1864.] 



of Instruments with Fixed Tones, 



413 



7z-\2y 



7z^\2y 



7z—l2y 



7z-\2y 



0, 



1, 



Many of these cycles are quite useless. The following selection is ar- 

 ranged in order of magnitude, from the greatest to the smallest cycle. 



No. 33 (38). Cycle of 118; ^=-002551 1, log i;=69A=-1760259. 

 This is Drobisch's cycle (Mus. Ton. § 58) representing No. 32. 



No. 34(8). Cycle of 93; A=-0032368, log ij=54A= -17478/2. 

 This may represent No. 2. 



No. 35 (3). Cycle of 81 ; A='0037164, log ?;=47A = - 1746 708. 

 This may represent No. 11(2). 



No. 36 (39). Cycle of 77; ^=-0039095, logi?=45A='1759275. 

 This is the same as No. 52. 



No. 37(19). Cycle of 74; A=-004068, log v=43A=-1749200. 



This is another of Drobisch's cycles (Nachtrage, § 7) representing No. 27. 



No. 38 (22). Cycle of 69 ; ^=-004363, log z?=40A=- 1745200. 



No. 39 (28). Cycle of 67; ^='004493, log2;=39A=-1752270. 



No. 40 (40). Cycle of 65; A=-0046123, log v=38A=-17598674. 



No. 41 (27). Cycle of 57; ^=-0052812, log?;=33A=-1742796. 



No. 42 (30). Cycle of 55; ^='0054733, log«;=32^=-1751456. 



This is mentioned by Sauveur (Mem. de I'Acad. 1707) as the commonly 

 received cycle in his time. Esteve {loc. cit. p. 135) calls it the Musicians' 

 Cycle. 



No. 43(11). Cycle of 50; ^='0060206, logi;=29A=-1745974. 



This is Henfling's cycle {loc. cit. p. 281), and is used by Dr. Smith to 

 represent No. 9. 



No. 44 (43). Cycle of 53; ^ = -0056798, log v=3U=-1760800. 



This is the cycle employed by Nicholas Mercator (as reported by Holder, 

 'Treatise on Harmony,' p. 79) to represent approximately the just scale. 

 He did not propose it as a system of temperament as has been recently 

 done by Drobisch (Musik. Tonbestim. Einleit.). It was the foundation of 



