MU´SICA
MU´SICA The term
μουσικὴ signified the art or circle of arts over which the Muses
presided, viz. poetry in its various kinds, with the music, whether of voice
or instrument, required for its worthy presentation. The word which most
nearly denotes what we call the
science of Music is
ἁρμονική, but that word does not
include the subject of rhythm or “time” (
ῥυθμική). “Harmonic,” therefore, deals only
with sounds and their relations in respect of tune:
Ἁρμονική ἐστιν ἐπιστήμη θεωρητικὴ καὶ πρακτικὴ τῆς τοῦ
ἡρμοσμένου φύσεως: ἡρμοσμένον δέ ἐστι τὸ ἐκ φθόγγων καὶ
διαστημάτων ποιὰν τάξιν ἐχόντων συγκείμενον
(Pseudo-Euclid.
Introd. Harm. p. 1). The ancient science of
rhythm dealt not only with musical sounds, but with everything susceptible
of rhythmical division, including (in particular) spoken language, and the
movement of the dance. Accordingly it has been made the subject of a
separate article [
RHYTHMICA].
The Greek technical writers on “Harmonic” usually treat the
subject under seven heads:--I. Of Sounds (
περὶ
φθόγγων). II. Of Intervals (
περὶ
διαστημάτων). III. Of Genera (
περὶ
γενῶν). IV. Of Systems or Scales (
περὶ
συστημάτων). V. Of Keys (
περὶ
τόνων1). VI. Of Transition (
περὶ
μεταβολῆς). VII. Of Composition (
περὶ
μελοποιίας). This division will be generally made use of in
the present article.
A Sound is musical when it has a determinate pitch (
τάδις); that is to say, when it is produced by vibrations in
which waves of a particular length sensibly predominate. The pitch must
also, of course, be maintained sufficiently long to make a distinct
impression on the memory. When two musical sounds differ in pitch, one is
said to be more
acute (
ὀξύς), the other more
grave
(
βαρύς): in common language, one is
called higher, the other lower. The term
ἐμμελής, applied to a sound, signifies that it is capable of
being used in the same melody with other sounds.
An Interval is the difference or distance in respect of pitch between two
musical sounds. The interval between any pair of sounds can be compared in
point of magnitude with that between any other pair, and the magnitude of an
interval can be measured with more or less
[p. 2.193]accuracy by the ear. Further, certain intervals--the Octave, the Fifth,
&c.--are recognised as possessing a definite pleasing character; and
thus become the foundation of systems of music.
If two strings, similar in material, thickness and tension, be made to
vibrate, the rate of vibration is inversely proportional to their length:
and the interval between the sounds produced depends only on the ratio of
the lengths, i. e. of the numbers of vibrations. Thus:
If the ratio be |
2 : 1, |
the interval is an |
Octave. |
If the ratio be |
3 : 2, |
the interval is an |
Fifth. |
If the ratio be |
4 : 3, |
the interval is an |
Fourth. |
If the ratio be |
9 : 8, |
the interval is an |
Major Tone. |
The discovery of these ratios is attributed to Pythagoras, and probably with
truth, although the details with which it is told by later writers
(Nicomachus, p. 10;
D. L. 8.12) are plainly
false. According to these writers, Pythagoras happened to be passing a
blacksmith's workshop, and noticed that the musical intervals were produced
by four hammers, whose weights he found to be in the proportion of 12, 9, 8,
and 6. He then stretched four similar strings by weights which were in the
same proportion, and found that they gave the Octave (12 : 6), the Fifth (12
: 8 or 9 : 6), the Fourth (12 : 9 or 8 : 6), and the Tone (9 : 8). But under
these conditions the vibrations would have been as the
square roots of these numbers. The discovery of Pythagoras
strongly impressed the imagination of Greek thinkers, and had a great effect
upon the general course of speculation, but did not lead at once to progress
in musical theory. His followers busied themselves with
à priori combinations of numbers, but neglected the
observation of new facts. This led to a reaction, and the rise of a school
which left the physical basis of music out of sight, and adopted (in
principle at least) the method of “equal temperament.” Thus
Greek writers are divided, in their general treatment of intervals, into (1)
the Pythagorean or mathematical (called by themselves
κανονικοί or
ἁρμονικοί),
who identified each interval with a ratio, and (2) the
“musical” (
μουσικοί), who
measured all intervals as multiples or fractions of the Tone. Of the former
school were Archytas (400 B.C.), Euclid the geometer, Eratosthenes, and the
later writers Thrasyllus, Didymus, and Ptolemy: of the latter were
Aristoxenus (pupil of Aristotle) and his followers, the chief of whom were
Aristides Quinctilianus and the author of the
εἰσαγωγὴ ἁρμονικὴ which bears (quite wrongly) the name of
Euclid.
Intervals were distinguished as
consonant
(
σύμφωνα) or dissonant (
διάφωνα), according as the two sounds could or
could not be heard together without offending the ear (Ps.-Eucl. p. 8). The
intervals reckoned as consonant were the Octave (
διὰ
πασῶν), the Fifth (
διὰ
πέντε), the Fourth (
διὰ
τεσσάρων), and any interval produced by adding an octave to one
of these.
2 All other intervals (as the Third, Sixth, Tenth) were considered as
dissonant. It is curious that this class should have included the double
tone (
δίτονον) and the tone and half
(
τριημιτόνιον), even after these
intervals had been identified with the natural Major Third (5 : 4) and Minor
Third (6 : 5). But the distinction between consonant and dissonant is a
matter of degree, and doubtless the Pythagorean tradition tended to keep up
the notion of a special character for the Octave, Fifth, and Fourth.
Aristotle and other writers use the term
ὁμοφωνία of unison,
ἀντιφωνία
of the consonance of the Octave. Later writers (as Gaudentius) distinguish a
third relation, intermediate between consonance and dissonance, to which
they apply the term
παραφωνία. The
instances given are the ditone and the tritone.
An aggregate of intervals, or rather of sounds separated from one another by
a particular series of intervals, constituted a System, of scale.
Every system capable of use in music (
σύστημα
ἐμμελές) could be analysed as a combination of Tetrachords
or systems of four notes, either
conjunct or
disjunct. Tetrachords are “conjunct”
(
συνημμένα) when the highest note of
one is the same as the lowest note of the other (as with the octaves of a
modern scale). They are “disjunct” (
διεζευγμένα) when the highest note of one is separated by a
Major Tone from the lowest note of the other. This Tone is called
τόνος διαζευκτικός. In reality the Octave scale
had much the same place in ancient as in modern music: but the tetrachord
was taken as the theoretical unit. Thus the scale
a b c d
e f g a would be regarded as composed of the conjunct tetrachords
b c d e and
e f g a,
plus the tone
a--b: and the scale
e f g a b c d e as composed of the disjunct
tetrachords
e f g a and
b c d
e.
The Genus of a system depended upon the relation of the three intervals into
which the tetrachord composing it was divided. The Greeks made use of three
Genera,--the Diatonic, the Chromatic, and the Enharmonic: and of the two
former of these there were certain varieties called Colours (
χρόαι). It was allowed, moreover, under certain
restrictions, to combine the intervals of one Genus or Colour with those of
another, so as to produce “mixed” divisions of the tetrachord.
The different forms of the Chromatic and Enharmonic genera were broadly
distinguished from the Diatonic by the use of two small intervals in
succession--so small that taken together they were less than the third. Two
such intervals were said to form a
πυκνόν,
or “crowding” of notes, and the three notes were sometimes
called, from their position in the group,
βαρύπυκνος,
μεσόπυκνος, and
ὀξύπυκνος.
The Enharmonic again is distinguished from every Colour of the Chromatic by
the
δίεσις or quarter-tone, the smallest
interval known to Greek music.
It is not easy to harmonise the different accounts of the Genera and Colours,
especially as it is impossible to say how far these accounts rest upon
actual observation. The following list includes the chief varieties
mentioned or recognised by writers of both schools:--
- 1. The “highly strung” Diatonic (διάτονον σύντονον). According to
Aristoxenus, the intervals [p. 2.194](in the
ascending order) were semitone, tone, tone (e f g
a). The ratios given by the Pythagoreans, such as Euclid
and Eratosthenes, are 25 6/243 [multi] 9/8 [multi] 9/8
(λεῖμμα, τόνος, τόνος).
Didymus (a contemporary of Nero) proposed the ratios 16/15
[multi] 10/9 [multi] 9/8 , thus introducing the Minor Tone
(10 : 9), and with it the true Major Third (10/9 [multi] 9/8 =
5/4 ). Ptolemy inverted the order of the tones, making the division
16/15 [multi] 9/8 [multi] 10/9, thus obtaining also the true
Minor Third (16/15 [multi] 9/8 = 6/5 ).
- 2. The Diatonic, called by Ptolemy “middle soft”
(διάτονον μέσον μαλακόν), or
“Tonic” (δ.
τονιαῖον), formed by the ratios 2 8/27 [multi] 8/7
[multi] 9/8 . These ratios were given for the ordinary Diatonic
by Archytas--apparently as a simplification of the Pythagorean
scheme. No corresponding division appears among the Colours of the
Aristoxeneans: but Aristoxenus himself says (p. 27, 9 Meib.; cp. p.
52, 15) that a musically correct system (σύστημα ἐμμελές) may be formed by combining the
Diatonic λιχανὸς (second highest
note) with the παρυπάτη (second
lowest note) of a Soft Chromatic. Such a tetrachord would correspond
to the “middle soft Diatonic” of Ptolemy and Diatonic
of Archytas. In the system of Ptolemy it is taken as the standard
division of the octave. We shall see that its existence is confirmed
by the notation.
- 3. The Soft Diatonic (διάτονον
μαλακόν), formed, according to Aristoxenus, of the
intervals semitone, three-quarters of a tone, tone and a quarter.
The ratios given by Ptolemy are 2 1/20 [multi] 10/9 [multi]
8/7 .
- 4. The standard or tonic Chromatic (χρῶμα
σύντονον or τονιαῖον). Aristoxenus gives the intervals semitone,
semitone, tone and a half: Ptolemy the ratios 2 2/21 [multi]
12/11 [multi] 7/6 . In this, and also in the preceding Colour,
if Ptolemy is right, the highest interval is slightly over-estimated
by Aristoxenus.
- 5. The Soft Chromatic (χρῶμα
μαλακόν), for which Ptolemy gives the ratios 2 8/27
[multi] 15/14 [multi] 6/5 . It answers to two Colours in the
scheme of Aristoxenus, the χρῶμα
μαλακόν, in which the two small intervals are each a
third of a tone, and the χ.
ἡμιόλιον, in which they are each three-eighths of a
tone. The distinction between these two Colours is rejected by
Ptolemy; but as he mentions that they were both obsolete in his
time, his opinion can only rest upon à
priori considerations. The earliest analyses of the
Chromatic scale agree partly with the standard kind, partly with
this “soft” variety. The following schemes are
mentioned:--
Chromatic of
Archytas, |
2 8/27 [multi]
24 3/224 [multi] 3 2/27; |
Chromatic of
Eratosthenes, |
20/19 [multi]
19/18 [multi] 6/5 ; |
Chromatic of
Didymus, |
16/15 [multi] 2
5/24 [multi] 6/5 . |
It will be seen that Eratosthenes was the first to recognise the
natural Minor Third, and (by consequence) the Minor Tone.
- 6. The Enharmonic, in which the intervals, according to
Aristoxenus, were diesis, diesis, ditone. The schemes proposed by
Pythagorean writers were:--
Enharmonic of Archytas, |
2 8/27 [multi] 3
6/35 [multi] 5/4 ; |
Enharmonic of
Eratosthenes, |
40/39 [multi] 3 9/38
[multi] 19/15; |
Enharmonic of Ptolemy, |
4 6/45 [multi] 2
4/23 [multi] 5/4. |
The scheme of Archytas is interesting as the earliest recognition of the
natural Major Third. The 19 : 15 of Eratosthenes is almost exactly the
Pythagorean ditone 81 : 64, and is doubtless meant as a simplification of
it. It is to be observed that the true Major and Minor Thirds were admitted
in the Enharmonic and Chromatic genera long before they replaced the
Pythagorean division in the Diatonic.
All these scales, except the first, are so unlike anything now known, at
least in European music, that modern writers have great difficulty in
forming any idea of their real character and effect. The most plausible view
of the Enharmonic, and of the Chromatic “colours,” is that the
pair of small intervals which gives them their peculiar character was due in
each case to the insertion of a note that stood in no harmonic relation to
the rest of the scale, and consequently was not essential to the melody, but
might be used as a “passing” or ornamental note (
appoggiatura). At the same time, or more probably as
an earlier step, the large interval which belongs to the Chromatic and
Enharmonic scales was created by the omission of a note from the Diatonic
scale. Thus the tetrachord
e f g a, by the omission
of
g, and the insertion of a dividing note between
e and
f, would give
the Enharmonic
e e* f a. Similarly, from the
trichord
e f a, by inserting a passing
f#, we obtain the Chromatic
e f
f# a. In the case of the Enharmonic there is direct evidence that
this was the actual. process by which it was formed. Aristoxenus (quoted by
Plut.
de Mus. p. 11) says that this genus was
discovered by the musician Olympus, who observed that a peculiarly beautiful
character (
ἦθος) was given to a melody by
the omission of the second highest note of the Diatonic tetrachord. Hence
certain of his compositions, in particular those called
σπονδεῖα, employ only the notes common to all
three genera, viz.
e f--a b c--e (omitting
g and
d as peculiar to the
Diatonic). The Enharmonic
πυκνόν
(Aristoxenus goes on to say) does not appear to be due to Olympus. Further,
in the archaic style of flute-playing the semitone is undivided: afterwards
it was divided (into quarter-tones), both in the Lydian and the Phrygian
music. On this view the distinctive character of the Enharmonic is given by
the largeness of the highest interval in the tetrachord rather than the
smallness of the two others.
This method of explanation evidently fails in the case of genera in which the
large interval cannot have been obtained by the omission of a note in a
Diatonic scale. Such are the “Soft” Diatonic, in which the
large interval is founded on the ratio 8 : 7, and the standard Chromatic, in
which (according to Ptolemy) it is founded on 7 : 6. These intervals,
however, may have been obtained by direct observation. They exist in the
natural scales of the horn and trumpet, and are in fact used instead of the
Minor Third and Tone ( 6/3 [multi] 10/9) in the harmony of the dominant
Seventh, both by stringed instruments and voices when unaccompanied by
tempered instruments. (See the instances quoted by
Gevaert, vol. i. p. 315.)
All that we know of the history of the non-Diatonic scales tends to show that
they were used in combination with the Diatonic rather than as an
independent form of music. In the time of Ptolemy only one division, that of
the “middle soft” Diatonic, could be used for the
[p. 2.195]whole of a scale. The four others that were still
in ordinary use--the Pythagorean, the
διάτονον
σύντονον, the
δ. μαλακόν,
and the standard Chromatic--could only be used in combination with the
“middle soft.” Thus there were five varieties of the
octave, one in which the standard genus only was used, and four in which it
was “mixed” with a tetrachord of a different kind. The curious
rule is given that the “highly strung” genera, the Pythagorean
and the
διάτονον σύντονον, must be in the
upper tetrachord of the octave; the relaxed genera, the “soft”
Diatonic and the Chromatic, in the lower one. We cannot indeed extend such
rules to the earlier periods of Greek music; but it would seem from the
stress which all writers lay on the subject of “mixture”
(
μίγμα) of genera--viz. the combination
of the intervals of different genera either within the same tetrachord, or
in different tetrachords of the same system--that this was the way in which
some at least of these strange varieties found their way into practice.
All writers recognise the natural priority of the Diatonic genus. Next to it
Aristoxenus places the Chromatic, the most difficult being the Enharmonic:
πρῶτον μὲν οὖν καὶ πρεσβύτατον αὐτῶν
θετέον τὸ διάτονον, πρῶτον γὰρ αὐτοῦ ἡ τοῦ ἀνθρώπου φύσις
προστυγχάνει, δεύτερον δὲ τὸ χρωματικόν, τρίτον δὲ καὶ
ἀνώτατον (v. l.
νεώτατον)
τὸ ἐναρμόνιον: τελευταίῳ γὰρ αὐτῷ καὶ
μόλις μετὰ πολλοῦ πόνου συνεθίζεται ἡ αἴσθησις (p.
19). Elsewhere he complains of the tendency to depart from the severity of
the Enharmonic, and pass into the “sweeter” and more emotional
Chromatic. In the second century A.D. (as we learn from Ptolemy) the
Enharmonic and the “Colours” of the Chromatic had gone out of
use.
Regarding the systems actually employed in Greek music, something has already
been said in connexion with the instruments. [See
LYRA p. 105
b.] At an
early period we find evidence of an octachord system or octave scale of
eight notes, named as follows:--
ὑπάτη,
lit. “highest,” in our terminology the lowest (sc.
χορδή).
παρυπάτη,
“next to
ὑπάτη.”
λιχανός, the “forefinger” note.
μέση, the “middle” note.
παραμέση.
τρίτη, the “third finger” note.
παρανήτη.
νεάτη or
νήτη, the “lowest,” our highest.
The octave consisted of two disjunct tetrachords, (1) from
ὑπάτη to
μέση,
and (2) from
παραμέση to
νήτη. The names were the same for all the
genera; but the genus was specified if necessary in the case of the
“movable” notes (e. g.
λιχανὸς
διάτονος, λ. χρωματική, λ. ἐναρμόνιος, and so on). In the
Diatonic genus it may be represented in our notation by the octave
e f g a b c d e.
This scale was in ordinary use in the time of Plato and Aristotle: see Plat.
Rep. p. 443 D (
ξυναρμόσαντα τρία
ὄντα ὥσπερ ὅρους τρεῖς ἁρμονίας ἀτεχνῶς, νεάτης τε καὶ
ὑπάτης καὶ μέσης, καὶ εἰ ἄλλα ἄττα μεταξὺ τυγχάνει
ὄντα), and Arist.
Probl. xix. (especially
§ § 3, 4, where he discusses the difficulty of singing the
παρυπάτη, though it is only separated
by a
δίεσις from the
ὑπάτη). The technical writers describe two systems,
obtained from this octave by the addition of tetrachords at each end. One of
these consisted of two complete octaves, viz.
|
ZZZ
|
This was called the
greater perfect system. Another
system, called the
smaller perfect system, was
composed of three conjunct tetrachords, called
ὑπατῶν, μέσων, and
συνημμένων, with
προσλαμβανόμενος, thus--
|
ZZZ
|
and these two together constituted the
immutable system, i.e. system without “transition” or
modulation (
σύστημα ἀμετάβολον),
described by all the writers later than Aristoxenus.
The sounds in these systems were named in the way before described, the names
of the tetrachord only being added, except in the case of
μέση and
παραμέση. Thus, taking the sounds in the ascending order--
So far the sounds are common to the greater and smaller systems. Then follow,
in the greater,
The interval between
μέση and
παραμέση is a tone. But in the smaller system
μέση) serves also for the lowest sound
of the tetrachord
συνημμένων, which
terminates the scale, thus--
This system is “perfect” and “unmodulating,” in the
sense that any particular musical scale, provided that modulation is
excluded, must be similar to some part of it. Let us now suppose that a
partial scale, of a certain number of notes, is to be taken on the Perfect
System. By taking different notes as limits, the order of the intervals in
any such partial scale may be varied, while the genus remains the same. The
varieties obtained in this way are called Species. It is evident, further,
that the number of species of a scale of a given compass is the same as the
number of its intervals. Thus the Diatonic tetrachord has three species, as
the semitone is first, second, or third: 1st. 1/2 1 1, 2nd. 1 1/2 1, 3rd. 1
1 1/2
The Octachord has seven species, viz. in the Diatonic genus--
[p. 2.196]
1st. |
1/2 |
1 |
1 |
1/2 |
1 |
1 |
1 |
(b--b) |
2nd. |
1 |
1 |
1/2 |
1 |
1 |
1 |
1/2 |
(c--c) |
3rd. |
1 |
1/2 |
1 |
1 |
1 |
1/2 |
1 |
(d--d) |
and so on, the semitones changing their place by successive steps.
Similarly in the Enharmonic genus there were seven species, to which,
according to the statement of one writer (Ps.-Eucl. p. 15), names were
anciently given as follows:--
1. Mixolydian |
1/4 |
1/4 |
2 |
1/4 |
1/4 |
2 |
1 |
2. Lydian |
1/4 |
2 |
1/4 |
1/4 |
2 |
1 |
1/4 |
3. Phrygian |
2 |
1/4 |
1/4 |
2 |
1 |
1/4 |
1/4 |
4. Dorian |
1/4 |
1/4 |
2 |
1 |
1/4 |
1/4 |
2 |
5. Hypolydian |
1/4 |
2 |
1 |
1/4 |
1/4 |
2 |
1/4 |
6. Hypophrygian |
2 |
1 |
1/4 |
1/4 |
2 |
1/4 |
1/4 |
7. Hypodorian |
1 |
1/4 |
1/4 |
2 |
1/4 |
1/4 |
2 |
A late writer, Aristides Quinctilianus (p. 21), describes six very ancient
divisions of the scale (
διαιρέσεις αἷ καὶ οἱ
πάνυ παλαιότατοι πρὸς τὰς ἁρμονίας κέχρηνται), which he
tells us are the six “Modes” (
ἁρμονίαι) characterised by Plato in the well-known passage of
the
Republic (p. 398). He gives the order of the intervals as
follows (assuming that
δίεσις may be
represented by a quarter-tone):--
Lydian |
1/4 |
2 |
1 |
1/4 |
1/4 |
2 |
1/4 |
|
Dorian |
1 |
1/4 |
1/4 |
2 |
1 |
1/4 |
1/4 |
2 |
Phrygian |
1 |
1/4 |
1/4 |
2 |
1 |
1/4 |
1/4 |
2 |
Ionian |
1/4 |
1/4 |
2 |
1 1/2 |
1 |
|
|
|
Mixolydian |
1/4 |
1/4 |
1 |
1 |
1/4 |
1/4 |
3 |
|
Syntonolydian |
1/4 |
1/4 |
2 |
1 1/2 |
|
|
|
|
No satisfactory attempt has been made to reconcile this scheme with the
Species of the Octachord, but traces of a connexion may be pointed out. The
Lydian of Aristides agrees with the Hypolydian species;
and as Plato opposes his
λυδιστί, as a
“slack” or low-pitched scale, to the
συντονολνδιστί, we may regard it as the “mode”
elsewhere called Hypolydian. The
Mixolydian of Aristides is
derived from the corresponding species (
b--b)
by combining the Diatonic with the Enharmonic in the lower tetrachord, and
omitting the second highest note. The
Dorian exhibits the
central octave, which is of the Dorian species, with an additional tone at
the lower end. The
Phrygian is unlike the Enharmonic Phrygian
species, but may be derived from the Diatonic by dividing the semitones and
omitting the diatonic
λιχανός: thus
d e e* f (
g)
a b b* c d. The upper tetrachord is a
“mixture” of Diatonic and Enharmonic. The
Ionian
(
ἰαστί) and
Syntonolydian present the greatest difficulties, since so
many notes are wanting. Westphal makes it probable that the names have been
interchanged; if so, the Ionian may be regarded as an octave of the Diatonic
g-species, with four notes omitted, and the
semitone divided enharmonically: (
g a)
b b* c (
d)
e (
f)
g; and the Syntonolydian becomes a Diatonic
a-species, with like omissions and subdivision: (
a)
b b* c (
d)
e (
f)
g a. These results,
however, are of very doubtful value. In particular, they are open to the
serious objection that they are partly obtained by connecting the Enharmonic
scales of Aristides with the species of the Diatonic genus: whereas the
writer who is our authority for the list of the Species (Pseudo-Euclid)
connects their names only with the Enharmonic.
3 Nevertheless the scales of Aristides are of interest, as confirming
the view that the Enharmonic divisions were formed upon the basis of
Diatonic or other natural scales, and that the two genera were practically
employed in combination. It has been noticed that the upper tetrachord of
his Phrygian, and the lower tetrachord of his Mixolydian, are in fact
Diatonic scales with the Enharmonic notes added.
The fifth head of Greek musical science is that which treats of the Keys or
“pitch” of the various scales (
περὶ
τοὺς τόνους ἐφ᾽ ὧ τιθέμενα τὰ συστήματα μελωδεῖται,
Aristox. p. 37 Meib.). The distinction of keys was of high antiquity; but
the arrangement and completion of the system was first carried out by
Aristoxenus, who thus did for Greek music what was done for that of the
modern world by the
Wohltemperiertes Clavier of John
Sebastian Bach. In the important passage already quoted (p. 37) he goes on
to tell us that in his time there was a great want of agreement as to the
names and relative pitch of the keys. Each part of Greece had its own, as
each had a different calendar, with different names for the months. The most
generally recognised keys were:--
Mixolydian4 |
interval of a
semitone. |
Lydian |
Phrygian |
interval of a tone. |
Dorian |
interval of a tone. |
Hypodorian |
interval of a semitone. |
Some added a Hypophrygian below the Hypodorian. Others, again, made an
interval of three quarters of a tone between the successive keys, except
between the Dorian and Phrygian, which seem to have been always separated by
a tone.
To these six keys Aristoxenus, or some one in his time, added a new
Hypodorian, a tone lower than the Hypophrygian: the old Hypodorian was then
called Hypolydian. Thus the convention was arrived at by which the prefix
hypo-always denoted a key a Fourth lower than the key to whose name it was
prefixed. The next step, expressly attributed to Aristoxenus himself
(Ps.-Eucl. p. 19), was the addition of six new keys, thus giving one for
every semitone of a complete octave. At a later time two more were invented,
obviously for the sake of symmetry, and the whole list was as follows:--
Hypolydian |
Lydian |
[Hyperlydian] |
Hypo-aeolian |
Aeolian |
[Hyper-aeolian] |
Hypophrygian |
Phrygian |
Hyperphrygian |
Hypo-ionian |
Ionian |
Hyper-ionian |
Hypodorian |
Dorian |
Mixolydian |
Each of these keys was a transposition of the
σύστημα
ἀμετάβολον: but we are told that
[p. 2.197]only that part of each was used which was within the compass of the human
voice.
It will be seen that the order in pitch of the seven oldest keys--Hypodorian,
Hypophrygian, Hypolydian, Dorian, Phrygian, Lydian, Mixolydian--is exactly
the reverse of that of the seven species of the same names on the Perfect
System. This is the chief fact which a theory of the Greek
“modes” has to explain.
The fifteen keys kept their ground, at least in theory, until the time of
Ptolemy, in whose
Harmonics a new scheme is set forth at
great length. In this scheme the keys are again reduced to seven, and are
brought into direct relation to the species of the Octachord. The use of
different keys, according to Ptolemy, is not that the pitch of a melody may
be higher or lower. That can be done by raising or lowering the pitch of the
whole instrument. The object is that different successions of intervals may
be brought within the ordinary compass of the voice: and that object will be
fully attained if every octave contains as many different scales
(successions of intervals) as possible. But the number of possible scales is
not greater, in any one genus, than the number of species, viz. seven. Let
us take, then, as the part of the scale most completely within the reach of
all voices, the old central octave, from
ὑπάτη
μέσων to
νήτη διεζευγμένων,
in the Dorian key. It is also of the Dorian species (
e--e). If now we take an octave a tone
lower on the scale (
d--d), we have the
Phrygian species. But if we at the same time raise the scale into the
Phrygian key, we obtain the Phrygian species in an octave of the same pitch
as the Dorian, viz.
e f# g a b c# d e. Similarly the
Lydian species, taken on a scale in the Lydian key, is
e
f# g# a b c# d# e. Proceeding thus, we obtain what Ptolemy aims
at--an octave of fixed absolute pitch, furnishing every possible succession
of intervals or species.
The octave scales obtained by this process are of the same absolute pitch,
but are relatively different parts of the Perfect System. The notes which
compose them have therefore a double character. They have a place in the
Perfect System, and a place in the new octave. Hence a double nomenclature.
The notes are called
ὑπάτη, παρυπάτη,
&c., from their place in the new octave (
τῇ
θέσει); the old names which belong to them as part of the
Perfect System are said to be
κατὰ
δύναμιν.
These octaves, again, may be varied by the use of different genera. Here
Ptolemy aids us very much by giving the scales actually used in his time on
the lyre and the cithara. Their limited number is in curious contrast to the
immense theoretical variety which he sats forth. The scales of the lyre were
of two kinds, called
στερεὰ and
μαλακά. The former or “hard” scale
was an octave of the standard or Middle Soft Diatonic genus. In the latter
or “soft” variety the lower tetrachord was Chromatic.
Apparently there was no limitation in respect of key or species.
The scales of the cithara were of at least six kinds:--
(1)
πρίται, Middle Soft Diatonic, and of the
Hypodorian species:
a b b# d e e# g a.
(2)
ὑπέρτροπα, the same genus, Phrygian
species (
d--d).
(3)
παρυπάται,
“mixture” of Soft and Middle Soft Diatonic, of the Dorian
species:
e 2 1/20
g
10/9
g 8/7
a 9/8
b 2 8/27
b#
8/7
d 9/8
e.
(4)
τρόποι, mixture of Chromatic and Middle
Soft Diatonic, of the Hypodorian species:
a 9/8
b 2 2/21
#c 12/11
c# 7/6
e 2 8/27
e# 8/7
g 9/8
a.
(5)
ἰαστιαιολιαῖα, mixture of Pythagorean
and Middle Soft Diatonic, of the Hypophrygian species:
g 9/8
a 9/8
b 25 6/243
c 9/8
d 9/8
e 2 8/27
e# 8/7
g.
(6)
λύδια, probably a mixture of
διάτονον σύντονον with Middle Soft Diatonic:
but the text of Ptolemy at this point (2.16) is defective. In another place
(1.16) Ptolemy speaks of the mixture in question as found “in the
λύδια and
ἰάστια.” Owing to the break in the text, it is
uncertain whether there were not more than these six varieties.
From an incidental notice in Athenaeus (xiv. p. 625) we learn that there was
an ancient
Locrian key, with a distinct character. The
Locrian and
Aeolian species are identified by the
Pseudo-Euclid with the Hypodorian. The ancient
Ionian
(
ἰαστί) is generally identified with
the Hypophrygian (Boeckh, p. 225). According to Aristotle (
Aristot. Pol. 4.3), there are two chief
keys, Dorian and Phrygian, of which the others may be regarded as varieties.
Plato opposes the Dorian as the true Hellenic key to the Ionian, Phrygian,
and Lydian (Lach. p. 188 E). In the
Republic he makes a
three-fold division: the “slack” keys, as Lydian and Ionian,
are soft and voluptuous (fit for drinkingsongs, &c.); the Mixolydian
and “tense” Lydian are plaintive and exciting; the Dorian and
Phrygian hold the middle place, and represent the two aspects of a good
ethos, the Dorian being the key of calm
endurance (
ἀνδρεία), the Phrygian of sober
enjoyment (
σωφροσύνη).
The nature of the Greek “modes” has been investigated by
Westphal with characteristic ingenuity and learning; and his conclusions,
which leave no part of the subject unexplained, have been generally adopted
by Gevaert. According to the view supported by this high authority, there
are three groups of “modes” (
mnodalités fondamentales, Gev.): the Dorian, based on
the octave
a--a, the modern Minor scale
(descending); the Phrygian, based on
g--g (the Major
with a flat seventh); and the Lydian, based on
f--f
(the Major with a sharp fourth). Each of these, again, has three possible
varieties, distinguished by the melody ending on the tonic, the dominant, or
the third. Thus we have--
Keynote |
a,
|
ending on |
a,
|
Hypodorian or Aeolian. |
Keynote |
a,
|
ending on |
e,
|
Dorian. |
Keynote |
g,
|
ending on |
g,
|
Hypophrygian. |
Keynote |
g,
|
ending on |
b,
|
Mixolydian. |
Keynote |
g,
|
ending on |
d,
|
Phrygian. |
Keynote |
f,
|
ending on |
f,
|
Hypolydian. |
Keynote |
f,
|
ending on |
a,
|
Syntonolydian. |
Keynote |
f,
|
ending on |
c,
|
Lydian. |
To discuss the combination of inferences upon which this theory rests would
take more space than we can afford. It will be enough to indicate the nature
of the doubts that may be felt on the subject. The chief difficulty is the
want of any direct statement regarding the tonality of the ancient modes, or
the note on
[p. 2.198]which the melody ended. The
locus classicus on the first point is the passage of
the Aristotelian
Problems, 19.20,
πάντα γὰρ τὰ χρηστὰ μέλη πολλάκις τῇ μέσῃ χρῆται, καὶ
πάντες οἱ ἀγαθοὶ ποιηταὶ πυκνὰ πρὸς τὴν μέσην ἀπαντῶσι, κἂν
ὰπέλθωσι ταχὺ ἐπανέρχονται, πρὸς δὲ ἄλλην οὕτως
οὐδεμίαν. The note here called
μέση, Westphal maintains, can only be the
μέση τῇ θέσει, or fourth note of the octave actually
used; for if it were the
μέση of the
Perfect System (
μέση κατὰ δύναμιν), the
keynote would have the same
relative pitch in
all the modes, and they would therefore be mere
transpositions of the same system. But (1) there is no trace in
the
Problems of any octave except the old one of the Dorian
species (
e--e), or of any notes being named in
more than one way. And (2) Westphal's argument only applies to those
“modes” in which, according to him, the
μέση
“by position” is the keynote, viz. the Dorian, Phrygian, and
Lydian. Still less evidence can be shown for Westphal's assumption that in
each mode the species of octave used is determined by the ending of the
melody. There is no certain trace in the ancient musical writers of a rule
about the end of the melody.
Other difficulties are suggested by the early history of the keys. We are
asked to believe that the
τόνοι of
Aristoxenus were wholly distinct from the
ἁρμονίαι of the same names of which we read so much in Plato
and Aristotle. Now up to the time of Aristoxenus, as he himself tells us
(
l.c.), the names of the keys, with their
relative pitch, were still unsettled. But the names of the seven Species, as
we have seen, are directly dependent on the Aristoxenean scheme of keys.
Consequently these names cannot have been given till the time of
Aristoxenus. stoxenus. It is true that Aristoxenus recognises the difference
of species, and indeed devotes much pains to ascertaining the number of
admissible species of the Octachord (p. 6 and p. 36 Meib.). But he never
connects them with his scheme of keys, or with any names such. as Dorian,
Phrygian, and the rest. It surely follows that the perplexing double
application of these ancient names is the work of a later theorist.
5
It may be said that the ethical character of a scale is more likely to have
depended upon its “mode” --i. e. upon a difference such as
distinguishes our Major and Minor scales--than upon its pitch. But the
writers who dwell most on the ethical value of the
ἁρμονίανι connect it expressly with the element of pitch.
Plato rejects one group of
ἁρμονίαι as too
low-pitched (
χαλαραί), another as too
“highly strung” (
σύντονοι), and therefore emotional. If we adopt the scheme of
Ptolemy, in which transposition is only used to obtain different species,
the arguments of Plato have no meaning.
It should be considered, further, that along with difference of Key the
ancients had an important source of variety in the Genera, which (as well as
the Keys) were regarded as possessing a distinct ethical or emotional
character. It is surely in the Genera, rather than in the Species of Ptolemy
and Aristides, that we find the true artistic analogue of the modern Modes.
Perhaps we may go further, and connect the loss of the Chromatic and
Enharmonic with the practical importance of the Species in the time of
Ptolemy. Thus the system of the second century A.D. would be midway between
the classical Greek music, with its Keys and Genera, and the Tones. of the
mediaeval Church.
On the last two of the heads enumerated at the beginning of the article, very
little real information can be obtained. In fact they could not be
intelligibly discussed without
examples, a
method of illustration which unfortunately is never employed by the ancient
writers.
Μεταβολὴ was the transition from
one genus to another, from one system to another (as from disjunct to
conjunct or
vice versâ), from one key to
another, or from one style of melody to another (Ps.-Euclid. 20), and the
change was. made in the same way as in modern
modulation (to which
μεταβολὴ partly
corresponds), viz. by passing through an intermediate stage, or using an
element common to the two extremes between which the transition was to take
place. (See Ps.-Euclid. 21.)
Μελοποΐα, or composition, was the
application or use of all that has been described under the preceding heads.
This subject, which ought to have been the most interesting of all, is
treated of in such a very unsatisfactory way that one is almost forced to
suspect that only an
exoteric doctrine is contained
in the works which have come down to us. On composition
properly so called, there is nothing but an enumeration of
different kinds of
sequence of notes, viz.:--1.
ἀγωγή, in which the sounds followed
one another in a regular ascending or descending order; 2.
πλοκή, in which intervals were taken alternately
ascending and descending; 3.
πεττεία, or
the repetition of the same sound several times successively; 4.
τονή, in which the same sound was sustained
continuously for a considerable time. (Ps.-Eucl. 22.) Besides this division,
there are several classifications of melodies, made on different principles.
Thus they are divided, according to
genus, into
Diatonic, &c.; according to
key, into
Dorian, Phrygian, &.; according to
system,
into grave, acute, and intermediate (
ὑπατοειδής,
νητοειδής, μεσοειδής). This last division seems to refer to
the general pitch of the melody; each of the three classes is said to have a
distinct
turn (
τρόπος), the grave being
tragic, the
acute
nomic (
νομικός), and the intermediate
dithyrambic. Again, melody is distinguished by its
character (
ἦθος), of which three
principal kinds are mentioned,
διασταλτικόν,
συσταλτικόν, and
ἡσυχαστικόν, and these terms are respectively explained to mean
aptitude for expressing a magnanimous and heroic, or low and effeminate, or
calm and refined character of mind. Other subordinate classes are named, as
the erotic, epithalamian, comic, and encomiastic. (Ps.-Euclid. 21; Aristid.
29.) No account is given of the
formal peculiarities
of the melodies distinguished by these different characters, so that what is
said of them merely excites our curiosity without tending in the least to
satisfy it.
It has long been a matter of dispute whether the ancients practised
harmony, or music in parts. The following are the
facts usually
[p. 2.199]appealed to on each side of the
question. In the first place, the writers who professedly treat of music
make no mention whatever of such a practice: this omission constitutes such
a very strong
primâ facie evidence against
it, that it must have settled the question at once but for supposed positive
evidence from other sources on the other side. It is true that
μελοποιΐα, which might have been expected to
hold a prominent place in a theoretical work, is dismissed very summarily;
but still, when the subjects which
ought to be
explained are enumerated,
μελοποιΐα is
mentioned with as much respect as any other, whilst
harmony is entirely omitted. In fact there seems to be no Greek
word to express it; for
ἁρμονία signifies
a well-ordered
scale of sounds, and
συμφωνία only implies the concord between a
single pair of sounds, without reference to succession. There is, however, a
passage in the Aristotelic
Problems (19.18) where succession
of consonances is mentioned:
διὰ τί ἡ διὰ πασῶν
συμφωνία ἄδεται μόνη; μαγαδίζουσι γὰρ ταύτην, ἄλλην δὲ
οὐδεμίαν. The word
μαγαδίζειν signifies the singing or playing in two parts at the
interval of an octave--a practice which would arise as soon as men and women
or boys attempted to sing the same melody at once. The obvious meaning of
the passage is that since no interval except the octave was
magadised (the effect of a similar use of any other
is known to be intolerable),
therefore no other was
employed at all in singing: implying that nothing of the nature of
counterpoint was thought of. And this interpretation is borne out by the
absence of any other reference to singing in parts, or to harmony in purely
instrumental music.
On the other hand, there are several indications of the use of harmony in the
κροῦσις or instrumental accompaniment.
The most decisive is a passage in the
Laws of Plato (vii. p.
712). Speaking of the musical education which is to be common to all
citizens, he says that the pupils are to learn to sing to the accompaniment
of the lyre, and that this is to be note for note the same as the melody,
eschewing all divergence and variation in the instrumental part, by which
the strings are made to yield a different melody from that which the poet
composed, combining “close” with “open” intervals,
quick time with slow, high with low notes, consonant and in octaves. In the
rhythm, too, they are to abstain from intricacy in the accompaniment,
because the effort to attend to opposites at the same time produces only
confusion and perplexity. It appears, therefore, that a note of the air
might be accompanied by a different note, or by two or more successive
notes, of the instrument; and that an accompaniment with variations and
ornaments of this kind, though not a matter of course, was familiar at least
to professional musicians. In the
Problems of Aristotle
(19.12) the question is asked, “Why the lower of two strings always
takes the melody” implying that the accompaniment, in
instrumental music at least, was always higher than the air. In another
passage (19.39) Aristotle speaks of the effect of an accompaniment, which
ends in unison with the air, after having been different from it:
τὰ ἄλλα οὐ προσαυλοῦντες ἐὰν εἰς ταὐτὸν
καταστρέφωσιν εὐφραίνουσι μᾶλλον τῷ τέλει ἢ λυποῦσι ταῖς πρὸ
τοῦ τέλους διαφοραῖς. His language is exactly what we
should use to describe the pleasure given by the resolution of a discord.
The use of dissonant as well as consonant intervals in ancient harmony is
shown by a passage in Plutarch's dialogue
de
Musica (100.19). Speaking of the use in the accompaniment
(
πρὸς τὴν κροῦσιν) of notes which do
not occur in the air,--a peculiarity of certain ancient styles,--he
instances the
τρίτη which was found as
accompaniment to the
παρυπάτη (the interval
being a fifth), and the
νήτη συνημμένων,
found with the
παρανήτη and the
μέση. The interval between
νήτη and
παρανήτη depends
on the genus, but in any case is reckoned by the ancients as dissonant. The
late writers Gaudentius and Bacchius apply a special term,
παραφωνία, to intervals which they say
“are intermediate between consonant and dissonant, but appear
consonant in the accompaniment” (
ἐν τῇ
κρούσει).
These notices make it clear that the Greeks were acquainted with some at
least of the effects out of which systems of harmony are formed. That their
harmonies were of a simple kind, and had a very subordinate place in their
music, is no less evident. There is no certain trace of the use of
chords or groups of more than two notes. The art of
harmony has no history; it is nowhere connected with national forms of
music, or with the names of eminent musicians. It never emerges from the
stage of the singer with the lyre in his hand.
The musical notation (
σημασία) of the Greeks
consisted of two distinct systems of signs,--one for the voice, the other
for the instrument. The vocal signs are taken from the common or Ionic
alphabet. The notes of the middle part of the scale are denoted by the
letters in their usual order; those of the lower part by an alphabet of
inverted or otherwise altered letters; the upper notes are distinguished by
accents--an an accent signifying that the note is an octave higher than that
of the unaccented letter. The nature of the instrumental notation was first
explained by Westphal, whose admirable investigation has thrown much light
on the early periods of Greek music, and even on the history of the
alphabet. The following is a brief summary of his discoveries:--
- 1. The instrumental notation was derived from the first fourteen
letters of a Peloponnesian alphabet, possessing digamma,
ϝ, the old form of iota, [music1], and two forms of lambda, 〈 and [music2]. In a
few cases the forms of the letters have been modified: thus alpha (originally [music3]) appears as
[music4], beta as C, delta as [music5], theta as
Ξ,
my (originally [music6]) as
[music7], iota as [music8]. By
treating the two forms of lambda as distinct
characten the number is raised to fifteen.
- 2. These characters are applied to denote a scale of two octaves,
as follows:--
|
Η [music8] Ε [music2] Γ [music7] Φ Ξ Κ [music5] 〈
C Ν Ζ [music4]
|
|
ZZZ
|
The arrangement of the letters is worth notice. The
inventor began by taking alpha for the
highest note of his scale. Then he took the other characters in
pairs, C [lceil] [music5] Ε, Φ Ζ,
Η Ξ, [music8] Κ, 〈 [music2], [music7] Ν, and made each pair stand for the
extreme notes of an octave. This [p. 2.200]scale may
be regarded as the framework of the system of notation.
- 3. A character may be varied by being reversed, i. e. written from
right to left (ἀπεστραμμένον), or
by being turned half round backwards (ἀνεστραμμένον, ὕπτιον). When reversed, it denotes
a note half a tone higher: when half reversed, it denotes a note a
quarter of a tone higher. The combination of the two varieties
evidently gives an Enharmonic πυκνόν, or group obtained by dividing a semitone: e. g.
if we take the four “stable” notes of the central
octave, [lceil] Ξ Κ Ξ, we
complete the scale in the Enharmonic genus by inserting the
varieties of [lceil] and Κ,
thus obtaining [lceil] Λ
[rceil] Ξ Κ [music9]
[music10] C. In some cases this method of varying the letters
is impracticable; e. g. Η
reversed does not change, Ν
half-reversed becomes Ζ, and
vice versâ. Other
modifications are accordingly employed, and we have the groups
[music4] [music11] [music12], Ζ [music13] [music14], Ν / \, [music5] [music15]
[music16], and Η
[music17] [music18].
- 4. In the Diatonic genus the second lowest note of a tetrachord is
not represented, as we should expect, by the reversed letter, but by
the half-reversed one, the same character as the second lowest
Enharmonic note. Westphal infers that the Diatonic for which the
notation was originally devised was a scale such as the Middle Soft
Diatonic of Ptolemy, or the Diatonic of Archytas, in which the
lowest interval was less than a semitone.
- 5. In the Chromatic genus the characters used are the same as in
the Enharmonic, but the reversed letter is distinguished by an
accent. Thus the Chromatic tetrachord e f f#
a is written [lceil] Λ
[rceil] 'Ξ or (in the upper
octave) C [music19] [music20] [music4]. Here again the
notation does not answer to the standard form of the genus, but is
exactly suited to the Chromatic of Archytas, in which the lowest
interval is the same as in the Enharmonic.
- 6. The system was enlarged by the addition of two tones, each with
the corresponding πυκνόν, at the
lower end of the scale, and an octave, except the highest note, at
the upper end. The two groups were denoted by the characters
[music21] [music22] Τ and
Ε Ω [music23], which are
evidently invented on the analogy of the letters already in use. The
new upper notes were denoted by accented letters, Κ᾽ to Ζ᾽, repeating the scale from Κ to Ζ an octave
higher. In this shape the system contained the notes of the Greater
Perfect System in all the fifteen Keys, and in the three
Genera.
It is remarkable that we find no trace of a distinction between Greek and
Roman music. The Latin writers--the chief of whom are Martianus Capella and
Boethius--derive their material from Greek sources.
The extant fragments of Greek music are as follows (see Gevaert, i. pp. 141
ff.):--
Hymn to Calliope, by a certain Dionysius, of unknown date.
Hymn to Apollo, ascribed to the same.
Hymn to Nemesis, probably by Mesomedes, a musician of the second century A.D.
These three hymns are edited with a commentary by Bellermann (Berlin, 1840).
The Anonymus, edited by the same scholar (Berlin, 1841), contains some
fragments in the instrumental notation, given to illustrate the technical
terms of
μελοποιΐα.
A melody for the first eight verses of the first Pythian ode of Pindar was
published by Kircher in his
Musurgia Vniversalis. He
professed to have taken it from a MS. of the monastery of S. Salvatore at
Messina; but the MS. has never been found. It is given by Boeckh (
De
Metr. Pind. 3.12), who accepts it as genuine. It is also
admitted, though with grave doubt, by Gevaert (i. p. 6).
A Hymn to Demeter, given in Greek notation by the Venetian composer Marcello,
is of still more doubtful authenticity (Gevaert,
ibid.).
The chief ancient authorities on the subject of this article are, the
“Antiquae Musicae Auctores Septem” --viz. Aristoxenus,
Euclid (including the
εἰσαγωγὴ ἁρμονικὴ
which bears his name), Nicomachus, Alypius, Gaudentius, Bacchius, Aristides
Quintilianus--and Martianus Capella, edited by Meibomius, in two vols.
(Amsterdam, 1652); the
Harmonics of Ptolemy (in vol. iii. of
Wallis,
Op. Mlathemat. Oxford, 1699); Theon Smyrnaeus,
De Musica (ed. Bullialdus, Paris, 1644);
the Anonymus edited by Bellermann (Berlin, 1841); the Dialogue of Plutarch
De Musica; Aristotle,
Probl.
xix.; and several chapters of Athenaeus, book xiv. The
Harmonic of Aristoxenus has also been edited by P. Marquardt
(Berlin, 1868), and translated with commentary by Ruelle (Paris, 1870) and
by Westphal (Leipzig, 1883). There is a new edition of Aristides
Quintilianus by Alb. Jahn (Berlin, 1882).
The chief modern sources of information <*> Boeckh,
De Metris Pindari; Fortlage,
Das musikalische
System der Griechen (Leipzig, 1847); the various writings of
Westphal, of which his book
Die Musik des griechischen
Alterthums (Leipzig, 1883) may be mentioned as an excellent
introduction to the subject in a comparatively small compass; Gevaert,
Histoire et Théorie de la Musique dans
l'Antiquité (Gand, 1875, 1881); Helmholtz,
Die
Lehre vonden Tonempfindungen, § § 13, 14.
[
W.F.D] [
D.B.M]