418 On the Scales of Clagget's and Loesc/iman's Organ, &c. 



The Vingtunave Scale of 2 1 Notes, on Dr. Robert Smith's 

 Harpsichords, made by Mr. Kiikmati about the year 1758, 

 effected by moving 6 slops sideways by the hands, (see 

 Dr. Smith's " Harmonics," 2nd Eait. p. 186,) is as fol- 

 lows, viz. 



C C*bb D D*Eb EFb eTf F*Gb G cTAb A 



I d J raid Ddld 11 dll 



A* Bb B cb B* c 



e ^ G ^ ^ 



d 1 dad 



Here 6"r? + 4<S + 2(J + 4£ -\-5q =VJ1I, and since 3S = 

 3o> + 3e. 2S = 25 + 2£, and sS = 2J + 2f + 2g. the 

 above equation reduces to 7S + 3 ' + 2 i = VIII, as 

 before. Also, lol + gd + 2) = VIII, and since d + 

 = 1 we have 12l = 7d, as for the 19 Notes above; or, 

 since 1 + d = L, we have 7L + 5l = VIII for-ia Notes, 

 as before. 



•The Vingtduxave Scale of 52 Notes, on the Teliochordan 

 Harps'ichoi-d in the Royal Library at Buckmgham-H )use, 

 made by Mr. Charles Clagget in 1790, effected by two 

 pedals, acting on movable Bridges, is as follows, viz. 



C C*bb D D^Eb E Fb eTf F»Gb F^Tg 



)dl IdldDdldDdl 

 cTkb A A*~Bb BTb bTc 



f ^ e ^ e ^ = 



d 1 1 d 1 d D d 

 Here5!3> + 4!S -h 3J+ 5£ + 5g — V:iT, and since 2S=s 

 So" + 2g, 2S = 2 1 + 2s, and 3S = 3? + 3£ i- 3g, we 

 have 7S + 3 B> 4- 2 il, as before. Also, gl + lOd h 3.; = 

 "VIII, and since 4L = 4l + 4d ; and sL = 6d + 3J, wc 

 have /L + 3l =VIII, as in the Douzeave. 



The Vingtquatreave Scale of 24 Notes, on the Patent 

 Harmonic Piano Forte and Organ invented by Mr. David 

 Loeschman in I8O9, now exhibiting at his house. No. 82, 

 Newman- street, effected by six Pedals, is as follows, viz. 



C C*Db (5**D l5*Eb EFb eTf prCb yT^G 

 idtldl dldOdldtldl 



gVai? 



