346 On Musical Scales. [July, 
Young in his ‘ Lectures on Natural Philosophy’ (Lect. 33), which, 
translated into our language, are respectively— 
Do Re Mi Fa Sol La Si do 
0, 75, 163, 245, 327, 415, 490, 583, 660, 745, 830, 908, 1000; 
And 0, 75, 164, 245, 322, 415, 490, 585, 660, 743, 830, 905, 1000; 
in the latter of which it will be seen that with the exception of the 
single interval of 583 instead of 585, between Mi and Sz, the semi- 
tones are all inserted by eight successive additions of 585 from Mz 
upwards: thus 823+ 583=905; 905+585 =1,490; 1,490 + 
585=2,075; 2,075-+-585 =2,660; 2,6604-585=3,245 ; 3245+ 
585 = 38,830; 3,830+585 = 4,415; 4,415+585 — 5,000: from 
which, rejecting the entire thousands so as to bring the notes all 
within the compass of one octave, we have a series of accidentals 
identical with the second of those set down in (VI1.). 
Let us now examine these three scales in succession, by forming 
out of them—Istly, all the Fifths; 2ndly, all the Major Thirds ; 
and 8rdly, all the Minor Thirds which can be made among them, 
and we shall find as follows: viz. Istly, for the scale (A)— 
Vths—585, 585, 567, 585, 585, 585, 601, 585, 585, 585, 567, 585; 
[lIrds—322, 322, 322, 322, 356, 322, 356, 322, 322, 356, 322, 356; 
3rds—263, 229, 245, 229, 263, 263, 245, 263, 229, 263, 245, 263; 
showing nine good Fifths, eight Major, and six Minor Thirds. The 
erroneous Fifths are, two of them, deficient by a Comma, and one in 
excess by nearly a Comma (16). The erroneous Major Thirds are 
all in excess by 34, or nearly two Commas; and the erroneous 
Minor Thirds all deficient, three by a Comma and three by 34. 
The scale (B) similarly tried, gives— 
Vths—585, 585, 567, 585, 585, 585, 567, 585, 585, 585, 601, 585; 
IIIrds—322, 356, 322, 356, 322, 322, 322, 322, 356, 322, 356, 322; 
3rds—229, 263, 245, 263, 263, 229, 245, 229, 263, 263, 245, 263; 
which singularly enough (as it seems at first sight) exhibits the 
same number of each harmonic as (A), and the same amount of 
deviation, and in the same direction for each. These two scales 
then are precisely on a par, nor does there seem any reason for pre- 
ferring one to the other. Both are rich in perfect Thirds both Major 
and Minor, which is a strong recommendation ; but, owing to the 
bad Fifths which they involve, three out of the eleven keys into 
which the fundamental scale may be transposed are spoiled by false 
dominants, and three others blemished by false sub-dominants, while 
the more erroneous Thirds cannot but prove objectionable wherever 
they may occur. 
Treating our scale (C) in the same manner, we get :— 
Vths—585, 585, 567, 585, 585, 585, 585, 585, 585, 585, 584, 584; 
IlIrds—322, 339, 321, 339, 339, 322, 340, 322, 339, 339, 339, 339 ; 
3rds—246, 246, 245, 245, 263, 246, 246, 246, 246, 263, 245, 263; 
