186 On Tuning Musical Instruments. 
pered, without adverting to the thirds and the sixths (where 
all the difficulties he) on which Mr. Smyth and Mr. Mer- 
rick seem at issue in your Magazine; I beg the favour of 
you to give a place to the smail Table of three columns in 
the margin; the Ist of which shows the numerical dif- 
ferences of lengths of strings, between Mr. Merrick’s equal 
temperament scale by experiments on the melody and 
= his calculated lengths, at page 113 of 
Cx | 4°7059x your last Number: the 2d, the notes : 
D | 4:9866* and the 3d, the differences in schismaé 
Dx | 5°2850x and decimals between these notes re- 
E 1:1167% spectively; as the same point out, I 
F | 1:1828% think, clearly, the source of Mr. M.’s 
Fx | 3°7681% mistaken assertions as to the truth of 
G | 39946» his tuning by this method; viz. the 
Gy} 2°8176* wrong estimate he forms of the power 
A | 1-48806 of such a monochord to decide, or 
Ax | 3:1647* rather, of the differences which the 
lengths of strings to 3 places or 1000dths of the whole 
string, show : Would he otherwise have boasted of his ac- 
euracy in tuning an equal temperament fifth CG, which. 
is very near 4 schismas sharp, instead of one schisma fiat, 
as it ought to be, very nearly, as shown in the 6th scholium 
to Mr. ‘Farey’ S éseftil theorem in your xxxvith vol. p. 47, 
or five times the real equal temperament, different from 
what it ought to be!!- The fourth F ought on a 3 place 
monochord to be °749, and not+750; this note therefore 
agrees as well as B; but all the other 9 notes differ, in no 
instance less than 1, and in one more than 5 times, the in- 
terval which is the true or proper equal temperament of the 
Jifth, by which the tuning is usually conducted, and on 
which so much stress 1s laid in the quotation from Dr. 
Chladni. From this Table, by observing what very different 
intervals a difference of 1(or*00)) on this monochord gives 
in different parts of the octave, the folly of Lord Stanhope 
and others, in pretending that these differences of length 
of strings are proper measures of the intervals, will strik- 
ingly appear; and it can scarcely be necessary to add, that 
unless a monochord will correctly show 4 places of decimals 
of the whole string, itis useless and highly mischievous 
as a tuning apparatus; since, in some parts of the scale, 
three figures are incapable of showing the temperaments, 
within more than half of the whole temperament of each 
fifth and fourth, in the equal temperament scales. Surely,. 
Mr. A.Coblenz and Dr. Bemetzrieder, or their like fellows, 
must have been the ¢ ere tuners,’’ who assisted in: 
this 
Gm 8 OO mt GS I 
