166 Mr. R. H. M. Bosanquet on Temperament, 



The history of the scale divides itself into three principal 

 periods, corresponding to (1) the ancient systems of perfect con- 

 cords, (2) the mean-tone and allied temperaments, and (3) the 

 equal temperament. The exact mode of origin of the first tem- 

 peraments is no doubt unknown. According to Smith (' Har- 

 monics/ 1759), Salinas found a temperament in use in Italy in 

 an empirical manner, its theory not being understood ; and on in- 

 vestigating the question, he arrived at certain forms, that which 

 he preferred being such that all the fifths were made | of a 

 comma flat; this is the mean-tone system. Zarlino is said to 

 have first published it ; so that the date of the origin of this 

 system is ascertained with some certainty as being in the latter 

 part of the sixteenth century. Its practical employment does 

 not appear to have spread very rapidly. Mersenne (Harmonico- 

 rum Liber \ 1636), who quotes Salinas, and certainly knew of the 

 system, confines himself almost entirely to perfect- concord sys- 

 tem. A century later the mean-tone system was almost univer- 

 sal (though Bach had by that time given it its death-blow as ap- 

 plied to 12-keyed instruments) ; and in Smith's f Harmonics ' it, 

 and modifications of it, are treated as being alone of any value. 

 The equal temperament, or the division of the octave into 12 

 equal intervals, has now almost universally superseded it. 



Mersenne himself belongs to the first period. His systems 

 are all based on perfect concords ; and he meets the difficulty of 

 the great number of notes required for such systems by means 

 of key-boards of greater or less complexity. These are in prin- 

 ciple of the same nature with the key-boards of General T. Per- 

 ronet Thompson; and indeed Thompson says himself that he 

 learnt much from Mersenne. 



The system of 31 equal divisions in the octave is known by 

 Huyghens's name. This system was known to Mersenne and 

 Salinas ; but they could not make any thing of it. Huyghens 

 points out that they were not acquainted with the methods re- 

 quired for dealing with it, and constructs it himself with the 

 aid of logarithms (Cyclus Harmonious — Opera Varia, vol. i.). All 

 parts of this system are, within an error small with respect to 

 the error of practical tuning, the same as the mean-tone system. 

 The original date of the Cyclus Harmonious was probably before 

 1700. 



Smith's ' Harmonics/ 1759 (2nd edit.) has always been re- 

 garded as a most important work. A curious remark in the 

 preface deserves attention. It amounts to a numerical coinci- 

 dence between the ratios interval of octave : interval of major 

 third, and circumference of circle : diameter. Of course the 

 coincidence is purely accidental, both ratios being a little greater 

 than 3; but that a practical mail should, as Smith relates, 



