of the Musical Scaie. 31 9 



as to frequency, although the same has never yet been 

 ascertained 01 expressed in numbers, for accurately stating 

 their proportionate frequency of occurrence ; and hence, a 

 large portion of practical musicians or performers on im- 

 perfect instruments*, as well as professional tuners, reject 

 the isotonic system ; and claim, some to make one key per- 

 fect (as they improperly call it), or nearly perfect, and some 

 another, without assigning any just or satisfactory reasons 

 for their assumptions, as may be fairly objected to lord 

 Stanhope, in liis very imperfect attempt at obtaining perfec- 

 tion in his key of C major. 



But further, we ought not merely to know how frequently 

 each key is likely to occur, and how long to be used, in pro* 

 portion to the use of the other keys, in order to make the 

 keys proportionally perfect, in the order in which they are 

 likely to be used ; but we are required to take into con- 

 sideration, the frequency with which chords, between almost 

 every two of the notes in the septave, (of which each key 

 must consist,) are likely to occur : and this, I humbly sub- 

 mit, leads to the conclusion on this subjectj which I came to 

 at p. 176 of your xxvith volume, to which the learned Pro- 

 fessor has in the Retrospect (no. 7- vol. ii. p. 420 and 4i;i) 

 objected, and whose objections I beg now the liberty of con- 

 sidering, in a way which I hope that he will not hesitate 

 to examine, whatever I may write on this or any other sub- 

 ject. In p. 4-20, Mr. Professor, after speaking of logarithms 

 as the measures of ratios, or means of deciding on the pre- 

 tensions of different systems proposed, says: "The best 

 system of temperament wijl be much more readily ascer- 

 tained by this mean" (logarithms) "than by endeavo'uring to 

 determine, as Mr. Farey likewise recommends, the propor- 

 tionate frequency of occurrence of tlie several harmonic in- 

 tervals," and " advising tliat the cliords most frequently 

 occurring may be made proportionally nuarer to pericction ; 



• it hai beta shown. I hope, that vocnl performers and those who use pir- 

 Jtct tnitTumenit liave nothing to do with this inquiry, all keys being alike 

 to them, whctlicr pitched exactly from any not*: in a given domtaitt or from 

 any possible intermediute pitch, ai a key, as every singer knows. 



VoU 27. No. 108. May l'i07. X because 



