On Musical Intonation and Temperament. By I. F. Holton. 

 Read Oct. 12th— 19th, and Nov. 2nd, 1846. 



The mathematical relations of musical sounds have received very 

 little attention from scientific writers, for the last quarter of a cen- 

 tury. Almost every branch of science has been greatly simplified du- 

 ring this period; this still repels the beginner with a formidable array 

 of difficulties. It is the object of this paper to present the first ele- 

 ments only of the Mathematics of Music, in a form so simple as to be 

 understood, on a careful perusal, by any one familiar with the main 

 principles of common arithmetic. 



Sound is produced by vibrations of air. The sound produced by 

 more frequent vibrations is called more acute or HIGHER — that by 

 less frequent vibrations, graver or lower. This difference is a dif- 

 ference in pitch. The difference in the pitch of two sounds when esti- 

 mated, measured or calculated, is called an interval. 



When drops of water fall on a board at a uniform rate of 16 per 

 second, a uniform sound is heard, about as grave as the human car 

 is capable of appreciating. This sound is called by the English and 

 Germans, £. {great twice marked C,) and by the Italians, French, 

 Spanish and Portuguese, Do 1 , (first Do.) Any thing will produce a 

 sound ofthis pitch which will make 16 uniform impressions on the 

 air in a second, as comb teeth striking against the finger-nail — a 

 vibrating string striking against the air — or air itself vibrating in a 

 tube ; sounds from different sources, as the vibration of a wire and 

 of a silk cord, for instance, though the same in pitch, will differ in qual- 

 ity. The French call this difference in quality, Timbre. 16 pul- 

 sations per second produce Do 1 ;* 32 produce a higher sound, named 

 Do a ; 64 make Do 8 ; 128 make Do' ; 256 make Do', or Middle Do ; 

 512 make Do' ; 1,024 make Do T ; 2,048 make Do'; 4,096 make Do'; 

 8,192 make Do"; and 10,384 uniform pulsations make Do". A 



* I use the Italian names because they are much more convenient ; hut I muflt 

 caution the reador against confounding Do, Jlc, Mi, &c., as the Italians use them, 

 with the same terms as used in American singing school*. 



