352 On Musical Scales. [July, 
accompaniment, however, to instruments without a fixed scale, and 
more especially to vocal music in parts, where the performers, if 
they have any ear, will naturally endeavour to keep their Thirds 
perfect in those passages in which many of them follow in succes- 
sion, on which so much of the beauty of vocal music depends, the 
advantage of a scale abounding in perfect Thirds is evident; espe- 
cially if the composer, aware of the existence of faulty ones in the 
scale, should avoid their introduction, or avoid, at least, dwelling 
long on them. 
To show the composition of the several numbers which occur in 
the foregoing scales, or what musical intervals they represent, we 
subjoin the following table, in which it is to be remembered that the 
entire thousands (expressive of octaves), whether + or —, are re- 
jected ; or in other terms, that — V (a Fifth tuned downwards) is 
to be considered as equivalent to + IV = 415, a Fourth tuned up- 
wards ; and — III., a descending Third, to = 678, its complement to 
the octave, ascending ; and in which it must also be borne in mind 
that though these equations may be added to or substracted from 
one another or multiplied by any whole number, they must not be 
halved, quartered, or otherwise divided. 
Table of Musical Equivalents in the foregoing pages, the Octave 
being 1000. 
1= — 2111+ 37V. | 247=+ IT.+ SV. | 644= + 21I1. 
2=+ I+ 8vV./263=- I.+ V.| 660= =, AVE 
16= -—21011.-— 4V.| 265= + 9V. | 662=+4 III.+ 4Y. 
i~@=— H+ 4V. | 320= = $V. | 6738i= — it 
20 = +12V. | 322=+ OL 680 = + 8V. 
34 = — 3 III. 338 = — Ti = 4 Vi || 730) = - 9V. 
36 = — 211I.+ 8 V. | 340= + 4V.| 7237=+ MI. - Ve 
52= -4II1.+ 4V. | 415= - V. | 758=— DL— 5V. 
59=+201.- V.| 483=— I.+ 8V. | 755 = => (one 
7) = — OnVen|saoo IDV.) 71 = — 20 =) ave 
W7=+ L+ 3V.) 474=+200.— 2V.| 796=+38111.— 2YV. 
93 = — IIL —- V. | 490 = — 6Y. | 814 = - 2.10 = 2 
95 = + 7V.|/492=+ IIL+ 2Vv.| 830= - 2V. 
111 = - 2101.+ 3V./508=—-— TL- 2V.| 832=+ MTI.+ 6V. 
150 = -— 10 V. | 510 = — 6V. | 850 = + 10V. 
152=-+ IIIl.-— 2V./ 526= —-2111.+ 2V.| 889=+2II.-— $8V. 
168=— I.— 6V. | 565= — Ven s900%— — TV. 
17{0) = - 2 Y. | 06% = =) T= 3Ve 907 = =F iL -- eve 
186 = — 2110.- 2V.|583=- Ill—- 7V.|923=— I.- 8V. 
229=+2I10.+ #£«xV-./} 585 = ap. We |p SPs + SV. 
245 = — 8V.|601='-21.— 38V.)/ 941 =—20I-- Vi 
