Part 6
Even in the accounts of the pseudo-Euclid and the later writers, who treat of the Species of the Octave under the names of the Keys, there is much to show that the species existed chiefly or wholly in musical theory. The seven species of the Octave are given along with the three species of the Fourth and the four species of the Fifth, neither of which appear to have had any practical application. Another indication of this may be seen in the seventh or Hypo-dorian species, which was also called Locrian and Common (ps. Eucl. p. 16 Meib.). Why should this species have more than one name? In the Perfect System it is singular in being exemplified by two different octaves, viz. that from Proslambanomenos to Mesê, and that from Mesê to Nêtê Hyperbolaiôn. Now we have seen that the higher the octave which represents a species, the lower the key of the same name. In this case, then, the upper of the two octaves answers to the Hypo-dorian key, and the lower to the Locrian. But if the species has its two names from these two keys, it follows that the names of the species are derived from the keys. The fact that the Hypo-dorian or Locrian species was also called Common is a further argument to the same purpose. It was doubtless 'common' in the sense that it characterised the two octaves which made up the Perfect System. Thus the Perfect System was recognised as the really important scale.
Another consideration, which has been overlooked by Westphal and those who follow him, is the difference between the species of the Octave in the several genera, especially the difference between the Diatonic and the Enharmonic. This is not felt as a difficulty with all the species. Thus the so-called Dorian octave _e - e_ is in the Enharmonic genus _e e* f a b b* c e_, a scale which may be regarded as the Diatonic with _g_ and _d_ omitted, and the semitones divided. But the Phrygian _d-d_ cannot pass in any such way into the Enharmonic Phrygian _c e e* f a b b* c_, which answers rather to the Diatonic scale of the species _c-c_ (the Lydian). The scholars who connect the ancient Modes with the species generally confine themselves to octaves of the Diatonic genus. In this they are supported by later Greek writers--notably, as we shall see, by Ptolemy--and by the analogy of the mediaeval Modes or Tones. But on the other side we have the repeated complaints of Aristoxenus that the earlier theorists confined themselves to Enharmonic octave scales. We have also the circumstance that the writer or compiler of the pseudo-Euclidean treatise, who is our earliest authority for the names of the species, gives these names for the Enharmonic genus only. Here, once more, we feel the difference between theory and practice. To a theorist there is no great difficulty in the terms Diatonic Phrygian and Enharmonic Phrygian meaning essentially different things. But the 'Phrygian Mode' in practical music must have been a tolerably definite musical form.
§ 25. _The Ethos of Music._
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 ([Greek: 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. [Greek: hetera gar êthê tois oxyterois, hetera tois baryterois epitrechei, kai hetera men parypatoeidesin, hetera de lichanoeidesin]). Again, under the seventh head, that of [Greek: melopoiia] or composition, he treats of the 'regions of the voice' ([Greek: topoi tês phônês]). There are three kinds of composition, he tells us (p. 28), viz. that which is akin to Hypatê ([Greek: hypatoeidês]), that which is akin to Mesê ([Greek: mesoeidês]), and that which is akin to Nêtê ([Greek: nêtoeidês]). The first part of the art of composition is the choice ([Greek: lêpsis]) which the musician is able to make of the region of the voice to be employed ([Greek: 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 ([Greek: 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 ([Greek: tropoi]) because according to the melody adopted they express the ethos of the mind. Thus it happens that composition ([Greek: 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" ([Greek: systaltikê]), viz. that by which we move painful feelings; another "expanding" ([Greek: diastaltikê]), that by which we arouse the spirit ([Greek: thymos]); and another "middle" ([Greek: 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 ([Greek: 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 ([Greek: 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' ([Greek: 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 ([Greek: 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 [Greek: topoi] or regions of the voice is clearly enough indicated.
The three regions are mentioned in the catechism of Bacchius (p. 11 Meib.): [Greek: topous] (MSS. [Greek: tropous]) [Greek: de tês phônês posous legomen einai? treis. tinas? toutous; oxyn, meson, baryn.] The varieties of ethos also appear (p. 14 Meib.): [Greek: 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.
§ 26. _The Ethos of the Genera and Species._
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 ([Greek: 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: [Greek: kai hetera men parypatoeidesin, hetera de lichanoeidesin.] By [Greek: parypatoeideis] and [Greek: lichanoeideis] he means all the moveable notes ([Greek: 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 ([Greek: arrhenôpon d' esti kai austêroteron]), the Chromatic sweet and plaintive ([Greek: hêdiston te kai goeron]), the Enharmonic stirring and pleasing ([Greek: 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[1].
§ 27. _The Musical Notation._
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 ([Greek: 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 ([Greek: parasêmantikê]) had come to be considered by some persons identical with the science of music ([Greek: 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.
[Footnote 1: Ptol. _Harm._ ii. 6. After drawing a distinction between difference of key as affecting the whole of a melody or piece of music and as a means of change in the course of it--the distinction, in short, between transposition and modulation proper--he says of the latter: [Greek: hautê de hôsper ekpiptein autên] (sc. [Greek: tên aisthêsin]) [Greek: poiei tou synêthous kai prosdokômenou melous, hotan epi pleon men syneirêtai to akolouthon, metabainê de pê pros heteron eidos, êtoi kata to genos ê kata tên tasin.] That is to say, the sense of change is produced by a change of genus or of pitch. A change of _species_ is not suggested. So Dionys. Hal. _De Comp. Verb._ c. 19 [Greek: hoi de ge dithyrambopoioi kai tous tropous] (keys) [Greek: meteballon, Dôrikous te kai Phrygious kai Lydious en tô autô asmati poiountes; kai tas melôdias exêllatton, tote men enarmonious poiountes, k.t.l.]]
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 [Symbols: Li], and two forms of lambda, [Symbols: <] and [Symbols: F], the latter of which is peculiar to the alphabet of Argos. Of the other characters [Symbols: M], which stands for alpha, is best derived from the archaic form [Symbols: NJ]. For beta we find [Symbols: c], which may come from an archaic form of the letter[1]. The character [Symbols: El], as Westphal shows, is for [Symbols:7], or delta with part of one side left out. Similarly the ancient [Symbols: O], when the circle was incomplete, yielded the character [Symbols: C]. The crooked iota ([Symbols:'-i]) appears as [Symbols:h]. The two forms of lambda serve for different notes, thus bringing the number of symbols up to fifteen. Besides these there are two characters, [Symbols: O] and [Symbols: 6], 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:
[Symbols: H h E r P F C K r l < E N Z M] [Greek: ê i e l^1 g m [digamma] th k d l^2 b n z a] _a b c d e f g a b c d e f g a_
[Footnote 1: Since this was written I have learned from Mr. H. S. Jones that the form [Symbols:E] for beta occurs on an inscription dated about 500 B.C., viz. Count Tyszkiewicz's bronze plate, published simultaneously by Robert in the _Monumenti Antichi pubblicati per cura della reale Accademia dei Lincei_, i. pp. 593 (with plate), and Fröhner in the _Revue Archéologique_, 1891 July-August, pp. 51 ff. Pl. xix. Mr. Jones points out that this [Symbols:E] connects the crescent beta ([Symbols: C]) of Naxos, Delos, &c. with the common form, and is evidently therefore an early form of the letter.
I take this opportunity of thanking Mr. Jones for other help, especially in regard to the subject of this section.]
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, [Symbols: E], stands for our _c_: and accordingly [Symbols: W] ([Symbols: E] [Greek: anestrammenon] or [Greek: hyption]) stands for _c*_, and [Symbols: 3] ([Symbols: E] [Greek: apestrammenon]) for _c[Symbols: #]_. The Enharmonic scale _c-c*-c[Symbols: #]-f_ is therefore written [Symbols: E W 3 f'], the two modifications of the letter [Symbols: E] representing the two 'moveable' notes of the tetrachord. Similarly we have the triads [Symbols: h I rl, F "q, Cup, KY>1, <V>, CUm]. As some letters do not admit of this kind of differentiation, other methods are employed. Thus [Symbols: D] is made to yield the forms [Symbols: ri] (for [Symbols: 7]) [Symbols: L A]: from [Symbols: H] (or [Symbols: B]) are obtained the forms [Symbols: Li] and [Symbols: R]: and from [Symbols: Z] (or [Symbols: i]) the forms [Symbols: A] and [Symbols: A]. The modifications of [Symbols: N] are [Symbols: /] and [Symbols: \]: those of [Symbols: 'I] are [Symbols: A] and [Symbols: N].
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[Symbols: #] d f_ is written [Symbols: E W 3' /`'].
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 ([Greek: 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 [Symbols: h E H r], but [Symbols: Fix I-r]: and _d e[Symbols: b] f g_ is not [Symbols: I], but [Symbols: I-tl F].
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 ([Greek: 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, [Greek: 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 higher and lower _e_ are denoted by [Greek: b] and [Greek: g] " " " _c_ " " [Greek: d] " [Greek: e] " " " _g_ " " [Symbol: digamma] " [Greek: z] " " " _a_ " " [Greek: ê] " [Greek: th] " " " _b_ " " [Greek: i] " [Greek: k] " " " _d_ " " [Greek: l^1] " [Greek: l^2] " " " _f_ " " [Greek: m] " [Greek: n]
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 ([Symbols: a] and [Symbols: e]), or by the use of accents ([Symbols:?'], &c.). The Hypo-dorian and Hypo-phrygian, which employ the new characters [Symbols: a] and [Symbols: e], 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 ([Greek: 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:--