Royal Society. 23 
equal parts; for then the vibrations of the remainder r, not fuit- 
ing with thofe of the other parts, immediately make a confufion 
in the whole : Now in the trumpet-marine, you do not flop clofe 
as in other inftruments, but touch the firing gently with your 
thumb, whereby there is a mutual concurrence of the upper and 
lower parts of the firing to produce the found 3 which is fuffi< 
ciently evident from this, that if any thing touch the firing below 
the flop, the found will be as effc6lually fpoiled, as if it were 
laid upon that part, which is immediately flruck with the bow; 
from hence therefore we may colle6l, that the trumpet-marine 
yields no mufical found, but when the flop makes the upper part 
of the firing an aliquot of the remainder, and confequently of 
the whole; otherwile, as was jull now remarked, the vibra- 
tions of the parts will flop each other, and make a found, fuitable 
to their motion, altogether confuled: Now, that thcfe aliquot 
parts are the very flops, which produce the trumpet-notes, will 
be plainly fhewn in the treating of the 2d enquiry; viz, what is 
the reafon that the 7th, iith, 13th, 14 notes are out of tune, and 
the refl exactly in tune. 
All writers on the arithmetical part of mufick agree, 
f half *\ ^ an eighth 
■Ti * u n. ♦ Na third part/ \ a fifth 
That by (horten- J ^ ^^^^^^^ t The found is nifed< a fourth 
V a fixth 3 C a flat third 
From this foundation all the other notes are derived ; tli^ flat 
and iharp fixth are to^be the flat and fharp third to the fourth, 
and the 7th the like to the fifth; the fecond to be a fifth to the 
fourth below, ^c. By this rule let us examine what notes a mono= 
chord fretted in its aliquot parts will produce ; iuppofe the mo- 
nochord F Fig. 1 7. to confifl of 720 parts, and its tone double C-fa- 
ut, the firft note in the table ; then half of it will be 36^3, iind a 
third part 240, ^c. Now 1 fay, fretting (or flopping with the 
thumb) at 360 mufl produce C-fa-ut; becaufe 350 being half 
720, the found will rile an eighth from double C-fa-ut; Again 
3<So being C-fa-ut, 24c muft make G-ibl-re-ut the third note in 
the table; becaufe 240 being jufl a third part ]q^s than 3^0, the 
Ibund will rife a fifth from that note ; after the lame msnn.T pro- 
ceeding flep by flep it will be evident that, 
180 
