Part 3

The statement that the 'relaxed Lydian' was the opposite of the Mixo-lydian, and similar to the Ionian, has given rise to much speculation. In what sense, we naturally ask, can a key or a mode be said to be 'opposite' or 'similar' to another? I venture to think that it is evidently a mere paraphrase of Plato's language. The relaxed Lydian is opposed to the Mixo-lydian because it is at the other end of the scale in pitch; and it is similar to the Ionian because the two are classed together (as [Greek: chalarai]) by Plato.

The Mixo-lydian, according to Aristoxenus, was employed by the tragic poets in close union with the Dorian mode ([Greek: labontas syzeuxai tê Dôristi]). The fact that the Mixo-lydian was just a Fourth higher than the Dorian must have made the transition from the one to the other a natural and melodious one. As Aristoxenus suggested, it would be especially used to mark the passage from grandeur and dignity to pathos which is the chief characteristic of tragedy ([Greek: hê men to megaloprepes kai axiômatikon apodidôsin, hê de to pathêtikon, memiktai de dia toutôn tragôdia]). It is worth noticing that this relation obtained in the scheme of the musicians who did not arrange the keys according to the diatonic scale, but in some way suggested by the form of the flute ([Greek: hoi pros tên tôn aulôn trypêsin blepontes]). It may therefore be supposed to have been established before the relative pitch of other keys had been settled.

[Footnote 1: It seems not impossible that this difficulty with regard to the 'slack Lydian' and Hypo-lydian may be connected with the contradiction in the statement of Aristoxenus about the schemes of keys in his time (p. 18). According to that account, if the text is sound, some musicians placed the Mixo-lydian a semitone below the Dorian--the Hypo-dorian being again a semitone lower. In this scheme, then, the Mixo-lydian held the place of the later Hypo-lydian. The conjecture may perhaps be hazarded, that this lower Mixo-lydian somehow represents Plato's 'slack Lydian,' and eventually passed into the Hypo-lydian.]

So far the passage of Plutarch goes to confirm the view of the Platonic modes according to which they were distinguished chiefly, if not wholly, by difference of pitch. We come now, however, to a statement which apparently tends in the opposite direction, viz. that a certain Lamprocles of Athens noticed that in the Mixo-lydian mode the Disjunctive Tone ([Greek: diazeuxis]) was at the upper end of the scale ([Greek: epi to oxy]), and reformed the scale accordingly. This must refer to an octave scale of the form _b c d e f g a b_, consisting of the two tetrachords _b-e_ and _e-a_, and the tone _a-b_. Such an octave may or may not be in the Mixo-lydian key: it is certainly of the Mixo-lydian species (p. 57).

In estimating the value of this piece of evidence it is necessary to remark, in the first place, that the authority is no longer that of Aristoxenus, but of a certain Lysis, of whom nothing else seems to be known. That he was later than Aristoxenus is made probable by his way of describing the Mixo-lydian octave, viz. by reference to the notes in the Perfect System by which it is exemplified (Hypatê Hypatôn to Paramesê). In Aristoxenus, as we shall see (p. 31), the primitive octave (from Hypatê to Nêtê) is the only scale the notes of which are mentioned by name. But even if the notice is comparatively early, it is worth observing that the Mixo-lydian scale thus ascribed to Lamprocles consists of two tetrachords of the normal type, viz. with the semitone or [Greek: pyknon] at the lower end of the scale (Diatonic _e f g a_, Enharmonic _e e* f a_). The difference is that they are conjunct, whereas in the primitive standard octave (_e - e_) the tetrachords are disjunct (_e-a b-e_). This, however, is a variety which is provided for by the tetrachord Synêmmenôn in the Perfect System, and which may have been allowed in the less complete scales of earlier times. In any case the existence of a scale of this

## particular form does not prove that the octaves of other species were

recognised in the same way.

(2) In another passage (c. 6) Plutarch says of the ancient music of the cithara that it was characterised by perfect simplicity. It was not allowed, he tells us, to change the mode ([Greek: metapherein tas harmonias]) or the rhythm: for in the primitive lyrical compositions called 'Nomes' ([Greek: nomoi]) they preserved in each its proper pitch ([Greek: tên oikeian tasin]). Here the word [Greek: tasis] indicates that by [Greek: harmoniai] Plutarch (or the older author from whom he was quoting) meant particular _keys_. This is fully confirmed by the use of [Greek: tonos] in a passage a little further on (c. 8), where Plutarch gives an account of an innovation in this matter made by Sacadas of Argos (fl. 590 B.C.). 'There being three keys ([Greek: tonoi]) in the time of Polymnastus and Sacadas, viz. the Dorian, Phrygian and Lydian, it is said that Sacadas composed a strophe in each of these keys, and taught the chorus to sing them, the first in the Dorian, the second in the Phrygian, and the third in the Lydian key: and this composition was called the "three-part Nome" ([Greek: nomos trimerês]) on account of the change of key.' In Westphal's _Harmonik und Melopöie_ (ed. 1863, p. 76, cp. p. 62) he explains this notice of the ancient modes ([Greek: harmoniai], _Tonarten_), observing that the word [Greek: tonos] is there used improperly for what the technical writers call [Greek: eidos tou dia pasôn].

(3) In a somewhat similar passage of the same work (c. 19) Plutarch is contending that the fewness of the notes in the scales used by the early musicians did not arise from ignorance, but was characteristic of their art, and necessary to its peculiar ethos. Among other points he notices that the tetrachord Hypatôn was not used in Dorian music ([Greek: en tois Dôriois]), and this, he says, was not because they did not know of that tetrachord--for they used it in other keys ([Greek: tonoi])--but they left it out in the Dorian key for the sake of preserving its ethos, the beauty of which they valued ([Greek: dia dê tên tou êthous phylakên aphêroun tou Dôriou tonou, timôntes to kalon autou]). Here again Westphal (_Aristoxenus_, p. 476) has to take [Greek: tonos] to mean [Greek: harmonia] or 'mode' (in his language _Tonart_, not _Transpositionsscala_). For in the view of those who distinguish [Greek: harmonia] from [Greek: tonos] it is the [Greek: harmonia] upon which the ethos of music depends. Plutarch himself had just been saying (in c. 17) that Plato preferred the Dorian [Greek: harmonia] on account of its grave and elevated character ([Greek: epei poly to semnon estin en tê Dôristi, tautên proutimêsen]). On the other hand the usual sense of [Greek: tonos] is supported by the consideration that the want of the tetrachord Hypatôn would affect the pitch of the scale rather than the succession of its intervals.

It seems to follow from a comparison of these three passages that Plutarch was not aware of any difference of meaning between the words [Greek: tonos] and [Greek: harmonia], or any distinction in the scales of Greek music such as has been supposed to be conveyed by these words. Another synonym of [Greek: tonos] which becomes very common in the later writers on music is the word [Greek: tropos][1]. In the course of the passage of Plutarch already referred to (_De Mus._ c. 17) it is applied to the Dorian mode, which Plutarch has just called [Greek: harmonia]. As [Greek: tropos] is always used in the later writers of the keys ([Greek: tonoi]) of Aristoxenus, this may be added to the places in which [Greek: harmonia] has the same meaning.

§ 13. _Modes employed on different Instruments._

In the anonymous treatise on music published by Bellermann[2] (c. 28), we find the following statement regarding the use of the modes or keys in the scales of different instruments:

'The Phrygian mode ([Greek: harmonia]) has the first place on wind-instruments: witness the first discoverers--Marsyas, Hyagnis, Olympus--who were Phrygians. Players on the water-organ ([Greek: hydraulai]) use only six modes ([Greek: tropoi]), viz. Hyper-lydian, Hyper-ionian, Lydian, Phrygian, Hypo-lydian, Hypo-phrygian. Players on the cithara tune their instrument to these four, viz. Hyper-ionian, Lydian, Hypo-lydian, Ionian. Flute-players employ seven, viz. Hyper-aeolian, Hyper-ionian, Hypo-lydian, Lydian, Phrygian, Ionian, Hypo-phrygian. Musicians who concern themselves with orchestic (choral music) use seven, viz. Hyper-dorian, Lydian, Phrygian, Dorian, Hypo-lydian, Hypo-phrygian, Hypo-dorian.

[Footnote 1: Aristides Quintilianus uses [Greek: tropos] as the regular word for 'key:' e.g. in p. 136 [Greek: en tê tôn tropôn, hous kai tonous ekalesamen, ekthesei]. So Alypius (p. 2 Meib.) [Greek: dielein eis tous legomenous tropous te kai tonous, ontas pentekaideka ton arithmon]. Also Bacchius in his catechism (p. 12 Meib.) [Greek: hoi tous treis tropous adontes tinas adousi; Lydion, Phrygion, Dôrion; hoi de tous hepta tinas; Mixolydion, Lydion, Phrygion, Dôrion, Hypolydion, Hypophrygion, Hypodôrion, toutôn poios estin oxyteros? ho Mixolydios, k.t.l.] And Gaudentius (p. 21, l. 2) [Greek: kath' hekaston tropon hê tonon]. Cp. Dionys. Hal. _De Comp. Verb._ c. 19.]

[Footnote 2: _Anonymi scriptio de Musica_ (Berlin. 1841).]

In this passage it is evident that we have to do with keys of the scheme attributed to Aristoxenus, including the two (Hyper-aeolian and Hyper-lydian) which were said to have been added after his time. The number of scales mentioned is sufficient to prove that the reference is not to the seven species of the octave. Yet the word [Greek: harmonia] is used of these keys, and with it, seemingly as an equivalent, the word [Greek: tropos].

Pollux (_Onom._ iv. 78) gives a somewhat different account of the modes used on the flute: [Greek: kai harmonia men aulêtikê Dôristi, Phrygisti, Lydios kai Iônikê, kai syntonos Lydisti hên Anthippos exeure]. But this statement, as has been already pointed out (p. 22), is a piece of antiquarian learning, and therefore takes no notice of the more recent keys, as Hyper-aeolian and Hyper-ionian, or even Hypo-phrygian (unless that is the Ionian of Pollux). The absence of Dorian from the list given by the _Anonymus_ is curious: but it seems that at that time it was equally unknown to the cithara and the water-organ. There is therefore no reason to think that the two lists are framed with reference to different things. That is to say, [Greek: harmonia] in Pollux has the same meaning as [Greek: harmonia] in the _Anonymus_, and is equivalent to [Greek: tonos].

§ 14. _Recapitulation--[Greek: harmonia] and [Greek: tonos]._

The inquiry has now reached a stage at which we may stop to consider what result has been reached, especially in regard to the question whether the two words [Greek: harmonia] and [Greek: tonos] denote two sets of musical forms, or are merely two different names for the same thing. The latter alternative appears to be supported by several considerations.

1. From various passages, especially in Plato and Aristotle, it has been shown that the modes anciently called [Greek: harmoniai] differed in pitch, and that this difference in pitch was regarded as the chief source of the peculiar ethical character of the modes.

2. The list of [Greek: harmoniai] as gathered from the writers who treat of them, viz. Plato, Aristotle, and Heraclides Ponticus, is substantially the same as the list of [Greek: tonoi] described by Aristoxenus (p. 18): and moreover, there is an agreement in detail between the two lists which cannot be purely accidental. Thus Heraclides says that certain people had found out a new [Greek: harmonia], the Hypo-phrygian; and Aristoxenus speaks of the Hypo-phrygian [Greek: tonos] as a comparatively new one. Again, the account which Aristoxenus gives of the Hypo-dorian [Greek: tonos] as a key immediately below the Dorian agrees with what Heraclides says of the Hypo-dorian [Greek: harmonia], and also with the mention of Hypo-dorian and Hypo-phrygian (but not Hypo-lydian) in the Aristotelian _Problems_. Once more, the absence of Ionian from the list of [Greek: tonoi] in Aristoxenus is an exception which proves the rule: since the name of the Ionian [Greek: harmonia] is similarly absent from Aristotle.

3. The usage of the words [Greek: harmonia] and [Greek: tonos] is never such as to suggest that they refer to different things. In the earlier writers, down to and including Aristotle, [Greek: harmonia] is used, never [Greek: tonos]. In Aristoxenus and his school we find [Greek: tonos], and in later writers [Greek: tropos], but not [Greek: harmonia]. The few writers (such as Plutarch) who use both [Greek: tonos] and [Greek: harmonia] do not observe any consistent distinction between them. Those who (like Westphal) believe that there was a distinction, are obliged to admit that [Greek: harmonia] is occasionally used for [Greek: tonos] and conversely.

4. If a series of names such as Dorian, Phrygian, Lydian and the rest were applied to two sets of things so distinct from each other, and at the same time so important in the practice of music, as what we now call modes and keys, it is incredible that there should be no trace of the double usage. Yet our authors show no sense even of possible ambiguity. Indeed, they seem to prefer, in referring to modes or keys, to use the adverbial forms [Greek: dôristi], [Greek: phrygisti], &c., or the neuter [Greek: ta dôria], [Greek: ta phrygia], &c., where there is nothing to show whether 'mode' or 'key,' [Greek: harmonia] or [Greek: tonos], is intended.

§ 15. _The Systems of Greek Music._

The arguments in favour of identifying the primitive national Modes ([Greek: harmoniai]) with the [Greek: tonoi] or keys may be reinforced by some considerations drawn from the history and use of another ancient term, namely [Greek: systêma].

A System ([Greek: systêma]) is defined by the Greek technical writers as a group or complex of intervals ([Greek: to ek pleionôn ê henos diastêmatôn synkeimenon] Ps. Eucl.). That is to say, any three or more notes whose _relative_ pitch is fixed may be regarded as forming a particular System. If the notes are such as might be used in the same melody, they are said to form a _musical_ System ([Greek: systêma emmeles]). As a matter of abstract theory it is evident that there are very many combinations of intervals which in this sense form a musical System. In fact, however, the variety of systems recognised in the theory of Greek music was strictly limited. The notion of a small number of scales, of a particular compass, available for the use of the musician, was naturally suggested by the ancient lyre, with its fixed and conventional number of strings. The word for _string_ ([Greek: chordê]) came to be used with the general sense of a _note_ of music; and in this way the several strings of the lyre gave their names to the notes of the Greek gamut[1].

§ 16. _The Standard Octachord System._

In the age of the great melic poets the lyre had no more than seven strings: but the octave was completed in the earliest times of which we have accurate information. The scale which is assumed as matter of common knowledge in the Aristotelian _Problems_ and the _Harmonics_ of Aristoxenus consists of eight notes, named as follows from their place on the lyre:

Nêtê ([Greek: neatê] or [Greek: nêtê], lit. 'lowest,' our 'highest'). Paranêtê ([Greek: paranêtê], 'next to Nêtê'). Tritê ([Greek: tritê], _i.e._ 'third' string). Paramesê ([Greek: paramesê] or [Greek: paramesos], 'next to Mesê'). Mesê ([Greek: mesê], 'middle string'). Lichanos ([Greek: lichanos], _i.e._ 'forefinger' string). Parhypatê ([Greek: parypatê]). Hypatê ([Greek: hypatê], lit. 'uppermost,' our 'lowest').

It will be seen that the conventional sense of high and low in the words [Greek: hypatê] and [Greek: neatê] was the reverse of the modern usage.

The musical scale formed by these eight notes consists of two _tetrachords_ or scales of four notes, and a major tone. The lower of the tetrachords consists of the notes from Hypatê to Mesê, the higher of those from Paramesê to Nêtê: the interval between Mesê and Paramesê being the so-called _Disjunctive Tone_ ([Greek: tonos diazeuktikos]). Within each tetrachord the intervals depend upon the _Genus_ ([Greek: genos]). Thus the four notes just mentioned--Hypatê, Mesê, Paramesê, Nêtê--are the same for every genus, and accordingly are called the 'standing' or 'immoveable' notes ([Greek: phthongoi hestôtes, akinêtoi]), while the others vary with the genus, and are therefore 'moveable' ([Greek: pheromenoi]).

[Footnote 1: This is especially evident in the case of the Lichanos; as was observed by Aristides Quintilianus, who says (p. 10 Meib.): [Greek: hai kai tô genei lichanoi prosêgoreuthêsan, homônymôs tô plêttonti daktylô tên êchousan autas chordên onomastheisai]. But Tritê also is doubtless originally the 'third string' rather than the 'third note.']

In the ordinary Diatonic genus the intervals of the tetrachords are, in the ascending order, semitone + tone + tone: _i.e._ Parhypatê is a semitone above Hypatê, and Lichanos a tone above Parhypatê. In the Enharmonic genus the intervals are two successive quarter-tones ([Greek: diesis]) followed by a ditone or major Third: consequently Parhypatê is only a quarter of a tone above Hypatê, and Lichanos again a quarter of a tone above Parhypatê. The group of three notes separated in this way by small intervals (viz. two successive quarter-tones) is called a [Greek: pyknon]. If we use an asterisk to denote that a note is raised a quarter of a tone, these two scales may be represented in modern notation as follows:

_Diatonic._ _Enharmonic._

e =Nêtê= \ e =Nêtê= \ d Paranêtê } ( c Paranêtê } c Tritê } +---( b* Tritê } b =Paramesê= / | ( b =Paramesê= / a =Mesê= \ | a =Mesê= \ g Lichanos } | ( f Lichanos } f Parhypatê } | +-( e* Parhypatê } e =Hypatê= / | | ( e =Hypatê= / | | [Greek: pyknon] [Greek: pyknon]

In the Chromatic genus and its varieties the division is of an intermediate kind. The interval between Lichanos and Mesê 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 passages from Aristotle and Aristoxenus to show that this is the succession of intervals assumed by them. The question is asked in the Aristotelian _Problems_ (xix. 4), why Parhypatê is difficult to sing, while Hypatê 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 Paramesê was left out, and consequently the Mesê became the lowest note of the upper [Greek: pyknon], _i.e._ the group of 'close' notes consisting of Mesê, Tritê, and Paranêtê. Similarly Aristoxenus (_Harm._ p. 23) observes that the 'space' of the Lichanos, _i.e._ the limit within which it varies in the different genera, is a tone while the space of the Parhypatê is only a diesis, for it is never nearer Hypatê 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 passage of the Aristotelian _Problems_:

_Probl._ xix. 47 [Greek: dia ti hoi archaioi heptachordous poiountes tas harmonias tên hypatên all' ou tên nêtên katelipon: hê ou tên] [Greek: hypatên] (leg. [Greek: nêtên]), [Greek: alla tên nyn paramesên kaloumenên aphêroun kai to toniaion diastêma; echrônto de tê eschatê mesê tou epi to oxy pyknou; did kai mesên autên prosêloreusan [hê] oti ên tou men anô tetrachordon teleutê, tou de katô archê, kai meson eiche logon tonô tôn akrôn?]

'Why did the ancient seven-stringed scales include Hypatê but not Nêtê? Or should we say that the note omitted was not Nêtê, but the present Paramesê and the interval of a tone (_i.e._ the disjunctive tone)? The Mesê, then, was the lowest note of the upper [Greek: pyknon]: whence the name [Greek: mesê], 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 pasôn], not [Greek: di' oktô],--as the Fourth is [Greek: dia tessarôn], the Fifth [Greek: dia pente]. The answer suggested is that there were anciently seven strings, and that Terpander left out the Tritê and added the Nêtê. That is to say, Terpander increased the compass 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 oktô] was inappropriate.

Among later writers who confirm this account we may notice Nicomachus, p. 7 Meib. [Greek: mesê dia tessarôn pros amphotera en tê heptachordô kata to palaion diestôsa]: and p. 20 [Greek: tê toinyn archaiotropô lyra toutesti tê heptachordô, kata synaphên ek duo tetrachordôn synestôsê 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 compass less than an octave by one tone; and (2) a scale of the compass of an octave, but wanting a note, viz. the note above Mesê. 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: systêma 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: systêma 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 Hypatê we have a new tetrachord Hypatôn ([Greek: tetrachordon hypatôn]), the notes of which are accordingly called Hypatê Hypatôn, Parhypatê Hypatôn, and Lichanos Hypatôn: and similarly above Nêtê we have a tetrachord Hyperbolaiôn. Finally the octave downwards from Mesê is completed by the addition of a note appropriately called Proslambanomenos.

The Lesser Perfect System ([Greek: systêma teleion elasson]) is apparently based upon the ancient heptachord which consisted of two 'conjunct' tetrachords meeting in the Mesê. 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 constitute the Perfect and 'unmodulating' System ([Greek: systêma teleion ametabolon]), which may be represented in modern notation[1] as follows:

a Nêtê Hyperbolaiôn \ Tetrachord g Paranêtê Hyperbolaiôn } Hyperbolaiôn f Tritê Hyperbolaiôn / e Nêtê Diezeugmenôn d Paranêtê Diezeugmenôn \ Tetrachord c Tritê Diezeugmenôn } Diezeugmenôn b Paramesê / d Nêtê Synêmmenôn \ Tetrachord c Paranêtê Synêmmenôn } Synêmmenôn b flat Tritê Synêmmenôn/ a Mesê \ g Lichanos Mesôn } Tetrachord f Parhypatê Mesôn } Mesôn e Hypatê Mesôn / d Lichanos Hypatôn \ Tetrachord c Parhypatê Hypatôn } Hypatôn b Hypatê Hypatôn / a Proslambanomenos