350 On Musical Scales. [July, 
by 20, or by what is called a “ Pythagorean Comma,” and so throw- 
ing “the wolf,’ as the phrase is, deliberately mto one key, whose 
dominant, deficient by that amount, shall render it altogether unfit 
for use. To find the values of the notes in this scale, we have only 
to form the eleven first multiples of 585, reject the thousands, and 
arrange the results in order of magnitude, which gives the scale— 
Do ‘Re Mi Fa Sol La Si do 
(d) 0, 95, 170, 265, 340, 435, 510, 585, 680, 755, 850, 925, 1000. 
This scale, tried by the same test of Fifths and Major and Minor 
Thirds, gives us eleven perfect Fifths, and one deficient by 20 ; four 
Major Thirds deficient only by 2, and which therefore may be re- 
ceived as good, and all the other eight excessive by a Comma; and 
four Minor Thirds excessive by 2, and therefore to be received as 
good, all the rest being deficient by a Comma. ‘This scale, then, so 
far from meriting the unreserved condemnation with which it has 
been received, stands in no very unfavourable comparison with (C) 
or (c) (though certainly inferior to both), in the original key, while 
in its transpositions (taking C as the original key) it exhibits some 
remarkable peculiarities which render it otherwise worthy of atten- 
tion, as the following table will show :— 
Gd. | ie: |p. iD: Bp. | EB | | Gb. |G | Ap. | a: | Bp ae 
Domes 0 0 0 0 0 0 0 
Rey -ce| LON) 270) L700) L70) | 270) 1500) 170) 704) L700) ON Loon eae 
Mi .. | 340 | 340 | 340 | 320 | 340 | 320 | 340 | 340 | 320 | 340 | 320 | 340 
Fa .. | 435 | 415 | 415 | 415 | 415 | 415 | 415 | 415 | 415 | 415 | 415 | 415 
Sol .. | 585 | 585 | 585 | 585 | 585 | 565 | 585 | 585 | 585 | 585 | 585 | 585 
La .. | 755 | 755 | 755 | 735 | 755 | 735 | 755 | 755 | 755 | 755 | 735 | 755 
St .. | 925 | 905 | 925 | 905 | 925 | 905 | 925 | 925 | 905 | 925 | 905 | 925 
do .. |1000 1000 1000 1000 1000 |1000 |1000 1000 |1000 1000 |1000 |1000 
(e))|| PAD | Bp. |B | ee} Dy | Deh, Bel eee el ieee 
(f) Do) Bes) OMe) ES ISG peat eal AR BEE eGRe kage Dp. 
This table, as it stands, with the headings of the columns as on 
the upper horizontal line marked (d), exhibits the transpositions of 
the scale (d), starting with C as a fundamental note. It affords two 
very good scales, vz. a good, almost a perfect, diatonic scale in Eb, 
and an equally good co-diatonic in Bh; so that in those keys it will 
afford excellent harmony. What seems to condemn it is, that it 
throws “the wolf” into F, one of the most useful keys, and what 
may be called “the counter-wolf” (that which results from a faulty 
IVth—for every faulty Fifth im one key necessitates an equally 
faulty Fourth in the key a fourth below it) into the original key C 
itself. This unlucky defect, however, it is evident, will be evaded by 
starting, and beginning to tune our Fifths upwards, not from C but 
