'20 



C M M A. 



fVi.iims, No. 1. in the above Table, is a comma mentioned by 

 *-— -y««- ^j_ Chladni. — No. 2. is the comma minimum of some 

 writers, it is the semi-comma minims of Rameau, but is 

 our Schisma (2), which see. — No 3. is the ^J— th part 

 of the €d >vc, and is the undecomma or artificial comma 

 of Mr Farey, in that particular case where it measures 

 tiie octave; see the Phil Mas:, vol. xxxix. p. 420, and 

 our article Common-measures o' Intervals. — No. 4. is a 

 comma of Philolaus, which he -states to be very near 

 to another comma, the T Vth part of a tone-major, which 

 next follows No. 5. — No. 6. is a comma mentioned by 

 Galileo, but owing to a mistake, in the numerical ope- 

 ration by which he derived it, otherwise he would have 

 obtained the comma of Pythagoras (No. 19. in this 

 Table), as Mr Ovcrend has shewn in his manuscripts. — 

 No. 7. is the smaller comma of M. Chladni. — No. 8. is a 

 comma mentioned by M. Chladni; it is the error or flat- 

 tening of the false minor third on the trumpet and horn ; 

 see Chromatic French horn. — No. 9. is the comma of 

 M. Chladni and the lesser comma of some writers, it is our 

 Minor Comma (C), already fully described. — No. 10. is 

 the half of the enharmonic diesis, which Dr Callcott has 



called a comma. — No. 11. is the „„ ., -th part of an oc- 



58.25 



tave, and is said to be the artificial comma of Mersennus, 



-according to Dr Holder. — 'No. 12. is the Major Comma 



(c), of which we have fully treated. — No. 13. is fth 



of the major semitone, a comma of Boethius, and one 



which Dr Callcott mentions. — No. 1 4. is |th of the limma, 



and is another comma of Boethius.— No. 15. is the 



r \d part of the octave, the artificial comma of N. Mer- 



eator, in that particular case where it measures the oc- Comm*. 

 tave. — No. 16. is -^th part of the major tone, and is ano- ""^"Y~"* 

 ther comma of Boethius, D. Nichola, &e. mentioned also 

 by Dr Callcott. — No. 1 7. is the ^ th part of the minor 

 tone, and is mentioned as a comma by Dr Callcott.— 

 No. 18. is ith part of the semitone medius, and is ano- 

 ther of the commas noticed by Dr Callcott. — No. 19. is 

 the comma of Pythagoras, Boethius, &c. the ancient 

 comma, the comma maximum of some writers ; the 

 comma syntonum, the comma diatonicum, and the ma- 

 jor comma of Kollmann, but is our Diaschisma (d), see 

 that article. — No. 20. is the \d part of a minor semitone, 

 that is mentioned as a comma by Dr Callcott. — No. 21. 

 is a comma mentioned by M. Cliladni, and is the error 

 or flattening of the minor seventh on the trumpet and 

 horn ; see the article above quoted. — No. 22. is the 

 double minor comma, and is =2€, = £ — 2 = f — d. 

 No. 23. is the comma greater of some writers, and one 

 of the commas of M. Chladni, but it is our Enharmonic 

 Diesis (£), which see. — No. 24. is the double major 

 comma, and is = 2 c, = £ -f- 2, = / — %, = d -f- "C, 

 =/— c, = § — /,= P — J, =5T + 2S— VIII.— 

 No. 25. is the bearing comma of Mr Holder. — And 

 No. 26. is the ancient comma of Galileo and one of the 

 commas of M. Chladni, and is =r 2 c -f- C, = £ -f- c, 

 3€ + 2 2, = S — t, = S -/=T— 'i( + 2S. 



Comma and Half. Besides the above commas and 

 artificial commas, &c. of authors, certain intervals have 

 been called comma and half, we shall insert these as a 

 continuation of the above Table, viz, 



No. 2 7 



2S 



195.T125 



625 

 Si ? 



—13 —5 

 — 3—4 



.9917338,2182 

 .9843050,1147 



17. 



— 1 



1 6.850339 







32. 







1} 



.0274596 

 .0521371 



1.532183 

 2.909156 



No. 27 is called the comma and half by Rameau, and is = 1 6.866064 X 2, = c -f- R, = d + F + 42, 

 = € + R-f 2, = c4-F + 52, =C- r -F + 62, =/— *•, =£ — i€, = d + R — 2, =4€+ 22 — /, = 2 S 

 -f § — 4 6, =T— 4 1 -j- 5 S, = 5 3 — 4 III. — No. 28. is the comma and half of Galileo, and is our Semitone 

 minimum (/), which see : it is a repetition of No. 26, above. 



Semi Commas various. The following have been called Semi Commas, viz. 



29 

 SO 



31 



32 



1 5 5 5 S 



1 .5 5 2 ~3 



2 7 15 2 

 2"log375 



530625 

 i 3 a 32 15 



: 8 I 2 5 



b 7 3 5" 



6 5 —6 



21 —3 —7 



9979662,2157 

 .9974761,1443 



4. 1 



5. 1 



.0067561 



.0083842 



3769725 

 .4678167 



—17 —1 8 



.9971288,5368 



f6. -1 11 



(5.850339 13 



.0095377 



.5321834 



— 2—9 7 



.9966387,4655 



r - 1 l \ 



V6.850339 1 3 



.0111659 



.6230275 



No. 29. is the Semi-comma major of Rameau (j£), see 

 that article: it occurs between two of the adjacent 

 notes on Mr Liston's enharmonic scale, viz. between 

 F' b and F$, and between B'bb and A v $, seethe Phil. 

 Mag., vol. xxxix. page 419.— No. 30. is the Semi-comma 

 viaxi me of Rameau (/c), see that article: it is also called 

 a hyperoche by Dr Busby.— No. 31. is called, in the 

 Callcott manuscripts in the library of the Royal Insti- 

 tution, the semi-comma minor of Rameau (but which is 

 inconsistent with the major above), and is the eschaton 

 of M. Henfling and Mr Travers : it is our Major Re- 

 sidual (R), which see.— No. 32, is the mean semi- 

 comma of Rameau : its schisma logarithm is 6.858202 ; 

 in elements of perfect tune it is / -f- 3€ -f 2 2 ; in dia- 

 tonic elements 2 T — 4>t + 3 S; in chromatic elements 

 S -f 2 S — 4 d; and in concordant or tunable elements 

 it is 6 3 — III — 3 4, by which it might be tuned, on 

 Liston's organ, or any similar instrument if want- 

 ed. It is equal R-f- 2, = F -f 62, z=f—/,— € — /, 



&c. The above list, which might probably be extend- 

 ed, if our reading had been still more extensive, shews 

 how necessary it is, for authors and readers of musical 

 works, to be on their guard, as to the numerous and 

 variable uses of the word comma. For want of this at- 

 tention, and using No. 12, 15, and. 19 indiscriminately 

 in part of his writings, a late author on temperament, 

 Mr Hawkes, has drawn some very erroneous conclu- 

 sions, as to his own scale of temperament, as has beeH 

 shewn in the Philosophical Magazine, vol. xxxvii. p. 

 321, and where he is stated to adopt the intermediate 

 comma of the three above, as the foundation of his pro- 

 ceedings ; and yet since that period, he is said to have 

 changed his mind, and preferred the first comma or 

 No. 12, according to which Mr Listen has calculated the 

 temperaments of his system at page 22 of his " Essay 

 on perfect Intonation," viz. the third of the schemes of 

 temperament there given. With respect to artificial 

 commas, it will be necessary to say something more par- 



