Table X. — Duplicated Forms of the Concoidant Triad. (See p. 400.) 



No. 



Simple. 



Duplicated. 



Simple. 



Duplicated. 



1 

 2 



4 



5 



l', 3, 5 

 3, 4, 5 



3^ 5' 8 



2, 3, 4, 5 



1, 2, 3, 5 



3, 4, 5, 6 



2, 4, 5, 6 



3, 5, 6, 8 



2, 3, 5, 8 



1, 3, 4, 5 



3, 4, 5, 8 



2, 5, 6, 8 



3, 5, 8,10 



2,3,5, 6 



sUJeJ 10 



C Ge 

 C'Ge 

 G c e 



C G c e 

 0^ CGe 

 G c e g 

 C c eg 

 G egc= 



C Ge c= 

 C*Gc e 

 G c e c'' 



G ec-e= 



C Ge g 

 C'Ge g 

 G c e e- 



6 

 7 

 8 

 9 

 10 



4, 5, 6 



1^ 3^10 

 1, 5, 6 

 3, 4,10 



4, 5, 6, 8 



5, 6, 8,10 

 1, 2, 3,10 



9, i, 



4, 5, 6,10 



5, 6, 8,12 

 1, 3, 4,10 

 1, 4, 5, 6 



4, 5, 6, 12 

 1, 3, 6, 10 



e e g 



C* 6 G e- 

 G c t ^2 



c e g e- 

 c e g 



c e g g- 

 C^Gg e- 



11 

 12 

 13 

 14 

 16 



2, 3,10 



2, 5,12 



3, 8,10 

 1, 5,12 



4, 5,12 



2, 3, 4,10 



2, 4, 5,12 



3, 6, 8,10 

 1, 2, 5,12 



4, 5, 8,12 



2, 3, 8,10 

 2, 5, 8,12 



1, 4, 5,12 

 4, 5,10,12 



1, 5,8,12 

 4, 5, 8, 10 



C G e -^ 



lis 



C' e g= 

 c eg- 



C G c e- 

 C c e g- 

 C g c=e- 

 C^6 e^g^ 



C Gc^'e- 

 C e cV 



C* c e t 

 c e c^g- 



G* e c- g- 

 c e c- e- 



16 



18 

 19 

 20 



5, 8,12 



8^ 5', 16 

 5, 6,16 

 5, 12, 16 



5, 8,10,12 

 3, 6,10,16 

 3, 5, 6,16 

 5, 6,10,16 

 5, 10, 12, 16 



3, 10, 12, 16 

 3, 5,10,16 

 5, 6,12,16 





e c- 

 G e'' c' 

 G e e' 

 e g 

 e g=c* 



e e-g-c" 



G e=g=c; 

 Gee- c' 

 e g g2 c4 





Table XI. (See p. 400.) 



Forms of tlie Minor Triad. 



Index. 



No. 



Form. 



DifiF. Tones 



Form. 



Difterential Tones. 





No. 



2 



4 

 6 



8, 6,15 

 12, 15, 20 

 10, 12, 15 

 5, 12, 15 

 6, 10, 15 



2, 10, 12 

 3, 6, 8 



2, 3, 5 



3, 7,10 



4, 5, 9 



G' E b 

 g b e- 

 e g b 

 E g b 

 G 6 b 



C ', e, g 

 G', E, c 

 C, G', E 

 6', gBb, e 

 C, E,d 



3, 5,15 

 3, 10, 15 

 3, 15, 20 

 8, 15, 40 

 5, 6,15 



1 

 8 

 12 

 18 

 11 



6 

 7 

 8 



10 



15, 20, 24 

 6, 15, 20 

 3, 10, 15 

 12, 15, 40 

 10, 15, 24 



4, 5, 9 



5, 0,14 

 5, 7,12 

 3, 25, 28 

 5, 9,14 



b e-g- 

 G b?= 

 G' e b 

 g b e'^ 

 e b t 



C,E, d 

 E, d, zW 



G', Ig%sb* 

 E, d, gbl? 



5, 12, 16 

 6, 15,24 

 5, 15,48 

 6, 10, 15 

 6, 15, 20 



4 

 16 

 19 

 5 

 7 



11 

 12 

 13 

 14 

 15 



5, 6,15 

 3, 15, 20 

 15, 20, 48 

 15, 24, 40 

 15, 40, 48 



1, 9,10 



b, '2S', 33 

 9, 16, 25 

 8, 25, 33 



E G e 

 G'b e- 

 b e= g' 

 b g=e' 

 b e' g' 



C^d,e 

 E, g, Igd^b 

 E, 5bT7,xj c' 



c, Xf% xj c' 



6, 15, 40 

 10, 12, 15 

 10, 15, 24 

 10, 15, 48 

 12, 15, 20 



17 

 10 



2 



16 



18 

 111 

 20 



5, 15, 24 

 (i. 15,40 

 y, 15. 40 

 5. 15. 48 

 10, 15, 48 



9, 10, 19 

 9. 25, 34 

 12, 25, 37 

 10, 33, 4.3 

 5, 23, 38 



E b g= 

 G b e' 

 G' b e' 

 E b g' 

 e b g' 



d,e, Hi-Id's 

 d, tg=?; Iprt 

 g, Xf^.XXf7 



E, m tf-^. \m 



12, 15, 40 

 15, 20, 24 

 15, 20, 48 

 15, 24, 40 

 15, 40, 48 



6 

 13 

 14 

 15 



Table XII.— General Table of Equal Temperament. (See p. 407.) 



Just 

 note. 



Tem- 

 pered 

 note. 



T, 



log of tem- 

 pered pitch. 



J- 



log of iust 

 pitch. 



T-J. 



ft 



beat meter. 



Inter- 

 val. 





c 



clt 



ss> 



ex 



■0000000 

 ■0285191 -7x 

 ■0226335 -|-6x 

 ■0570382 -14x 



1 ■OOOOOOO 

 1 ■0063950 

 ■0177287 

 ■0280285 







-k 



2k -7x 

 -k-|-6x 





tl 



•3( 

 }f 



d 



ebb 



1 



■0511526 -2x 

 ■0452670-l-lOx 

 ■0796717 -9x 

 ■0737861-I-3X 



) ■0457574 

 1 ■0511526 



■0688813 

 ■0791812 



k-2x 

 -2x 



2k-9x 

 -k-|-3x 



-6k-|-18x 



tll 



n 



tnjt 





% 



■1023052 -4x 

 ■0964196-I-8X 

 ■1308243 -llx 



■0969100 



k-4x 



5k-20x 



ni 



f ( 



*li 



f 



t 



•1249387-1-x 

 ■1534578 -6x 

 ■1475722-I-6X 

 ■1819769 -13x 



J ■1249386 

 ■1303338 

 ■1426675 



\ ■1480626 



-k-l-x 

 2k -6x 

 k-6x 



4x 



4 



t4 



trv 



IV 



5 



'li 



g 



abb 

 gx 



■1760913-x 

 ■1702057-l-llx 

 ■2046104- 8x 

 ■1987248-I-4X 

 ■2331296 -16x 



1 -1706961 

 ] ■1760913 



■1938200 

 ■2041199 



k-x 



2k- 8x 

 -k^-4x 



-3x 



-8k-|-32x 



tv 



V 



xn 



u\ 



tbb| 



bbb 



ajf 



bb 



■2272439-3X 

 ■2213583-I-9X 

 ■2667630- lOx 

 ■2498774-1- 2x 



1 ■2218486 

 ) -2272438 



J -2498773 

 1 -2552725 



k-3x 

 -3x 



2x 



-k-f-2x 



5k-15x 



VI 



tvi 



7 

 t7 



tb 1 

 b f 



b 



cb 



b# 



■2783965 - 5x 

 ■2725109-1-7X 

 •0058851-12X 

 •3010300 



1 -2676061 

 j -2730013 



■3010300 



2k-5x 

 k-5x 









tvn 

 vn 











St- 



=32k- 



-2121tx 



-I-420X- 



= 150k- 



-1078kx 



-I-1998X- 





Where ^=-0053950 and x ia arbitrary. 



