24 
MEMOIRS^ /y&^ 
1 80 
144 
90 
80 > 
''240'^ 
180 
144 
180 
"a fourthl 
a fifth 
a fixth f 
half I S 
I'^C-foI-fa-ut 
E-la-mi 
G-fol-re-ut 
C-fol-fa 
72 
60 
48 
45 
;< i20<"'^<a third >^< D-la.fol 
.2^ 
J2 
go 
.- 
<J 
90 
^ 
60 
. 90J 
' 
E-la 
G-fol-re ut 
B-fa-b-mi 
C-fol.fa 
By the fame reafbn, 
B-fa-b-mi-flat 
F-fa-ut 
A-la-mi-re 
B-fa-b-mi-flat 
And confequently, 
I02f the 7th" 
65 f I iithi 
55^3 n^J;< 
14th 
5>^ 
Note in the^ 
■Table, is 
Jittle 
■flatter 
ifhaiper 
|flatter " 
flatter 
than 
I B-fa-b mi-flat 
F-fa-ut 
*A-la mi-re 
)B-fa-b-mi-flat 
Which anfwers the fecond inquiry. 
Now to apply this to the trumpet, where the notes are pro- 
duced only by the different llrength of the breath, it is reafonable 
to imagine that the ftrongefl: blafl railes the found by breaking 
the air within the tube into the fhorteft vibrations, but that no 
mufical note will arife, unlefs they are fuited to fome aliquot part, 
and fo by reduplication exadly meafure out the whole length of 
the inftrument as in Fig. 15. for otherwife a remainder will caufe 
the fame inconvenience in this cale, as in Fig. I6'. to which if we 
add, that in a pipe, which is fliortened according to the propor- 
tions jufl now difcourfed of in a ilring, the found is raifed in the 
lame ratio, it renders the cafe of the trumpet exa6tly the fame 
with the monochord. 
For a corollary to this difcourfe, we may obferve that Ae 
diftances of the trumpet notes, afcending continually, decreafed 
in the ratio of 7, j) §> i> h i^^ infinitum -^ for, 
Cfecond "7note in therfirfl O 
The «? third Stable differs^ fecond >by 
Cfourth, ^(?.jfromthe c^^^^> ^fO 
^Jf the 
^ilring e'r, 
"th 
