I N T
INT.
- ne tone-minor rncreafed by a comma is e'qual to a tone-ma-
jor, and vice verfa, T = / fhews that the tone-major dimi- nifhed by a comma is equal to the tone-minor. The figps -f , — , =, are here taken in the Came fenfe, as in algebra, to ftgnify addition,, fubftradtion, and equality. So likewife the dot placed between two numbers,, or between a number and the fymbol of an Interval, hgnines that the Interval is to be multiplied by the number. Thus i . IV fhews that the fourth is doubled; and thus,. y b = VI -j-S:= 2. IV = VIII — T, fhews T that the lefler flat feventh is equal to the fixth major and femi tone-major, or alfo to two fourths, or to the octave when the tone-major has been taken from it. Laft- ly, the fixth column of trie table fhews the meafures, or lo- garithms of the ratios in the fecond column. Thefe are not
the common logarithms of the tables where i.oocoooo" ifr the logarithm ot 10. But here i , ooooo is afiUmed as the logarithm of -|£ or of the comma, as before mentioned. Thefe logarithms are eafily derived from the common, of the larger tables of Vlacq. or Briggs. Thus the logarithm of 2, or the octave = o. 3010299957 ; the logarithm of |, or of the fifth == 0. 1760912590 ; and laftly, the logarithm of ^, or of the third major = o. 0969100130. Now thefe logarithms being feverally divided by the logarithm of f^, or of the comma = 0. 00539503.19 ; the quotients will give the number of commas in an octave = 55. 79763 ; in a fifth. = 32. 63952 ;• and in- a third major =17. 962S2. Hence all the reft may be found by addition and fubftra£tion only,. Here follows the Table.
A TABLE of Mufical Intervals, with their Meafures.
Names of the Intervals.
Proportions exp rerun g the Intervals
Efchaton Diafch'ifma .
Comma —
Comma of Pythagoras — —
Hyperoche -— - —
Enharmonic Diefis, or diminifhed fecond — Semi- tone Minor, or leaft Chromatic Diefls
Limma of the Greek Scale, or deficient 1 Semi-tone Major ■ 5
Lefler Limma, or redundant Semi-Sone Minor
- Semi-tone Major ■
Apotome of the Greek Scale . ■ 1
Greater Limma, or redundant Semi-tone
Major ■ ■
Double Semi-tone Minor >
Greateft Limma, or redundant double Semi- 1 tone Minor ■ ■ V
Tone-Minor 1
Tone-Major — ,
Compofition of the Pro- portions from 2, 3, and 5.
Diminifhed Third
Superfluous Second
Trihcmitone of the Greek Scale, or defi- cient third Minor
Third Minor
Trihemitonc Major «— Extreme diminifhed Fourth
Third Major .
Ditonus of the Greek Scale, or redundant third Major ■
Diminifhed fourth ■ ■
Superfluous third ■■■ — —
Fourth — ■ ■ ■■ -—
Redundant fourth
Superfluous fourth
Semidiapente of the Greek Scale
393^x6
390625
2048
2025
81
5242S8
3125
307 2 128
125
21 24
243
J 35
128
i6_
- 5
2187
2048
27
25 . 625
S76 1 1 25
1024 10
9
_9
8
256
225
3-5*
144
2t 3 >
125
S i
125
5 3
108
2-3 3
75
3-5*
64
2 6
32
2 J
2 l
3 3
6
2-3
5
5
4096
2 I2
3375
3 ; 53
768
2*3
625
5+
5
5
4
2*
81
3 4
64
2«
32
2 s
25
5*
125
5 !
96
2-'3
4
2»
3
3
27
3'
20
2*5
25
5*
18
2-3 2
1024
2 Ia
729
3 s
Simple Signs.
T
III
IV
Complex Signs to fliew the Compofition of In- tervals.
d
T—t
6 T — VIII
-d=S — 2d S — s
S = i4./; = III_ 3 S = IV — 2T
/=T — S
s + d = lV-~W
T — S=V
S = T— 1
is = t— d
s + s=T — d
S+j=T=IV— 3 >=ni— T
t = V — IV
f -f d = 2S
T4.i=3 b -i
(+,
T + s = 3*-d
3» = i4-S = IV_T
T + S = V_ III
3 S=T+S + d t
3" + rf = IV— 2j
ni=v_3*
in = 2T
Iil4-rf = IV — j
ni + i
iii + s=vm— v
IV = 3" +T IV+f
iv+s
Meafures
by Commas.
o. 53222 0. 90917 I. ooooo 1.09083
'■3769s
r. 90917 3. 28612 4. 19529 4.28612 5- 19529 5.28612 6. 19529 6. 57224 7.57224 8. 48 141 9.48141 10. 39058 11.39058 11.76753 12. 76753 13.67670 14. 67670 15.58587 16.58587 17.96282 18.96282 19.87199 21. 24894
23. 15811 24. 15811
26. 44423
27- 353+0 Triton us,
