OF ARTS AND SCIENCES. 499 



XXVIII. 



CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF THE 

 MASSACHUSETTS INSTITUTE OF TECHNOLOGY. 



XXV. — NOTES ON EQUAL TEMPERAMENT AND THE 

 CHARACTER OF MUSICAL KEYS. 



By Charles R. Cross. 



CommunicateJ February 16, 1886. 



The question as to how closely the tuner of a keyed instrument actu- 

 ally realizes the isotonic scale upon the instrument is one of much 

 interest, regarding which there has hitherto been but little information 

 accessible. Some very recent and valuable results of measurement 

 will, however, be found on page 485 of the new edition of Mr. Ellis's 

 translation of Helmholtz's Tonempjindungen, which should be com- 

 pared with those which are given farther on in this paper. 



The following measurements were made by Mr. William T. Miller 

 and myself several years since, but have not been published hitherto, 

 in the hope that they might be extended further, and to additional 

 instruments. But this has not thus far proved feasible. 



The best available instrument upon which to make such experi- 

 ments appeared to be a good cabinet organ, and therefore a freshly 

 tuned single-reed cabinet organ, made by Messrs. Mason and Hamlin, 

 was hired of them for the purpose. The insti-ument was not tuned 

 especially for us, however, but taken at random from the ware-rooms. 

 The tonometer used was made by Koenig, and consisted of a set of 

 thirteen forks tuned carefully to the isotonic scale, running from mid- 

 dle C, of 269.2 vibrations per second, to the octave of this. These 

 forks, according to the maker, were correct within less than one 

 tenth of a vibration. The notes of the cabinet organ throughout the 

 octave, from Cg to C^, were carefully compared by the method of beats 

 with the corresponding forks. The temperature varied but little from 

 78° F. during the experiments. 



As considerable change in the rate of the reeds could be made by 

 varying the strength of the air-pressure from the bellows, care was 



