1864.] on Instruments with Fixed Tones > 105 



Table I.— Principal Musical Intervals. 



Name. 



Example. 



Ratio. 



or 



Log. 



Deg. 





c 



: c 



1 



:1 





1 



:1 





•00000 











• c 



32805 



: 32768 



38.5 



:2*5 





•00049 



0' 





c 



• BJt 



2048 



:2025 





2" 



:3^ 



52 



•00491 







tc 



c 



81 



:80 





Q4 

 O 



:24 



5 



•00540 





t1[ Pythagorean Comma § 



ttBlf 



c 



531441 



: 52488 





312 



219 





•00589 



1 





db 



let 



+ TP 



128 



: 125 





2? 



:53 





•01030 







H 



c 



25 



:24 





52 



23 



3 



•01773 



3" 





c 



tB 



256 



:243 





08 



35 





•02263 



4 



Sharp, or Greater Limma 





c 



135 



:128 



o 



. 5 



27 





•02312 



4' 



tVjf Equal Semitone*. . . . 



\\4 



c 



V 



:1 





*294 



349 



57 



•02509 



4 7 





c 



B 



16 



: 15 





2* 



3 



5 



•02803 



5^ 





tclt 



c 



2187 



: 2048 







2" 





•02852 



5 





td 



cti 



27 



: 25 . 





33 



5» 





•03343 



6" 





e 



d 



10 



: 9 



2 



. 5 



33 





•04576 



8' 





d 



c 



9 



:8 





3' 



23 





•05115 



9 





8' 





8 



:7 





23 



7 





•05799 









d 



7 



:6 





7 



2 



3 



•06695 





Pythagorean Minor 3rd . . 



f 



d 



32 



:27 





2^ 



33 





•07379 



13 







e 



6 



:5 



2 



. 3 



5 





•07918 



14' 





e 



c 



5 



:4 





5 



2» 





•09691 



17' 



Pythagorean Major 3rd . . 



te 



c 



81 



;64 





34 



26 





•10231 



18 



±1 ourth, or Perfect 4th .... 



f 



c 



4 



:3 





2^ 



3 





•12494 



22 





d 



A 



27 



:20 





32 



22 



6 



•13033 



23' 







b 



7 



:5 





7 



5 





•14613 



254 





f 



b 



64 



:45 





2^ 



32 



5 



•15297 



27' 





a 



d 



40 



:27 



2' 



, 5 



33 





•17070 



30' 





Il8- 



c 





:1 





*2i4 



37 



5 



•17560 



3r 



Fifth, or Perfect 5th 



D' 

 O 





3 



: 2 





3 



2 





•17609 



31 



Pjrthagorean Minor 6th . . 



C 



IE 



128 



:81 





27 



34 





•19872 



35 



Minor 6th 



C 



E 



8 



:5 





23 



5 





•20461 



36' 





a 



c 



5 



:3 





5 



3 





•22185 



39' 



Pythagorean Major 6th . . 



ta 





64 



:32 



2 



.33 



2-5 





•22724 



40 





f 



tilt 



128 



:75 





27 



3 



52 



•23215 



41" 



Extended 6th 



d 





12 



:7 



22 



.3 



7 





•23408 



41 3 



Perfect 7th 





'I 



7 



:4 





7 



22 





•24304 



421- 







G 



16 



:9 





2^ 



33 





•24988 



44' 







c 



9 



:5 





32 



5 





•25527 



45' 





b 



c 



15 



:8 



3 



.5 : 



23 





•27300 



48' 



_ 



c 







2 



:1 





2 



1 





•30103 



53 



§ Hence the symbol ^ for Pythagoras, with the f (comma) prefixed. 

 * Approximately. 



