Po seriay 
LVI. 4 Taste of :the Beats, on Mr. William Hawkes’s 
Patent Organs and Piano-Fortes, calculated by the Rev. 
C.J.Smyts; and communicated, with some Remarks, 
' by Mr. Joun Farey. 
To Mr. Tilloch. 
Sir, (ompinicpadishe discussions occurred some time ago, 
in Dr. Kémp’s quarto Musical Magazine, published monthly, 
on the merits and defects of the patent Instruments with 17 
sounds in each octave (or dixseptave) and a single pedal, in- 
vented by Mr. W. Hawkes, and on their comparative merits, 
with other patent Instruments more recently invented by 
Mr. David Loeschman, having 24 sounds in the octave (or 
vingtquatreave) and six pedals: without it appearing from 
such discussions, what the precise temperament is, which 
Mr. Hawkes has now adopted. That gentleman also pub- 
lished a small pamphlet in the last year, on his ** Improved 
Musical Scale ;” from which it was easy enough to discover, 
that he had abandoned his former temperament, of 4th of 
a major comma as the flat temperament of g of his fifths, 
(the beats of which system were calculated by Mr. Barraud 
from my Theorems, as given at page 129 of your present 
volume), and had, at page 14, adopted “ th of a comma,” 
as the degree of temperament, which he has “¢ made choice 
of for his patent organ and piano-forte:”’ but, from three 
different commas, viz. the major comma = 115 +m, the 
artificial comma of Mercator (in that particular case where 
it measures the 54 part of the octave, for in all other si- 
tuations it has different meanings) = 11°58106= +m, and 
the comma of Pythagoras (or Diaschisma) = 125 +m, 
having been mentioned by Mr. H. in the preceding pages, 
it was impossible to discover from his pamphlet, which of 
these commas he meant; which induced me to write to 
Mr. Hawkes, at Newport in Shropshire, to point out the 
different commas above referred to, and to request to 
know, which of these commas was to be divided into six 
parts tor his temperament; and-his answer, dated the 23d 
of February last, says, ‘*I most undoubtedly mean Mer- 
cator’s comma of =!;d of a diapason, which, from its ap- 
proximation to the truth, and the inexpressibility of any 
difference to the auricular organ, it may be supposed the 
true comma,” 
_This information I communicated to my able and zealous 
friend im these pursuits, the Rev. Mr. Smyth of Norwich, 
who has calculated and sent me the inclosed Table of Beats 
Vol. 37.No. 157, May i811. | X of 
td 
