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 tôn allôn kai
tou teleiou]). But we cannot assume 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 Quintilianus, p.
11 Meib. [Greek: synêmmenôn de eklêthê to holon systêma hoti tô
prokeimenô teleiô tô mechri mesês synêptai], 'the whole scale was
called conjunct because it is conjoined to the complete scale that
reaches up to Mesê' (_i.e._ the octave extending from
Proslambanomenos to Mesê). So p. 16 [Greek: kai ha men autôn esti
teleia, ha d' ou, atelê 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 compass 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: kitharôdoi]). 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:
epêuxêmenês de tês mousikês kai polychordôn kai polyphthongôn
gegonotôn organôn tô proslêphthênai kai epi to bary kai epi to oxy
tois pro[:y]parchousin oktô phthongois allous pleionas, homôs 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 assembly), 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: Iôn])
[Greek: en dekachordô lyra] (_i.e._ in a poem on the subject of the
ten-stringed lyre):--
[Greek: tên dekabamona taxin echousa
tas symphônousas harmonias triodous;
prin men s' heptatonon psallon dia tessara pantes
Hellênes, 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: cheirôn] 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 Pronomus 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. Pronomus 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 ê aulêtas paradexei eis tên polin? ê ou
touto polychordotaton?] Plato may have had the invention of Pronomus
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 tês en Timaiô psychogonias]) speaks of the
Proslambanomenos as having been added in comparatively recent times
(p. 1029 _c_ [Greek: hoi de neôteroi ton proslambanomenon tonô
diapheronta tês hypatês epi to bary taxantes to men holon diastêma
dis dia pasôn epoiêsan]). The rest of the Perfect System he ascribes
to 'the ancients' ([Greek: tous palaious ismen hypatas men dyo, treis
de nêtas, mian de mesên kai mian paramesên tithemenous]). An earlier
addition--perhaps the first made to the primitive octave--was a note
called Hyperhypatê, which was a tone below the old Hypatê, in the
place afterwards occupied on the Diatonic scale by Lichanos Hypatôn.
It naturally disappeared when the tetrachord Hypatôn came into use.
It is only mentioned by one author, Thrasyllus (quoted by Theon
Smyrnaeus, cc. 35-36[1]).
[Footnote 1: The term [Greek: hyperypatê] had all but disappeared
from the text of Theon Smyrnaeus in the edition of Bullialdus (Paris,
1644), having been corrupted into [Greek: hypatê] or [Greek:
parypatê] 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 Quintilianus (p. 10 Meib.), where the plural
[Greek: hyperypatai] is used for the notes below Hypatê, and in
Boethius (_Mus._ i. 20).
It may be worth noticing also that Thrasyllus uses the words [Greek:
diezeugmenê] and [Greek: hyperbolaia] in the sense of [Greek: nêtê
diezeugmenôn] and [Greek: nêtê hyperbolaiôn] (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 pass
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: eisagôgê
harmonikê]) 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 assigned 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 katatomê]) 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' hôn tithemena ta systêmata melôdeitai]). If then we
speak of Hypatê or Mesê (just as when we speak of a moveable Do), we
mean as many different notes as there are keys: but the Dorian Hypatê
or the Lydian Mesê has an ascertained pitch. The Keys of Aristoxenus,
in short, are so many transpositions of the scale called the Perfect
System.
Such being the relation of the standard System to the key, can we
suppose any different relation to have subsisted between the standard
System and the ancient 'modes' known to Plato and Aristotle under the
name of [Greek: harmoniai]?
It appears from the language used by Plato in the _Republic_ that
Greek musical instruments differed very much in the variety of modes
or [Greek: harmoniai] of which they were susceptible. After Socrates
has determined, in the passage quoted above (p. 7), that he will
admit only two modes, the Dorian and Phrygian, he goes on to observe
that the music of his state will not need a multitude of strings, or
an instrument of all the modes ([Greek: panarmonion])[1]. 'There will
be no custom therefore for craftsmen who make triangles and harps and
other instruments of many notes and many modes. How then about makers
of the flute ([Greek: aulos]) and players on the flute? Has not the
flute the greatest number of notes, and are not the scales which
admit all the modes simply imitations of the flute? There remain then
the lyre and the cithara for use in our city; and for shepherds in
the country a syrinx (pan's pipes).' The lyre, it is plain, did not
admit of changes of mode. The seven or eight strings were tuned to
furnish the scale of one mode, not of more. What then is the relation
between the mode or [Greek: harmonia] of a lyre and the standard
scale or [Greek: systêma] which (as we have seen) was based upon the
lyre and its primitive gamut?
[Footnote 1: Plato, Rep. p. 399: [Greek: ouk ara, ên d' egô,
polychordias ge oude panarmoniou hêmin deêsei en tais ôdais te kai
melesin. Ou moi, ephê, phainetai. Trigônôn ara kai pêktidôn kai
pantôn organôn hosa polychorda kai polyarmonia dêmiourgous ou
threpsomen. Ou phainometha. Ti de? aulopoious ê aulêtas paradexei eis
tên polin? ê ou touto polychordotaton, kai auta ta panarmonia aulou
tynchanei onta mimêma? Dêla dê, ê d' hos. Lyra dê soi, ên d' egô, kai
kithara leipetai, kai kata polin chrêsima; kai au kat' agrous tois
nomeusi syrinx an tis eiê.]
The [Greek: aulos] was not exactly a flute. It had a mouthpiece which
gave it the character rather of the modern oboe or clarinet: see the
_Dictionary of Antiquities_, S. V. TIBIA. The [Greek: panarmonion] is
not otherwise known, and the passage in Plato does not enable us to
decide whether it was a real instrument or only a scale or
arrangement of notes.]
If [Greek: harmonia] means 'key,' there is no difficulty. The scale
of a lyre was usually the standard octave from Hypatê to Nêtê: and
that octave might be in any one key. But if a mode is somehow
characterised by a particular succession of intervals, what becomes
of the standard octave? No one succession of intervals can then be
singled out. It may be said that the standard octave is in fact the
scale of a particular mode, which had come to be regarded as the
type, viz. the Dorian. But there is no trace of any such prominence
of the Dorian mode as this would necessitate. The philosophers who
recognise its elevation and Hellenic purity are very far from
implying that it had the chief place in popular regard. Indeed the
contrary was evidently the case[1].
[Footnote 1: The passage quoted above from the _Knights_ of
Aristophanes (p. 7) is sufficient to show that a marked preference
for the Dorian mode would be a matter for jest.]
§ 20. _Tonality of the Greek musical scale._
It may be said here that the value of a series of notes as the basis
of a distinct mode--in the modern sense of the word--depends
essentially upon the _tonality_. A single scale might yield music of
different modes if the key-note were different. It is necessary
therefore to collect the scanty notices which we possess bearing upon
the tonality of Greek music. The chief evidence on the subject is a
passage of the _Problems_, the importance of which was first pointed
out by Helmholtz[1]. It is as follows:
Arist. _Probl._ xix. 20: [Greek: Dia ti ean men tis tên mesên
kinêsê hêmôn, harmosas tas allas chordas, kai chrêtai tô
organô, ou monon hotan kata ton tês mesês genêtai phthongon
lypei kai phainetai anarmoston, alla kai kata tên allên
melôdian, ean de tên lichanon ê tina allon phthongon, tote
phainetai diapherein monon hotan kakeinê tis chrêtai? ê
eulogôs touto symbainei? panta gar ta chrêsta melê pollakis tê
mesê chrêtai, kai pantes hoi agathoi poiêtai pykna pros tên
mesên apantôsi, kan apelthôsi tachy epanerchontai, pros de
allên houtôs oudemian. kathaper ek tôn logôn eniôn
exairethentôn syndesmôn ouk estin ho logos Hellênikos, hoion
to te kai to kai, enioi de outhen lypousi, dia to tois men
anankaion einai chrêsthai pollakis, ei estai logos, tois de
mê, houtô kai tôn phthongôn hê mesê hôsper syndesmos esti, kai
malista tôn kalôn, dia to pleistakis enyparchein ton phthongon
autês.]
'Why is it that if the Mesê is altered, after the other
strings have been tuned, the instrument is felt to be out of
tune, not only when the Mesê is sounded, but through the whole
of the music,--whereas if the Lichanos or any other note is
out of tune, it seems to be perceived only when that note is
struck? Is it to be explained on the ground that all good
melodies often use the Mesê, and all good composers resort to
it frequently, and if they leave it soon return again, but do
not make the same use of any other note? just as language
cannot be Greek if certain conjunctions are omitted, such as
[Greek: te] and [Greek: kai], while others may be dispensed
with, because the one class is necessary for language, but not
the other: so with musical sounds the Mesê is a kind of
'conjunction,' especially of beautiful sounds, since it is
most often heard among these.'
[Footnote 1: _Die Lehre von den Tonempfindungen_, p. 367, ed. 1863.]
In another place (xix. 36) the question is answered by saying that
the notes of a scale stand in a certain relation to the Mesê, which
determines them with reference to it ([Greek: hê taxis hê hekastês
êdê di' ekeinên]): so that the loss of the Mesê means the loss of the
ground and unifying element of the scale ([Greek: arthentos tou
aitiou tou hêrmosthai kai tou synechontos])[1].
These passages imply that in the scale known to Aristotle, viz. the
octave _e - e_, the Mesê _a_ had the character of a Tonic or
key-note. This must have been true _a fortiori_ of the older
seven-stringed scale, in which the Mesê united the two conjunct
tetrachords. It was quite in accordance with this state of things
that the later enlargement completed the octaves from Mesê downwards
and upwards, so that the scale consisted of two octaves of the form
_a-a_. As to the question how the Tonic character of the Mesê was
shown, in what parts of the melody it was necessarily heard, and the
like, we can but guess. The statement of the _Problems_ is not
repeated by any technical writer, and accordingly it does not appear
that any rules on the subject had been arrived at. It is significant,
perhaps, that the frequent use of the Mesê is spoken of as
characteristic of _good_ melody ([Greek: panta ta chrêsta melê
pollakis tê mesê chrêtai]), as though tonality were a merit rather
than a necessity.
Another passage of the _Problems_ has been thought to show that in
Greek music the melody ended on the Hypatê. The words are these
(_Probl._ xix. 33):
[Greek: Dia ti euarmostoteron apo tou oxeos epi to bary ê apo
tou]
[Footnote 1: So in the Euclidean _Sectio Canonis_ the propositions
which deal with the 'movable' notes, viz. Paranêtê and Lichanos
(Theor. xvii) and Parhypatê and Tritê (Theor. xviii), begin by
postulating the Mesê ([Greek: estô gar mesê ho B k.t.l.]).]
[Greek: bareos epi to oxy; poteron hoti to apo tês archês
ginetai archesthai? hê gar mesê kai hêgemôn oxytatê tou
tetrachordou; to de ouk ap' archês all' apo teleutês.]
'Why is a descending scale more musical than an ascending one?
Is it that in this order we begin with the beginning,--since
the Mesê or leading note[1] is the highest of the
tetrachord,--but with the reverse order we begin with the
end?'
There is here no explicit statement that the melody ended on the
Hypatê, or even that it began with the Mesê. In what sense, then, was
the Mesê a 'beginning' ([Greek: archê]), and the Hypatê an 'end'? In
Aristotelian language the word [Greek: archê] has various senses. It
might be used to express the relation of the Mesê to the other notes
as the basis or ground-work of the scale. Other passages, however,
point to a simpler explanation, viz. that the order in question was
merely conventional. In _Probl._ xix. 44 it is said that the Mesê is
the beginning ([Greek: archê]) of one of the two tetrachords which
form the ordinary octave scale (viz. the tetrachord Mesôn); and again
in _Probl._ xix. 47 that in the old heptachord which consisted of two
conjunct tetrachords (_e-a-d_) the Mesê (_a_) was the end of the
upper tetrachord and the beginning of the lower one ([Greek: hoti ên
tou men anô tetrachordou teleutê, tou de katô archê]). In this last
passage it is evident that there is no reference to the beginning or
end of the melody.
[Footnote 1: The term [Greek: hêgemôn] or 'leading note' of the
tetrachord Mesôn, here applied to the Mesê, is found in the same
sense in Plutarch, _De Mus._ c. 11, where [Greek: ho peri ton
hêgemona keimenos tonos] means the disjunctive tone. Similarly
Ptolemy (_Harm._ i. 16) speaks of the tones in a diatonic scale as
being [Greek: en tois hêgoumenois topois], the semitones [Greek: en
tois hepomenois] (sc. of the tetrachord): and again of the ratio 5:4
(the major Third) as the 'leading' one of an Enharmonic tetrachord
([Greek: ton epitetarton hos estin hêgoumenos tou enarmoniou
genous]).]
Another instance of the use of [Greek: archê] in connexion with the
musical scale is to be found in the _Metaphysics_ (iv. 11, p. 1018
_b_ 26), where Aristotle is speaking of the different senses in which
things may be prior and posterior:
[Greek: Ta de kata taxin; tauta d' estin hosa pros ti hen
hôrismenon diestêke kata ton logon, hoion parastatês
tritostatou proteron, kai paranêtê nêtês; entha men gar ho
koryphaios, entha de hê mesê archê.]
'Other things [are prior and posterior] in _order_: viz. those
which are at a varying interval from some one definite thing;
as the second man in the rank is prior to the third man, and
the Paranêtê to the Nêtê: for in the one case the coryphaeus
is the starting-point, in the other the Mesê.'
Here the Mesê is again the [Greek: archê] or beginning, but the order
is the ascending one, and consequently the Nêtê is the end. The
passage confirms what we have learned of the relative importance of
the Mesê: but it certainly negatives any inference regarding the note
on which the melody ended.
It appears, then, that the Mesê of the Greek standard System had the
functions of a key-note in that System. In other words, the music was
in the _mode_ (using that term in the modern sense) represented by
the octave _a-a_ of the natural key--the Hypo-dorian or Common
Species. We do not indeed know how the predominant character of the
Mesê was shown--whether, for example, the melody ended on the Mesê.
The supposed evidence for an ending on the Hypatê has been shown to
be insufficient. But we may at least hold that as far as the Mesê was
a key-note, so far the Greek scale was that of the modern Minor mode
(descending). The only way of escape from this conclusion is to deny
that the Mesê of _Probl._ xix. 20 was the note which we have
understood by the term--the Mesê of the standard System. This, as we
shall presently see, is the plea to which Westphal has recourse.
§ 21. _The Species of a Scale._
The object of the preceding discussion has been to make it clear that
the theory of a system of modes--in the modern sense of the
word--finds no support from the earlier authorities on Greek music.
There is, however, evidence to show that Aristoxenus, and perhaps
other writers of the time, gave much thought to the varieties to be
obtained by taking the intervals of a scale in different order. These
varieties they spoke of as the _forms_ or _species_ ([Greek:
schêmata, eidê]) of the interval which measured the compass of the
scale in question. Thus, the interval of the Octave ([Greek: dia
pasôn]) is divided into seven intervals, and these are, in the
Diatonic genus, five tones and two semitones, in the Enharmonic two
ditones, four quarter-tones, and a tone. As we shall presently see in
detail, there are seven species of the Octave in each genus. That is
to say, there are seven admissible octachord scales ([Greek:
systêmata emmelê]), differing only in the succession of the intervals
which compose them.
Further, there is evidence which goes to connect the seven species of
the Octave with the Modes or [Greek: harmoniai]. In some writers
these species are described under names which are familiar to us in
their application to the modes. A certain succession of intervals is
called the Dorian species of the Octave, another succession is called
the Phrygian species, and so on for the Lydian, Mixo-lydian,
Hypo-dorian, Hypo-phrygian, and Hypo-lydian. It seems natural to
conclude that the species or successions of intervals so named were
characteristic in some way of the modes which bore the same names,
consequently that the modes were not keys, but modes in the modern
sense of the term.
In order to estimate the value of this argument, it is necessary to
ask, (1) how far back we can date the use of these names for the
species of the Octave, and (2) in what degree the species of the
Octave can be shown to have entered into the practice of music at any
period. The answer to these questions must be gathered from a careful
examination of all that Aristoxenus and other early writers say of
the different musical scales in reference to the order of their
intervals.
§ 22. _The Scales as treated by Aristoxenus._