Onesicrates, Soterichus, Lysias.

1 THE wife of Phocion the just was always wont to maintain that her chiefest glory consisted in the warlike achievements of her husband. For my part, I am of [p. 103] opinion that all my glory, not only that peculiar to myself, but also what is common to all my familiar friends and relations, flows from the care and diligence of my master that taught me learning. For the most renowned performances of great commanders tend only to the preservation of some few private soldiers or the safety of a single city or nation, but make neither the soldiers nor the citizens nor the people any thing the better. But true learning, being the essence and body of felicity and the source of prudence, we find to be profitable and beneficial, not only to one house or city or nation, but to all the race of men. Therefore by how much the more the benefit and advantage of learning transcends the profits of military performances, by so much the more is it to be remembered and mentioned, as most worthy your study and esteem.

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:—

1 ὑπάτη e
2 παρυπάτη f
3 λιχανός g
4 μέση a
5 παραμέση b
6 τρίτη c
7 παρανήτη d
8 νήτη e (octave)

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:-

1 ὑπάτη e
2 παρυπάτη f
3 λιχανός g
4 μέση a
5 τρίτη b
6 παρανήτη c
7 νήτη d

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, &c.

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.)

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