TETRACIIORD, the Greek name for any part of the scale con sisting of four notes, the highest of which is a perfect fourth to the lowest. Thus in the common diatonic SCALE (we aseunio a knowledge of this article throughout) we have the following tetrachonls We despair of giving anything like a satisfactory account of the Greek music ; not that we think the difficulty lies in the Greek writers, but in the manner in which they have been treated. It was an assumption that the nation which produced models such as the moderns could not surpass in architecture, sculpture, and perhaps in painting, was to be considered as necessarily possessed of a system of music approaching to perfection. Their writers on the subject were to be taken as having an agreement with each other, which was to he detected and established, any apparent discrepancy, however evident, notwithstanding. The numerical relations which were the objects of inquiry in the settlement of the parte of the scale gave the subject the air of an exact science; and explanations which required the assistance of the scholar, the mathematician, and the musician,were undertaken by persona who were deficient in one character, if not iu two. The consequence has been such a mass of confusion as the world never saw iu any other subject; writers whose undertakings required them to say something, copying absolute contradictions from different other writers; others glad to adopt anything intelligible, whether true or not; others again, unable or unwilling to state the simplest facts of their ownpremises, so that their readers are not even made aware which of the most remarkable opposite opinions they mean to adopt.
We intend in the present article, without 'looking into any modern writer, to draw from Ptolemy and Euclid, writers who are known to be trustworthy on other subjects, all concerning the totrachord that we can find to bear the character of certainty and precision, and to be likely to aid an unbiassed reader in approaching, should it please him so to do, the mass of different accounts which have been given.
All parties seem agreed that the Greek scale, which at first consisted of only two or three leading consonances, was gradually enlarged until it comprehended two octaves, or fifteen notes. It is generally stated
that this scale, when it was what we now call diatonic (a word which means the same with us as with the Greeks), was minor in its character, so that in fact it would be represented by It is also known that the Greeks were early in possession of the mode of dividing a string so as to produce their several notes ; and that, by the time of Ptolemy at least, they took the rapidity of the vibra tions (on which they knew the pitch to depend) to be inversely as the lengths of the strings.
Their scales were numerous : three were considered classical, if we may use the word, and were called enharmonic, chromatic, and dia tonic ; the two first words not having the same meaning as with us. The remaining scales had names of locality attached to them, Lydian, Dorian, &o. The distinction between these lay in the different modes of dividing the octave, as seems to be now generally agreed, though there have been those who have thought that these terms, Lydian, &c., were the names, not of scales, but of single notes.
Of enharmonic, chromatic, and diatonic scales, Ptolemy lays down fifteen from his predecessors, and eight from himself. In each of them is an octave, and all of them agree in two particulars : first, each has the fourth and fifth of the fundamental note perfect ; secondly, each has the tetrachord made by the fundamental note and its fourth divided in precisely the same manner as .that of the and the octave. That is, if we call the notes of this octave— then c s is a fourth, and a a a fifth, always; and the interval o r, P Q, Q P are severally equal to the intervals a a, a s, Sc'. Thus it appears that the fourth was to the Greeks what the octave is to us, the unit, as it were, of the scale, in the subdivision of which consisted the differences of their systems. We now give a tetrachord from each of these twenty-three scales, assigning the intervals first by the ratios of the vibrations, next by the number of mean semitones they contain, as in the article SCALE. We prefix the Latin rendering of Ptolemy's appellatives from Wallis.