318 On. different Temperuments 



the HI 3= A; D, or the II = f; and C, the key or unison = f 

 (see vol. xxvi. p. 174, of vour Magazine); and go through 

 the comparison of the usuallv harmonies, which must be taken 

 when D, E, F, G, A, and B, become successively the bass 

 notes, in performing a piece of full music in that key, we 

 shall find several instances wherein av error of a whole cornnia 

 occurs in the harmony, and which cannot be cured by any 

 arrangement or alteration of the intermediate or half-notes 

 h or *, because none of these are or can be used in this key, 

 besides their laying, at the distance of several commas from 

 the notes which are erroneous, and therefore cannot be sub- 

 stituted for them : thus, in considering or using D as a 3d 

 below F, as a VI above F, or as a V below A, &c., we slial! 

 find that D, for such purposes, ought to have been yV (i'^' 

 stead of 3", at which it is properly fixed, for the other har- 

 monies in which it occurs), or a comma different from its 

 other value : in like manner, when B is to be used as a 3d 

 below or a VI nbove the D last determined, &c., we shall 

 find the same require the ratio of -j-^ (instead of -jSj-, at which 

 it is properly fixed for the other harmonies in which it oc- 

 curs), ov & comma, different; and thus has JNIr. Maxwell 

 ably shown that, no septave (or octave, as it is called, v/hen 

 the key note is repeated at top) can be perfect, as lord Stan- 

 hope (p. ly, and others of his essay) asserts his key of C 

 major to be; but every such contains wifhin it<:flf\.ciinpera.~ 

 inents, perhaps equal to or exceeding a comma i and nothing 

 short of a veufuve, or system of nine notes loilhin the octane, 

 for each key, both major and minor, can cure this inherent 

 defect or disagreement between melody and harmony. 



We have next to consider, that composers and performers 

 are in the constant habit of modulating into different keys, 

 or of making at times every note in their dojizeave a key- 

 note, major as well as minor: thus the keys in use are 

 not less than 54 in number, byt these arc by no means of 

 rqa.ll freqtt.en.cy in use ; if thcv were, I think every practical 

 tnusickuti would at once agree, in arlvipting the f.so/o/zic or 

 ctiual division of the dojizciivt, for imperfect instruments ; 

 and here our inquiries might end : but the fact is, tb.at the 

 occuriKUce of ihc^r dit'erent keys in practice, is very different , 



as 



