[ 26 7 ] 
f\c> What they were, and how far the Dodrine of 
the Ancients in this refped is reconcileabie with the 
true Nature of mufical Sounds, are, you know, Que- 
ftions which have not a little perplexed the Learned. 
That mufical Intervals are founded on certain Ra- 
tio's or Proportions expreffible in Numbers, is an old 
Difcovery. Nobody is better acquainted with thefe 
Proportions than yourfelf j and I am not a little 
obliged to you for the Light you have herein given 
me. It is well known, that ali mufical Ratios may 
be analyfed into the prime Numbers 2, 3, and 5 ; 
and that all Intervals may be found from theOdlave, 
Fifth and Third Major ; which refpedively correfpond 
to thofe Numbers. Thefe are the Muficians Ele- 
ments, from the various Combinations of which all 
the agreeable Variety of Relations of Sounds refult. 
This Syftem is fo well founded on Experience, that 
we may look upon it as the Standard of Truth. 
Every Interval that occurs in Mufic is good or bad, 
as it approaches to, or deviates from, what it ought 
to be on thefe Principles. The Dodrine of fome of 
the Ancients feems different. Whoever looks into the 
Numbers given us by Ptolemy, will not only find the 
Primes 2, 3, and 5, but 7, 11, introduced. Nay 
he feems to think all Fourths good, provided their 
component Intervals may be exprefied by fuperparti- 
cular Ratios . But thefe are juftly exploded Con- 
ceits 5 and it feems not improbable, that the Centra- 
didions of different numerical Hypothefes, even in 
the Age of Ariftoxenus, and their Inconfiftency with 
Experience, might lead him to rejed their Numbers 
altogether. It is Pity he did: Had he made a pro- 
per Ufe of them, we Ihould have had a clearer Infight 
into 
