T E T 



253 



T E T 



Leach. [BELEMNITE ; BELLEROPHON; CEPHALOPODA 

 CORNU AMMONIS ; GONIATITES ; NAUTILUS ; PAPER NAU- 

 TILUS ; POLYTHALAMACEA ; SEPIAD-S ; SpiRULiD.*: ; TEU- 



THID.E.] 



TETRACE'RATA. [POLYBRANCHIATA.] 

 TETRACHORD, the Greek name for any part of the 

 scale consisting of four notes, the highest of which is a 

 perfect fourth to the lowest. Thus in the common diatonic 

 SCALE (we assume a knowledge of this article throughout) 

 we have the following tetrachords : 



CT)EF, DEFG, EFGA, GABC, ABCD, BCDE. 



We despair of giving anything like a satisfactory account 

 (if 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 be detected and established, any apparent 

 discrepancy, however evident, notwithstanding. The nu- 

 merical relations which were the objects of inquiry in the 

 settlement of the parts 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 persons who were deficient 

 in one character, if not in two. The consequence has been 

 such a mass of confusion as the world never saw in 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 own pre- 

 mises, so that their readers are not even made aware which 

 11!' 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 tuist worthy on other subjects, 

 ;ill concerning the tetrachord that we can find to bear the 

 character of certainty and precision, and to be likely to aid 

 :MI 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 cha- 

 racter, so that in fact it would be represented by 

 A B C D E F G A' B 1 C 1 D> E 1 F' G l A'. 

 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 vibrations Con which they knew the 

 pitch to depend) to be inversely as the lengths of the 

 strings. 



Their scales were numerous : three were considered clas- 

 sical, if we may use the word, and were called enharmonic, 

 chromatic, and diatonic; the two first words not having 

 the same meaning as with us. The remaining scales had 

 names of locality attached to them, Lydian," Dorian, &c. 

 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. 



( )f 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 

 filth of the fundamental note perfect ; secondly, each lias 

 the U-trachord made by the fundamental note and its 

 fourth divided in precisely the same manner as that of the 

 fifth and the octave. That is, if we call the notes of this 

 octave 



CPQFGKSC 1 ; 



then CF is a fourth, and CG a fifth, always ; and the inter- 

 vals CP, PQ, QF are severally equal to the intervals GR, 

 US, SC 1 . 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. 



And first as to enharmonic scales, which are mentioned 

 first, and seem to have been antient, and regarded with 

 high approbation. 



Archytas 

 Aristoxenus ) 

 Eratosthenes} 

 Didymus 

 Ptolemy 



It seems then that the enharmonic system would allow 

 only of the following notes in an octave 



CEPFGBQC 1 ; 



where P means a note about half way between E and F, 

 and Q one half way between B and C. An odd scale truly 

 for a modern musician to look at ; but, it may be, not inca- 

 pable of pleasing effects to ears not accustomed to music 

 in j>arts. 



The chromatic scales come next in order, as follows : 



To make something as like as we can to these scales, we 

 should write down in modern music 



C El, EH F G Bb 8^ C 1 

 The diatonic scales, Ptolemy allows, are more agreeable 

 to the ear, and his specimens are as follows : we shall 

 now write the scale with the usual letters throughout. 



These scales have all so far the diatonic character that 

 they divide the tetrachord into two larger intervals fol- 

 lowed by a smaller one : the scale of Didymus would have 

 been exactly the modern untempered diatonic scale, if he had 

 inverted the order of the two larger intervals in his second 

 _ This is also Ptolemy's Ditonici Diatonica. 



