420 On the Scale and tuning of the Rev.Mr.Liston's Organ. 



have been called my Artificial Comvias^ in imitation of 

 Mercator's artificial commas 53 in tlie Octave, (Holder's 

 Treatise, 1st Edit. p. 79), the reason or derivation of whose 

 curious approximate conmjoii-mcasure to Intervals, was 

 unknown, I believe, until 1 had expressed atid arranged 

 Intervals in the notation bv 5:, f and m, wliea the number 

 of ms to any note in such new Notation, was found to 

 agree exactly with Mercator's numhers. With respect to 

 these and all other artificial commas, it is to be observed, 

 that they form a sort of musical (whole number) logarithms, 

 having the least Interval as lhe\r unit, and will, by addition 

 and subtraction, correctly show the values and relations of 

 intervals larger than their unit, and betivaen trhich no dif' 

 J'erences occur smaller than their unit ; all smaller intervals, 

 and some of those very near to the value of the unit, are 

 liowever erroneously expressed by them : but in perfect 

 Jlarmonv, as F have before observed (vol. xxxvii. p. 274), 

 no less Interval than 2 occurs, and thetefore they may be 

 safely used, in all its calculations. 



In the Table which I gave in vol. xxxvii. p. 276, of the 

 No»cs on Mr. Listen's former Instrument, nine of the above 

 notes are omilled, viz. 



B'bb 



Bbb 



F'b 



And the 10 following were inserted unnecessarily in that 

 Table, on account of there being no shades to produce 

 these notes, as being found unnecessary in the widest rantre 

 of modulation; viz. B'*, C'b, B'b, A\ G'*, G*b, F', E', 

 D'* and D'b, by which the scale for the new Organ is re- 

 duced to 5y Notes, as above. 



The shades by which the alteration of a comma is pro- 

 duced in the sounds of the Pipes, as explained in vol. xxxvii. 

 p. 328, and in Mr. Liston's Essay, p. 45, not being able 

 to raise their sounds, only to depress their pitch, one, or 

 two contmas, the Pipes in Mr. L.'s Organ, arc necessarily 

 tuned to the acute notes ; a standard Pipe, a major comma 

 liigher than Concert Pitch, being used for piichingC't* 

 from whence the Tuning is conducted upwards, thus, viz. 



f Or, having the pitch of C, we may tune upwards C y G y D y 

 A' y E', and then downwards f ' ... C which is the proper pitch for com- 

 mencing Tuning, as Mr. L. shows, p. 44. 



