A new experimental Organ proposed. 44 J 



Musical Persons (to which I would contribute) to undertake and 

 contrive an experimental Org a's, having a single diapason Stop 

 of 122-4, or more, Pipes, tuned to two Octaves or more, of this 

 extended Scale ; so contrived, with different sets of Finger-keys 

 and Sliders, that for the purposes of Experiment, any two, three 

 or four or more of the Notes, could be tried together, for deli- 

 beratelv ascertaining the effects on the Ear, of every possible 

 Chord,however compound, and the shades of differences between 

 such. 



And with other Finger-keys, of the ordinary kind, twelve in 

 the Octave, to which any of the 612 Notes could be attached at 

 pleasure; by means of which, every species of Temperament of 

 the common Scale, which has yet been proposed, or could l)e 

 invented, might readily and intelligibly be put to the test of Ex- 

 periment r although not with absolute mathematical precision, 

 yet with a nearer approach thereto, than has yet perhaps, ever 

 in a single instance been attained, even by the celebrated Dr. 

 Robert Smii/i, in tuning by the method of calculated BeatSf 

 which he invented. Provided, that the Notes of Tempered Sy- 

 stems, intended to be tried, were calculated to the nearest arti- 

 Jicial Comma, in every instance (than which nothing can be more 

 easy, by help of the Musical Corollaries which I gave in p. 374 

 of your xxxvith volimie) no greater error than about half a 

 Schisma, or the -^A part of a major Comma, or the t-tt^ part 

 of an Isotonic Semitone, need in any instance be committed, 

 <luring the trial of any system of Temperament, on such an In- 

 strument, and generally, not half as much : — errors, the small- 

 ness of which, the most fastidious Critic or Amateur, might 

 safely lay out of his consideration, in judging of the real and 

 comparative effects, of different systems of Temperament, with 

 the vit w to the adopting and recommending of that, which is 

 on the whole, best adapted to use on the Organ; — if such be not 

 already decided ?, in favour of the Mean-Tone, or perfect Major 

 Third System. 



dilTcrjiist f, whose ratio is 3''-i- 2^* x 5-, or -14966000 x S; 30 of them 

 difTer'sf— in, or a^-f-a'" x 5'", or -flOUSOS^ x 2, and the remaining 41 

 pairs, of these apparently equal Notes, within and without the Table, each 

 o( them differ 3*"— rn, or 3-'-i-2 x 5' -, or •441 1 2043 x 2 : — or, near enough 

 for every practicahlo or useful purpose, the small differences of the first 

 repeated Koics without the liniiis of my TahK, from those already pro- 

 duced hy the tuuini; process wiihin it, may lie stated to be _i -"^ tli, ^•'.''.-(h, 

 and ^*jJ*,-th of uSi/iismii, rcsjiectively ; that is, in every instaiice, such dif- 

 ferences, arc less than hull', what thus strikini^ly appears to I e, llie UN'lTo/" 

 the Euhurmonic Scale (as ohserved in p. '214 of your xlixth roluiue) ; and 

 in more than two-thirds ot these instances, the dilfcienccs, hut little ex- 

 ceed iiiif-fourth of the unit : — such arc the very reinarkahle proj)ertie«, 

 and uses of this Unit, in defining and calculating Musical Intervals, for 

 useful and practicable purposes, 



Bv 



