of the Musical Scale. 205 



assist the Inquiries of those who, possessing more leisure 

 than my professional duties at present leave me, may be dis- 

 posed to examine it thoroughly in all its bearings. 



Conceiving that the notation by tuveahle intervals, rather 

 than by T, t, and H, or tone major, tone minor, and kemi- 

 tone, which Sauveur, Dr. Smith, Maxwell, Hawkes, and 

 other writers on the scale of music have used, will greatly 

 facilitate the study of this curious and useful subject, I have 

 composed a table of all the combinations of the musical 

 primes 1, 2, 3, and 5, which when multiplied do not in any 

 case exceed 10,000; and another table of these composite 

 or musical numbers (17* in number), arranged numeri- 

 cally, with their factors and logarithms annexed ; by which, 

 in evtry possible case, any fraction or ratio, neither of whose 

 terms exceed four places of figures, can be resolved mto 

 tuneable intervals ; and, on the contrary, any com.binatioii 

 oUuneable intervals in whole numbers can be resolved into a 

 vulgar fraction or ratio, and its logarithm obtained, without 

 reference to any other tables : these tables, with examples 

 of their uses, I intended to have sent herewith ; but fearing 

 that I have already exceeded the limits of articles in your 

 Magazine, I shall defer them to another opportunity. 



I have too high an opinion of earl Stanhope's liberality of 

 mind, and zeal for the discovery of scientific truth, to offer 

 any apology for the freedom with which I have examined 

 and commented on his treatise; and should the pending in- 

 vestigations of Dr. Callcott and others, comparing the beats 

 made by every concord among themselves, as well as with 

 the key note, ultimately pronounce in favour of the Stan- 

 hope temperament, the actual number of beats of the tri-equal 

 quints and bi-cqual thirds can be readily calculated, and, 

 when arranged in tables, can be as easily applied in tuning 

 without a monochord or glasses, as if the numbers had been 

 equal; for they must have been counted during a given space 

 of time, in order to ascertain that equality with the necessary 

 precision. 



I profess to be influenced but little by the arguments re- 

 specting character in the difl'ercnt keys ; it has never ap- 

 peared 



