of the Musical Scale. 193 



pres-sing, as it is capable of doing, not only every possible 

 interval in the diatonic system, bat even the almost endless 

 variety of" intervals which arise, in considering the division 

 of harmonic intervals into aliquot parts, as is done by his 

 lordship in obtaining his hi-equal thirds and tri-equal qiiiiifs 

 (pages 301 and 302) : in this mode, column 5 and colnani 3 

 in my Tables I and II following (which are titled, and arc 

 to be read, from the bottom upwards) express all the in- 

 tervals mentioned by his lordship, and are to be read thus : 

 c the octave, or VIII, consists of the sum of a third and 

 jinnor sixth (III -j- 6th), of the sum of a Jifth and minor 

 fourth (V + 4th), or a iixth and minor third (VI + 3d), Sic, 

 and may be thus tuned as above cxi)laiiied ; alwavs observ- 

 ing, that the 3d, 6th, Vl, in this colunui are diat(/:iic or 

 perfect, and not Stanhope or tempered intervals : b B, or 

 the 7th, may be tuned by adding two 4ths in succession, or 

 two VIII upwards and two V downwards; b A, or the 

 Stanhope Cth, by tuning upwards an V^III and a III in suc- 

 cession, and bisecting the interval thus obtained above C by 

 a new sound ; of wl>ich more hereafter. It is here to be un^ 

 derstood, as in algebraic notation, that where neither of the 

 signs -}- or — (denoting addition and suhtracliou) is af- 

 fixed to any term or interval in these columns, -f- is to be 

 understood j as denoting ascent and the tuning or reading 

 the interval which it precedes upwards', while — denotes 

 that the following term or chord is to be tuned or read down- 

 wards : at the same time, these signs + and — may be con- 

 sidered as merely expressing contrariety in the direction in 

 which an interval is to be tuned or read; and, if a III was 

 wanted below C, instead of above it at E, the expression VI 

 + V — VIII may have all its signs changed, viz. — VI 

 — V -;- VIII, and the same will denote a VI and a \' down- 

 wards in succession, and thence an VIII upward.s, which 

 will bring us to a note called b A, which is the diatonic, or 

 perfect major third (III) below the key note C. 



Gentlemen who are conversant in the management of 



vulgar fractions, and no others should think of comparing 



the relations of musical intervals, will see no dilliculiy 



in adding or subtracting any of the intervals contained in 



N 2 colunms 



