GREEK Mow, Ancient. It appears from the wri tings of Aristoxenus, the earliest writer on the music of the Greeks whose works are extant, that before his time, their scale of music had been extended to two octaves, by the raising of a major tone, and then three succeeding minor fourths, upon the lowest of the notes of this double octave, and by the descending of two such succeeding minor fourths, from the upper note of this double octave : each of these fourths, or diatessara, being exactly of the same magnitude, and alike constituted, as to the situations of its two interior notes, throughout each of their several genera, and the colours or species of each.
The fourth being thus made the unvarying boundary of every one of the numerous Greek systems, as the octave is now with us, and as major sixth was with Guido, in the formation of his scale : In the genus DiAtromeum (which see) each fourth was made up of a semitone and two tones ; in the genus CHROMATICUM, of two semitones and a minor third ; and in the genus ENHARMONICUM (see GENERA) of two quarter tones or diesis, and a major third ; each of which semitones, tones, thirds, and diesis, were varied, or have different values assigned them, by almost every different writer, as references to our arti cles above mentioned will shew ; but so as always to pre serve the fourth entire and perfect : and it has been con cluded, that every one of these writers intended five of the fourths which he has described to be disposed within two octaves, from A to A, as above mentioned ; the third of these fourths, tuned from below, overlapping the se cond of those two tuned from above, by a grave or com ma-deficient minor third, as will be best explained by giving an example of the Diatonicum int epsum of Ptolemy, which can be done, with refrttric• to t.)c notes of Mr
Liston's scale, (see EUHAHMONIC Organ). using the arti ficial commas of Notation (which see.) for ex pressing the magnitudes of the several intervals ; viz.
The first of the above three columns contains the notes of Mr Liston's scale, and opposite to each of these, its value in the artificial comma (z) is placed. In column three, intermediary to the lines of the first two columns, the difference of the adjacent numbers in column two are placed, by which it will appear that each of the five te trachords or fourths, BE, EA, AD', and BE and EA, are exactly alike constituted, that is, rise each by the inter vals 57, 104, and 93 artificial commas each, answering to the major semi-tone, the major and the minor tones re spectively.
The interval AB, is in each case 104, or the major tone ; and thus, exclusive of the notes B1, and D', the system comprised in these two octaves may be more simply ex pressed thus, viz. T+4th +4th+ T + 4th+ 4th =2 VIII, forming thus far two similar octaves. The interval or 866-716— 150, is the comma-deficient minor third, by which interval the two series of fourths overcap each other.
It would bc.easy for the musical student to prepare a similar table to the above columns two and three, for each of the many Greek systems, whose fourths are given in S, in our articles on the Genera above referred to, and to place Liston's corresponding notes against them, in column one, as far as is practicable, by reference to the values of his notes in the Philat;aPhical Magazine, vol. xxxix. p. 419, whence the above numbers were derived, .by adding 161 from C to C, and 773 from C to a; that is, by reducing Liston's series to A as a bass or key-note, instead of C. (g)