( to6^ ) 
ed in Proportions, and the more cxad the Proportions, 
the better the Mufuvk : That the Proportions off.r'd v^x^re 
the fam,c that tliC ancient Grecians m& : That the Series 
of Notes ap.d Half Notes was the fame our Modern Mii- 
fick aim 4 at : which v/as there eiEhibited upon finger- 
boards ealculated in Mathematical proportion. This was 
demoiiilrated upon a Viol, becaufethe Strings were of the 
greaielt length, and the proportions more eafily difcern'd ^ 
bur may be accommodated to any. Inftrument, by fuch 
mechanical enncriv:ances as (hall reider thofe founds, vvhicli 
the Mufick requires. 
To prove the foregoing Propoficions, two Viols were 
Mathemarically fet ooc, with a particular Fret for each 
String, that every Stop might be in a perieS: exaanefs : 
Upon thefe, a Sonata was perform'd by thofe tw^o moft 
eminent Violifts, Mr Frederick and Mr Chrijiian Stefl^ns^ 
Servants to her Majefty 3 whereby it appear ci, that the 
Theory was certain, fince ail the Stops Were owned by 
them, to be pertefi:. And that they might be proved 
agreeable to what the beft Ear and the beft Hand performs 
in Modern pradice, the famous lulkn, Signior Garpenm\ 
plaid another Sonata upon the Violin in Confort with 
them^» wherein the moft compleat Harmony was heard. 
The foil knowledge and proof of this Experiment may 
be found in th:' two following Schemes, wherein Mufick 
is fet iortb, firft Arithmetically and then GeomeiricaUy: 
The M^thematicmn muf , by ceding up the proportions, 
be fatisficd, that the five forts of Halt-Notes here fet 
down, do cxaftly conftitute ail thofe intervals, of which 
our Mufick does eonfift. And afterwards he may fee them 
let forth upon a Monochord^. where the meafure of ail the 
Notes and Half Nc ie^ comes cx.i£!:ly to the middle of the 
Striflgw The Learnedrwili find; that the(e^ are the very 
proporions.v^hich the old Greek Authors have left us in 
their Wriringsr ^Jnd ffi^; ; Praftical Mufician will teftifie, 
that thefe are- chv htk Notes he e^er heard. 
Uuuunuuuuuuu 2 An 
