On the Nomenclature of Musical Intervals. 363 



to the common letter-press Printing : and likewise that several 

 of these Intervals, whose Niiines were selected or given by Mr. 

 Overendj siiould now be changed, for others, better adapted to 

 classifitTitioii, and a general Nomenclatiu'e. 



All these additions and corrections, I have included in a Table 

 to accompany this (see pages 360 and 3G1). The first column 

 of this Table contains the Symbols distinguishing the Intervals, 

 whose Names follow, in column 2. 



In column 3, the values of the Intervals are given, in the new 

 Notation which I had the pleasure of first presenting to the Public, 

 in p. 1 40 of your xxviiith volume : the terms of this notation are, 

 the Schisma S, lesser Fraction* f, and Most Minule m, in the 

 former engraved Tablef ; and each expression in this column, 

 coupled with the svmbol in the first column forms a simple 

 Equation, thus, y = 9S + m, IV = 301S + 6 f + 26m, &c. 



Column 4, shows the indices of t!ie powers of the musical 

 Primes 2, 3 and 5, composing the Ratios; the negative signs ( — ) 

 therein, indicating reciprocals, or the denorjiinalors of the Frac- 

 tions, which follow in column 5 ; thus, in the 5th, —6 2 1, 



indicates the fraction '—-, = At ; &c. 



The reciprocal Logarithms in column 6, are placed lowest, and 

 are the complements of the Logaritktns to 1 ; they denote the 

 same Interval, reckoned dnivnwards, as the Logiwithms do up- 

 wards; the first 7 figures of the logs, are pointed off, conform- 

 ably to the common Tables of logarithms. 



. The Corrections in the second page of the Table (page 361), 

 are, I think, sufficiently explained therein, except the compound 

 Symbols F, T, IP, IP, &c. ; wherein, the grave accent indicates, 

 the subtraction or fait of a major Comma c (I Is + m) ; and V 



* It will be Fcei! in t!:e second page of the Tal.lo now sent, tliat I pro- 

 pose to chnn;.'e tlie N:ime, of this smallest -hut -one of known Intervals, 

 to suhminimwn ilnsiDUAL; because the class oi Fractkma, as 1 wish now to 

 constitute it, ha.s iiKvays a ncgatvie sign to the f '•; therein. Insteud of mine 

 being called a Notation by Schisma'^, lesser J'ractions, and most Minutes; 

 it niiuht be said to usc, tiiinimimi Commas (S), suhniiiiiniuni Residuals (f), 

 and buliniininium Commas (m), in expressing Musical Intervals, in theii 

 utmost varieties. 



t In this Notation, each of tiie 3422 Intervals, formed between pairs of 

 Mr.IJston's Organ-Notes as aliove mentioned, have been calculated, includ- 

 ing every jmssible Jnlcriiul therenn, less than an Octave ; and as in no single 

 inst'ince, any number of Ss is found combined therein, with ii:ore than o!ic 

 comliination i.ri f and m, it is hereby dcoKjnstrated, that for every purpose 

 of expressing the values or comparing Mr. Liston's Intervals, f and m may 

 be omitted, and 2's only used with perfect accuracy .', under liie denomina- 

 tion of iirltjkiul. Commas. In p. 410 of your xxxixth volume, I could not 

 venture to speak thus pusilivelj/, after having in the preceding page, given 

 the 2'a or Artificial Commas, answering to each one of Mr, Liston's 59 

 Not*. 



and 



