greek music it is written in the Ionian key—a curious fact which has not been noticed by Dr. Wessely.
INSCRIPTION WITH MUSICAL NOTES.
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