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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 τοῦ ἀνθρώπου φύσις προστυγχάνει, δεύτερον δὲ τὸ χρωματικόν, τρίτον δὲ καὶ ἀνώτατον (v. l. νεώτατοντὸ ἐναρμόνιον: τελευταίῳ γὰρ αὐτῷ καὶ μόλις μετὰ πολλοῦ πόνου συνεθίζεται 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--

A προσλαμβανόμενος.  
B ὑπάτη ὑπατῶν.  
C παρυπάτη ὑπατῶν τετράχορδον ὑπατῶν.
D λιχανὸς ὑπατῶν
E ὑπάτη μέσων
F παρυπάτη μέσων τ. μέσων.
G λιχανὸς μέσων
A μέση

So far the sounds are common to the greater and smaller systems. Then follow, in the greater,

B παραμέση τ. διεζευγμένων.
C τρίτη διεζευγμένων
D παρανήτη διεζευγμένων
E νήτη διεζευγμένων
F τρίτη ὑπερβολαίων τ. ὑπερβολαίων.
G παρανήτη ὑπερβολαίων
A νήτη ὑπερβολαίων

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--

A μέση.
B τρίτη συνημμένων.
C παρανήτη συνημμένων.
D νήτη σμνημμένων.

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᾽ 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 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 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]

1 The word τόνος, lit. “tension,” “pitch,” has two distinct special senses. It is applied to the keys, as being scales which differed in pitch. It is also the name of an interval, a tone; perhaps as being the interval through which the voice is most naturally raised at one effort.

2 Euclid considers no intervals consonant but such as correspond to super-particular (ἐπιμόριοι) or multiple (πολλαπλάσιοι) ratios: the former being such as 3 : 2, 4 : 3, &c., the latter such as 2 : 1, 3 : 1, &c. On this theory the Octave and Fourth (8 : 3) would be dissonant, but the Octave and Fifth (3 : 1) consonant.

3 It will be evident that a species of the Diatonic genus and the similarly named species of the Enharmonic are two utterly different scales. Compare (e. g.) the Diatonic and Enharmonic Lydian, which can never have belonged to the same “mode.” This is a difficulty which the writers who maintain the practical importance of the Species have not recognised.

4 The passage is unfortunately corrupt. It seems clear from the context that Westphal is right in placing the Mixolydian highest in pitch and in condemning the word αὐλὸν after τὸν ὑποφρύγιον.

5 It is true that according to the Pseudo-Euclid (p. 15) these names were given to the species “by the ancients” (ὑπὸ τῶν ἀρχαίων). But the Romans and Byzantines used this term of Greeks of the Alexandrian period.

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