NUMERICAL RELATIONS OF THE MUSICAL SCALE. 



Keys to which the Note belongs. 



*Ci 



Dbb 



*Di 

 D, 



*E,l,b 



Eabb 



H 



H 



E.b 

 E, 



*E2 



E.b 

 E.| 



*Fi 



Ci, 



B»b. 



F^b. Aabb, ..••■• 



D,,Ei, Fi#, A,, 



Bz, f4 



Fab, Fi, Alb, Bib, Bibb, Gib, Cib, ^'bh, 



Gab, Bib, Cab 



Gi, Fi, Fi|;, Ai, Bib, • • • 

 Ci, Eab, G2, Bab, Ba, FjI • 



Bibb, Gib, Cib, 



Gab, Cab.Aabb 



^ 



C,#, El, Ba, Fa| 



Bib, G,b, 61, Cib 



Ci, Dib, Fob, Gab, G=, Alb, Bab, Cab, • 



Gi, 



Ci, Ci|, Di, Fi, Gj, Ai, Ba, . 



Gib, 



Dib, Aib, C,b, Bibb, Aabb. Eibb. 

 Ci|,Fi#, ...... 



H 



C, D,b, Di, Alb, Ai, Bib, Gib, • • 

 Eab. Gab.Bab, . • • ■ 



Ci|, Di, A,, G, 



Ea, Ga Ba, 



Interval from C. 



Logarithm. 



X 



8i 

 TO 



1 2 8 



In terms ofP, <?,^- 



VI. 



Interval in 

 Scale of 

 equal tem- 

 perament. 



•0000000 . -1 



•00.53950 P 



•0103000 P+ Q 



•0177288 2P+ Q+ S~ 



•0231238 3P+ Q+ R 



•0280287 ;iP+ 2Q+ R 



•0334238 4P-I- 2Q-I- R, 



■Oiolbib ()P+ 3Q+ 2iJ] 



•0511525 GP-I- 3Q+ 2iJ 



•0560575 6P+ iQ+ 2R 



•0614525 7P+ 4Q+ 2JJ, 



•0634862 7P+ 4Q+ 3^1 



•0688813 8P+ 4Q+ ZR 



•0737862 8P+ 5Q + ZR 



•0791813 0P+ 5Q+ ZR 



■0915150 10P+ 6Q4- 4fl 



•0969100 11P+ 6Q+ 4i? 



•1018150 \\r+ 7(3+ 4iJ 



•1072099 i;2P+ 7Q + il.2L 



•1146388 13P+ 7Q+ 5P 



•1200338 14P+ 7Q+ 5if 



■1249387 14P+ 8Q + oR 



•1303338 15P+ 8(2+ 5Pj 



•1426675 16P+ 9Q+ 6P 



•1480625 17P+ 9Q+ 6P 



Difference 



between 

 VI. and IV. 



VIII. 



Differ- 

 ence in 

 terms 

 of (a). 



•0000000 



•0250858 



•0501717 



•0752575 



•1003433 



•1254291 



•1505150 



f -0000000 



{ --0053950 



[,-•0103000 



f+^0073570 



+ •0019620 



I - ^0029429 



(^-•0083380 



f+^0044142 



- •0009808 



-•0058858 



^-•0112808 



r+ •0117713 



+ ■0063762 



+ •0014713 



-•0039238 



+ ^0088283 



+ •0034333 



-•0014717 



(^-•0068666 



r+ -0107903. 



+ •0053953 



+ ^0004904 



(^-•0049047 



+ •0078475 



+ -0024525 







- lla 



- 21a 

 + 15a 

 + 4a 



- Oa 



- 17« 

 + 9« 



- 2« 



- 12a 

 -■23« 

 + 24a 

 + 13a 

 + 3a 



- 8a 

 + 18« 

 + 7« 



- 3a 



- 14a 

 + 22« 

 + lla 

 + a 



- 10a 

 + 10a 

 + oa 



ICH the Note belongs. 



Ci 



C3 



n 



*Cab 

 *Cib 

 *B. 



Bi 

 *Bab 

 *Bib 



A.a# 



Ai# 



Babb 

 *Bibb 



Aa 

 *Ai 



Aab 

 *Aib 



Ga# 



Gi# 

 *Aabb 



A.bb 



*G2 



*Gi ■ 



*G.>b 



*Gib 



Ci, Dib, Eab, ii, Fi, Ga, Aib, Ai, Bib, 

 Gi, 



Ci#. 



Esb, F=b, Gab, Aib,'B,bb,Aabb, • 



Gib, Eibb, 



Ci, El, Go, A,, Fojj;, 



Di,' Fi#, Gi, 



Eab, Gab,'Ga, Alb, Cab, 

 Dib, Di, Fi, Gib, Gi, • 



Ba, F2I 



C,#,F,t, ...... 



Gab,Aabb, 



Dib, Fab, Gib,E,bb, • ■ ■ • 

 Ga, Bab,Fa#, . . .' . 



C„Di, El, F,, Fi#, Bib, Gi, 



Gab, 



Ci, Dib, Eab, Fab, Fi, Cab, Bibb^ 



H • • 



(:'i#. El, Fi| Ai, Bo, . 



Fab, Cab, 



Cib, Eibb, 



Ci, Bab, El, Fi, Alb, Bab, B'-' 

 Di, Bib, . . . . 



Eab, Fab; Bab, Cab, Aabu, • 

 Dib, Bib, Bibb, Cib, Eibb, • 



