1.
No one will attempt to
study this treatise on music, without some previous knowledge of the principles of Greek music, with its various moods, scales, and combinations of tetrachords. The whole subject is treated by Boeckh,
De Metris Pindari (in Vol. I. 2 of his edition of Pindar); and more at length in Westphal’s
Harmonik und Melopöie der Griechen (in Rossbach and Westphal’s
Metrik, Vol. II. 1).
An elementary explanation of the ordinary scale and of the names of the notes (which are here retained without any attempt at translation) may be of use to the reader.
The most ancient scale is said to have had only four notes, corresponding to the four strings of the tetrachord. But before Terpander’s time two forms of the heptachord (with seven strings) were already in use. One of these was enlarged to an octachord (with eight strings) by adding the octave (called
νήτη). This addition is ascribed to Terpander by Plutarch (§28); but he is said to have been unwilling to increase the number of strings permanently to eight, and to have therefore omitted the string called
τρίτη, thus reducing the octachord again to a heptachord. The notes of the full octachord in this form, in the ordinary diatonic scale, are as follows:—
The note called
ὑπάτη (hypate, or highest) is the lowest in tone, being named from its position. So
νήτη or
νεάτη or
lowest) is the highest in tone.
The other of the two heptachords mentioned above contained the octave, but omitted the
παραμέση and had other changes in the higher notes. The scale is as follows:—
This is not to be confounded with the reduced octachord of Terpander. This heptachord includes two tetrachords so united that the lowest note of one is identical with the highest note of the other; while the octachord includes two tetracllords entirely separated, with each note distinct. The former connection is called
κατὰ συναφήν, the latter
κατὰ διάζευξιν. Of the eight notes of the octachord, the first four (counting from the lowest),
ὑπάτη, παρυπάτη, λιχανός and
μέση, are the same in the heptachord;
παραμέση is omitted in the heptachord; while
τρίτη, παρανήτη, and
νήτη in the heptachord are designated as
τρίτη συνημμένων, παρανήτη συνημμένων, and
νήτη συνημμένων, to distinguish them from the notes of the same name in the octachord, which sometimes have the designation
διεζευγμένων, but generally are written simply
τρίτη, etc.
These simple scales were enlarged by the addition of higher and lower notes, four at the bottom of the scale (i.e. before
ὑπάτη), called
προσλαμβανόμενος, ὑπάτη ὑπατῶν, παρυπάτη ὑπατῶν, λιχανός ὑπατῶν; and three at the top (above
νήτη), called
νήτη, παρανήτη, τρίτη, each with the designation
ὑπερβολαίων. The lowest three notes of the ordinary octachord are here designated by
μέσων, when the simple names are not used. Thus a scale of fifteen notes was made; and we have one of eighteen by including the two classes of
τρίτη, παρανήτη, and
νήτη designated by
συνημμένων and
διεζευγμένων.
The harmonic intervals, discovered by Pythagoras, are the
Octave (
διὰ πασῶν,) with its ratio of 2:1; the
Fifth (
διὰ πέντε), with its ratio of 3: 2 (
λόγος ἡμιόλιος or
Sesquialter); the
Fourth (
διὰ τεσσάρων), with its ratio of 4: 3 (
λόγος ἐπίτριτος or
Sesquilerce); and the
Tone (
τόνος), with its ratio of 9: 8 (
λόγος ἐπόγδοος or
Sesquioctave). (G.)
