T/ieorems on Musical Temperament. 43 



Corollary 2. The sum of the 11 temperaments of the 

 minor fourth, and its wolf, is constantly 122 -fm, as 

 observed above. 



Corollary 3. The sum of the 8 temperaments and 4 

 wolves of the major thirds, is 842 + 8m, or four en- 

 harmonic Diesises. 



Corollary 4. The sum of the 8 temperaments and 4 wolves 

 of the minor sixths, is —842 — 8m, as above. 



Corollary 5. The sum of the o temperaments and 3 wolves 

 of the minor thirds, is —962 —9m, or three Semitones 

 minimum. 



Corollary 6. The sum of the 9 temperaments and 3 wolves 

 of the major sixths, is 962 -f 9m, as above. 



Corollary 7. The sum of the temperaments of the minor 

 third and of the major third, is equal to the tempera- 

 ment of the fifth. 



__ 3r— lis lis— Ar — r 



For H = , the first part of the 



temperament of the fifth, and so of the latter part. — 

 (See Dr. Smith's Harmonics, cor. 6, p. 42.) 



Corollary 8. The sum of the temperaments of the fifth 



and of the major sixth, is equal to the temperament 



of the major third. 



„ — r lis— 3r 115— Ar , — t u—3t 



For f- = 2: also f- 



s s s u u 



u—At lis— 4r , u— At . . 



_ m,or 2 -\ 'm, as in theorem 3. 



u s u 



(See Dr. Smith's Harmonics, cor. 8, p. 43.) 



Corollary 9. The difference between the wolf and the 



temperament of each of the six concords resncc- 



. . . . . 12r— 12? 12/— v 

 tively, is the same, viz. 2 ~\ m, and is 



- 5 ' s u 



what Dr. Smith, at pages 1 60, 223, &c. calls the Diesis ; 



it is the difference between adjacent flat and sharp 



notes, as between *D and bE, *A and bB, Sec. p. 163. 



I, llr— 12s — r 12r— 12-5 . 11/—?/ — t 



p or -s 2, and 



s s s ^ u u 



\2t—u . . rc , A1 Sr— s lis — Ar 



= m, 111 the fifths. Also, — = 



u ' s s 



Ur— 12* . 8/ u— At \2t—u . 



2, and = m, in the ma- 



s u u u 



jor third, as before, and so of all the others, 



Corollary 



