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