The Modes of Ancient Greek Music Part 3

_Diatonic._ _Enharmonic._

e =Nete= e =Nete= d Paranete } ( c Paranete } c Trite } +---( b* Trite } b =Paramese= / | ( b =Paramese= / a =Mese= | a =Mese= g Lichanos } | ( f Lichanos } f Parhypate } | +-( e* Parhypate } e =Hypate= / | | ( e =Hypate= / | | [Greek: pyknon] [Greek: pyknon]

In the Chromatic genus and its varieties the division is of an intermediate kind. The interval between Lichanos and Mese is more than one tone, but less than two: and the two other intervals, as in the enharmonic, are equal.

The most characteristic feature of this scale, in contrast to those of the modern Major and Minor, is the place of the small intervals (semitone or [Greek: pyknon]), which are always the lowest intervals of a tetrachord. It is hardly necessary to quote pa.s.sages from Aristotle and Aristoxenus to show that this is the succession of intervals a.s.sumed by them. The question is asked in the Aristotelian _Problems_ (xix. 4), why Parhypate is difficult to sing, while Hypate is easy, although there is only a diesis between them ([Greek: kaitoi diesis hekateras]). Again (_Probl._ xix. 47), speaking of the old heptachord scale, the writer says that the Paramese was left out, and consequently the Mese became the lowest note of the upper [Greek: pyknon], _i.e._ the group of 'close' notes consisting of Mese, Trite, and Paranete. Similarly Aristoxenus (_Harm._ p. 23) observes that the 's.p.a.ce' of the Lichanos, _i.e._ the limit within which it varies in the different genera, is a tone while the s.p.a.ce of the Parhypate is only a diesis, for it is never nearer Hypate than a diesis or further off than a semitone.

-- 17. _Earlier Heptachord Scales._

Regarding the earlier seven-stringed scales which preceded this octave our information is scanty and somewhat obscure. The chief notice on the subject is the following pa.s.sage of the Aristotelian _Problems_:

_Probl._ xix. 47 [Greek: dia ti hoi archaioi heptachordous poiountes tas harmonias ten hypaten all' ou ten neten katelipon: he ou ten] [Greek: hypaten] (leg. [Greek: neten]), [Greek: alla ten nyn paramesen kaloumenen apheroun kai to toniaion diastema; echronto de te eschate mese tou epi to oxy pyknou; did kai mesen auten proseloreusan [he] oti en tou men ano tetrachordon teleute, tou de kato arche, kai meson eiche logon tono ton akron?]

'Why did the ancient seven-stringed scales include Hypate but not Nete? Or should we say that the note omitted was not Nete, but the present Paramese and the interval of a tone (_i.e._ the disjunctive tone)? The Mese, then, was the lowest note of the upper [Greek: pyknon]: whence the name [Greek: mese], because it was the end of the upper tetrachord and beginning of the lower one, and was in pitch the middle between the extremes.'

This clearly implies two conjunct tetrachords--

[Music: _e f g a a# c d_ ---- /----- /]

In another place (_Probl._ xix. 32) the question is asked, why the interval of the octave is called [Greek: dia pason], not [Greek: di'

okto],--as the Fourth is [Greek: dia tessaron], the Fifth [Greek: dia pente]. The answer suggested is that there were anciently seven strings, and that Terpander left out the Trite and added the Nete.

That is to say, Terpander increased the compa.s.s of the scale from the ancient two tetrachords to a full Octave; but he did not increase the number of strings to eight. Thus he produced a scale like the standard octave, but with one note wanting; so that the term [Greek: di okto] was inappropriate.

Among later writers who confirm this account we may notice Nicomachus, p. 7 Meib. [Greek: mese dia tessaron pros amphotera en te heptachordo kata to palaion diestosa]: and p. 20 [Greek: te toinyn archaiotropo lyra toutesti te heptachordo, kata synaphen ek duo tetrachordon synestose k.t.l.]

It appears then that two kinds of seven-stringed scales were known, at least by tradition: viz. (1) a scale composed of two conjunct tetrachords, and therefore of a compa.s.s less than an octave by one tone; and (2) a scale of the compa.s.s of an octave, but wanting a note, viz. the note above Mese. The existence of this incomplete scale is interesting as a testimony to the force of the tradition which limited the number of strings to seven.

-- 18. _The Perfect System._

The term 'Perfect System' ([Greek: systema teleion]) is applied by the technical writers to a scale which is evidently formed by successive additions to the heptachord and octachord scales explained in the preceding chapter. It may be described as a combination of two scales, called the Greater and Lesser Perfect System.

The Greater Perfect System ([Greek: systema teleion meizon]) consists of two octaves formed from the primitive octachord System by adding a tetrachord at each end of the scale. The new notes are named like those of the adjoining tetrachord of the original octave, but with the name of the tetrachord added by way of distinction. Thus below the original Hypate we have a new tetrachord Hypaton ([Greek: tetrachordon hypaton]), the notes of which are accordingly called Hypate Hypaton, Parhypate Hypaton, and Lichanos Hypaton: and similarly above Nete we have a tetrachord Hyperbolaion. Finally the octave downwards from Mese is completed by the addition of a note appropriately called Proslambanomenos.

The Lesser Perfect System ([Greek: systema teleion ela.s.son]) is apparently based upon the ancient heptachord which consisted of two 'conjunct' tetrachords meeting in the Mese. This scale was extended downwards in the same way as the Greater System, and thus became a scale of three tetrachords and a tone.

These two Systems together const.i.tute the Perfect and 'unmodulating'

System ([Greek: systema teleion ametabolon]), which may be represented in modern notation[1] as follows:

a Nete Hyperbolaion Tetrachord g Paranete Hyperbolaion } Hyperbolaion f Trite Hyperbolaion / e Nete Diezeugmenon d Paranete Diezeugmenon Tetrachord c Trite Diezeugmenon } Diezeugmenon b Paramese / d Nete Synemmenon Tetrachord c Paranete Synemmenon } Synemmenon b flat Trite Synemmenon/ a Mese g Lichanos Meson } Tetrachord f Parhypate Meson } Meson e Hypate Meson / d Lichanos Hypaton Tetrachord c Parhypate Hypaton } Hypaton b Hypate Hypaton / a Proslambanomenos

[Footnote 1: The correspondence between ancient and modern musical notation was first determined in a satisfactory way by Bellermann (_Die Tonleitern und Musiknoten der Griechen_), and Fortlage (_Das musicalische System der Griechen_).]

No account of the Perfect System is given by Aristoxenus, and there is no trace in his writings of an extension of the standard scale beyond the limits of the original octave. In one place indeed (_Harm._ p. 8, 12 Meib.) Aristoxenus promises to treat of Systems, 'and among them of the perfect System' ([Greek: peri te ton allon kai tou teleiou]). But we cannot a.s.sume that the phrase here had the technical sense which it bore in later writers. More probably it meant simply the octave scale, in contrast to the tetrachord and pentachord--a sense in which it is used by Aristides Quintilia.n.u.s, p.

11 Meib. [Greek: synemmenon de eklethe to holon systema hoti to prokeimeno teleio to mechri meses syneptai], 'the whole scale was called conjunct because it is conjoined to the complete scale that reaches up to Mese' (_i.e._ the octave extending from Proslambanomenos to Mese). So p. 16 [Greek: kai ha men auton esti teleia, ha d' ou, atele men tetrachordon, pentachordon, teleion de oktachordon.] This is a use of [Greek: teleios] which is likely enough to have come from Aristoxenus. The word was doubtless applied in each period to the most complete scale which musical theory had then recognised.

Little is known of the steps by which this enlargement of the Greek scale was brought about. We shall not be wrong in conjecturing that it was connected with the advance made from time to time in the form and compa.s.s of musical instruments[1]. Along with the lyre, which kept its primitive simplicity as the instrument of education and everyday use, the Greeks had the cithara ([Greek: kithara]), an enlarged and improved lyre, which, to judge from the representations on ancient monuments, was generally seen in the hands of professional players ([Greek: kitharodoi]). The development of the cithara showed itself in the increase, of which we have good evidence even before the time of Plato, in the number of the strings.

[Footnote 1: This observation was made by ancient writers, _e.g._ by Adrastus (Peripatetic philosopher of the second cent. A.D.): [Greek: epeuxemenes de tes mousikes kai polychordon kai polyphthongon gegonoton organon to proslephthenai kai epi to bary kai epi to oxy tois pro[:y]parchousin okto phthongois allous pleionas, h.o.m.os k.t.l.

(Theon Smyrn. c. 6).]

The poet Ion, the contemporary of Sophocles, was the author of an epigram on a certain ten-stringed lyre, which seems to have had a scale closely approaching that of the Lesser Perfect System[1]. A little later we hear of the comic poet Pherecrates attacking the musician Timotheus for various innovations tending to the loss of primitive simplicity, in particular the use of twelve strings[2].

According to a tradition mentioned by Pausanias, the Spartans condemned Timotheus because in his cithara he had added four strings to the ancient seven. The offending instrument was hung up in the Scias (the place of meeting of the Spartan a.s.sembly), and apparently was seen there by Pausanias himself (Paus. iii. 12, 8).

[Footnote 1: The epigram is quoted in the pseudo-Euclidean _Introductio_, p. 19 (Meib.): [Greek: ho de] (sc. [Greek: Ion]) [Greek: en dekachordo lyra] (_i.e._ in a poem on the subject of the ten-stringed lyre):--

[Greek: ten dekabamona taxin echousa tas symphonousas harmonias triodous; prin men s' heptatonon psallon dia tessara pantes h.e.l.lenes, spanian mousan aeiramenoi.]

'The triple ways of music that are in concord' must be the three conjunct tetrachords that can be formed with ten notes (_b c d e f g a b-flat c d_). This is the scale of the Lesser Perfect System before the addition of the Proslambanomenos.]

[Footnote 2: Pherecrates [Greek: cheiron] fr. 1 (quoted by Plut. _de Mus._ c. 30). It is needless to refer to the other traditions on the subject, such as we find in Nicomachus (_Harm._ p. 35) and Boethius.]

A similar or still more rapid development took place in the flute ([Greek: aulos]). The flute-player p.r.o.nomus of Thebes, who was said to have been one of the instructors of Alcibiades, invented a flute on which it was possible to play in all the modes. 'Up to his time,'

says Pausanias (ix. 12, 5), 'flute-players had three forms of flute: with one they played Dorian music; a different set of flutes served for the Phrygian mode ([Greek: harmonia]); and the so-called Lydian was played on another kind again. p.r.o.nomus was the first who devised flutes fitted for every sort of mode, and played melodies different in mode on the same flute.' The use of the new invention soon became general, since in Plato's time the flute was the instrument most distinguished by the multiplicity of its notes: cp. Rep. p. 399 [Greek: ti de? aulopoious e auletas paradexei eis ten polin? e ou touto polychordotaton?] Plato may have had the invention of p.r.o.nomus in mind when he wrote these words.

With regard to the order in which the new notes obtained a place in the schemes of theoretical musicians we have no trustworthy information. The name [Greek: proslambanomenos], applied to the lowest note of the Perfect System, points to a time when it was the last new addition to the scale. Plutarch in his work on the _Timaeus_ of Plato ([Greek: peri tes en Timaio psychogonias]) speaks of the Proslambanomenos as having been added in comparatively recent times (p. 1029 _c_ [Greek: hoi de neoteroi ton proslambanomenon tono diapheronta tes hypates epi to bary taxantes to men holon diastema dis dia pason epoiesan]). The rest of the Perfect System he ascribes to 'the ancients' ([Greek: tous palaious ismen hypatas men dyo, treis de netas, mian de mesen kai mian paramesen t.i.themenous]). An earlier addition--perhaps the first made to the primitive octave--was a note called Hyperhypate, which was a tone below the old Hypate, in the place afterwards occupied on the Diatonic scale by Lichanos Hypaton.

It naturally disappeared when the tetrachord Hypaton came into use.

It is only mentioned by one author, Thrasyllus (quoted by Theon Smyrnaeus, cc. 35-36[1]).

[Footnote 1: The term [Greek: hyperypate] had all but disappeared from the text of Theon Smyrnaeus in the edition of Bullialdus (Paris, 1644), having been corrupted into [Greek: hypate] or [Greek: parypate] in every place except one (p. 141, 3). It has been restored from MSS. in the edition of Hiller (Teubner, Leipzig, 1878). The word occurs also in Aristides Quintilia.n.u.s (p. 10 Meib.), where the plural [Greek: hyperypatai] is used for the notes below Hypate, and in Boethius (_Mus._ i. 20).

It may be worth noticing also that Thrasyllus uses the words [Greek: diezeugmene] and [Greek: hyperbolaia] in the sense of [Greek: nete diezeugmenon] and [Greek: nete hyperbolaion] (Theon Smyrn. _l. c._).]

The notes of the Perfect System, with the intervals of the scale which they formed, are fully set out in the two treatises that pa.s.s under the name of the geometer Euclid, viz. the _Introductio Harmonica_ and the _Sectio Canonis_. Unfortunately the authorship of both these works is doubtful[1]. All that we can say is that if the Perfect System was elaborated in the brief interval between the time of Aristotle and that of Euclid, the materials for it must have already existed in musical practice.

[Footnote 1: _The Introduction to Harmonics_ ([Greek: eisagoge harmonike]) which bears the name of Euclid in modern editions (beginning with J. Pena, Paris, 1557) cannot be his work. In some MSS. it is ascribed to Cleonides, in others to Pappus, who was probably of the fourth century A.D. The author is one of the [Greek: harmonikoi] or Aristoxeneans, who adopt the method of equal temperament. He may perhaps be a.s.signed to a comparatively early period on the ground that he recognises only the thirteen keys ascribed to Aristoxenus--not the fifteen keys given by most later writers (Aristides Quint., p. 22 Meib.). For some curious evidence connecting it with the name of the otherwise unknown writer Cleonides, see K. von Jan, _Die Harmonik des Aristoxenianers Kleonides_ (Landsberg, 1870). The _Section of the Canon_ ([Greek: kanonos katatome]) belongs to the mathematical or Pythagorean school, dividing the tetrachord into two major tones and a [Greek: leimma]

which is somewhat less than a semitone. In point of form it is decidedly Euclidean: but we do not find it referred to by any writer before the third century A.D.--the earliest testimony being that of Porphyry (pp. 272-276 in Wallis' edition).]

-- 19. _Relation of System and Key._

Let us now consider the relation between this fixed or standard scale and the varieties denoted by the terms [Greek: harmonia] and [Greek: tonos].

With regard to the [Greek: tonoi] or Keys of Aristoxenus we are not left in doubt. A system, as we have seen, is a series of notes whose _relative_ pitch is fixed. The key in which the System is taken fixes the absolute pitch of the series. As Aristoxenus expresses it, the Systems are melodies set at the pitch of the different keys ([Greek: tous tonous, eph' hon t.i.themena ta systemata melodeitai]). If then we speak of Hypate or Mese (just as when we speak of a moveable Do), we mean as many different notes as there are keys: but the Dorian Hypate or the Lydian Mese has an ascertained pitch. The Keys of Aristoxenus, in short, are so many transpositions of the scale called the Perfect System.