COMMA. 



19 



>— -Y-— ' not more than ^279 S or 8618^6 °' wmcl1 would be 

 absolutely imperceptible in the most delicate experiments 

 in harmonics. The major comma is 7()7fi a fi rVIII, 



=73.55193 X/ =1400.0913 X.m, =5.120743 Xt. 



Comma Minor (-G), is an interval, tlie difference be- 

 tween two major semitones and a major tone, whose 



2025 . . -, 3 4 5* 



ratio is — — : the component primes of which are — — : 

 2048 -4 



its common logarithm is .9950950,7525 : its binary, or 

 Euler's logarithm, or decimal value of the octave, is 

 =.01629381 : in those where the major comma is the 

 -unit, =.9091561; and where the schisma is the unit, 

 •S 10.0078624: in the new notation of Mr Farey, it is 

 10 2 + to: in the elements of perfect tune, it is C : in 

 diatonic elements, 2 S — T, as before observed : in chro- 

 matic elements it is S — § : and, in corcordant or tu- 

 nable elements, 3 4 — III — 3, or 3 4 — V — 2 III, or 

 3 VIII — 2 III — 4 V. According to which last method, 

 this interval is tuned (between B and c b) on Mr Lis- 

 ton's organ, as shewn in the Philosophical Magazine, 

 vol. xxxvii. p. 275. 



The following equations exhibit the value of the mi- 

 nor comma, in terms of all the several intervals in the 

 Table, Plate XXX. of Vol. II. viz. 



=92 + F+f 

 =6z + F+* 

 =42 + R-j-f 



=22 + R + T 

 = z+R+k 



= rf + R-f 

 = 10d+30f—9m 



€= £— m— -112 

 = „■_ f-_52 

 = D— f— 42 

 = f— £__2 



= >_ ,r_2 



= S— S— 2 



= T— T— 2 

 = T— t— 2 

 = T— P— S 

 = t— S— 3 

 = t— 2cf— c 

 = t_P_/ 

 =2S— P— ? 

 -3d"— f 



€=102+m 

 = R+# 

 = 3^+d 



C= c— 2 

 = <1— 22 

 = £— c 

 = /-2c 

 = 2c— d 



= s— s 



= L— if 



= S— P 



= /— * 



= *— fc 

 = 0— f 

 = D-J€ 

 = rf— 3 

 =2S— T 

 = T— 2S 

 = 2£— / 



€=92+ d+3f 



€=212+2m— c 

 = 2 + £_d: 

 = R+ 2r— f 

 = «J + f_ r 



= c+ x—x. 

 = 5r + m — 5f 



= ,r+ R— c 



= ,r + f_R 

 = /+ R-E 

 — T + £— T 

 = 2S + c— T 

 • = /+ X— / 



This interval has been called the lesser comma by 

 some : M. Chladni calls it a comma : it is the apotome 

 minor of Salomon Delaus : the minor apotome of some 

 Avriters : the diaschisma of Euler : the diesis major of 

 Maxwell : the grave diesis, or grave diminished second* 

 of Listen ; and it is =. i976837 X /: it forms the inter- 

 val between 23 of the adjacent notes in his scale. See 

 Philosophical Magazine, vol xxxix, p. 373. M. Euler 

 states it to be nearly the ^st part of the octave. 



Comma Maximum, comma of Pythagoras, Boethius, 

 &c. or ancient comma, is an interval whose ratio is 

 f^TTT . = 1 22 + m, or the Diaschisma (d). This in- 

 terval has also been called the comma syntonum, the 

 comma ditonicum, and is the major comma of Koll- 

 mann. 



Commas, Various. We shall now proceed to o-ive, in 

 a Tabular form, as in Plate XXX. vol. ii. some of the 

 most useful particulars, of all the intervals which we 

 have met with in musical writings, under the name of 

 Comma, viz. 



No. 



1 



2 



3 



4 



5 



6 



•7 



8 



9 



10 



11 



12 



13 



14 



15 



16 



17 



18 



19 



20 



21 



22 



23 



24 



25 



26 



Ratios, or 

 Fractions. 



32768 

 32 8 05 

 14 9 8 3 1 

 1J0O58 



2 2 9 

 235 



5 2 144 1 



5 5 i 'i B » 



125 



125 



9 5 



35 



20 2 5 



204 8 



8 



ST 



5 24 2 8 8 

 531441 



f3 

 4 

 4)00625 

 4 "1 9 4" o 4" 

 12 5 



4 

 5T5T 

 3 5 

 35 

 6 2 5 

 54 8" 



Indices of the 

 Primes 

 2 3 & 5 



15 



-8 



—11 



4 —4 1 



19 —12 



—22 



8 



Common 11-place 

 Logarithms. 



8 —8 

 -3 ' —4 



.9995098,9287 



.9995104,3 



9995081,2092 



.9981076,4632 



.9981054,6213 



.9976352, 



.9965394,6789 



.9954523,7225 



.9950950,7525 



.9948500,2168 



.9948321,03 



.9946049,6811 



.9943942,5528 



.9943415.7707 



.9943201, 8S76 



.9943163,8639 



.9942803,1368 



.9942190.5029 



.9911148,6098 



.9940904,1101 



.9931605,7547 



.9901901.5050 



.9897000,4336 



■9' 92099.3622 



,9877655,4358 



.9843050.1147 



New Notation. 



f. m. 



1. 



0.998898 

 1.003615 

 3.861102 

 3.865559 

 4825125 

 7 052904 

 9.270982 

 10. 

 10.5 



10.536559 

 11, 



11.429932 

 11.537415 

 11.581055 

 11.588813 

 11.662416 

 11.7N7416 

 12. 



12.049887 

 13.947095 

 20. 

 21. 

 22. 



24.947096 

 32. 



























1 



1 



1 



1 



1 



1 



1 



1 



2 



2 



2 



2 



3 



Binary 

 Logarithms. 



.00162810 



.0016340 



.0062935 



.0162933 

 .0171076 



.0179219 

 .0186218 

 .0187972 

 .0188679 

 .018H806 

 .0190005 

 .0192040 

 .0195500 

 .0196313 



.0325976 

 .0342153 

 .0358438 



.0521376 



Comma 

 Logarithms. 



.09084418 



.0911726 



.351163 



.9091558 

 .9545785 



1.000000 



1.039058 



1.04SS22 



1.052786 



1 053490 



1.060176 



1.071532 



1.090843 



1.095S77 



1.2677 



1.818312 



1.909156 



2.000000 



2.909156 



Comm:-. 



