C 8i ) 
WH AT Method Is u fed by Simfon (in the Book men- 
tioned) to divide a String or Cbord^ I know not : 
Nor have 1 the Book at Hand to conrulr. 
That a String open (or at its full Length) will found (what 
we call Jan Odave (or Diapafofi) to that of the fame Stm^ftop- 
ped in the Middle (or at half its Length) is very true. And hence 
it is that we comnaonly aflign, to an Oiftawej the Duple Pro- 
portion (or that of 2 to I 0 becaufe fuch is the Proportion of 
Lengths (taken in che fame String) whichgive thole Sounds. 
And (upon a like Account) we affign to a Fifth Cor Dia» 
, pente) the Sefqui-alter Proportion (or that of 5 to 2 :) And^to 
a Fourth (or D ia- teffir on) thQ Sefquitertian (or that of 4 to 5 :) 
And to a lone (which is the Difference of a Fourth and Fitch) 
The Sefytii-oBa've (or that of p to 8 :) Becaufe Lengths (taken 
in the lame String ) in thefe Proportions, do give fuch 
Sound?. 
And (unlverfally) whatever Proportion of Lengths (taken 
in the (ame String, equally iiretchedj do give fuch and fuch 
founds ; fuch Proportions (o^ Gravity) weaffign tothe Sounds 
lb given. 
But when an Eighth(or Od:ave)is faidfin common Speechj 
to confift of 12 Hemi- tones, or 6 Tones 5 this is not to be Un- 
derftood according to the utmoft Rigour of Mathematical 
Exadlnefs, (of (uch 6 Tones, as what chey call the Diaz^euclick^ 
Tone, or that of la mi^ which is the Difference of a Fourth and 
Fifth 5) but, as exad enough for common Ufe For Sixfiich 
Tones (that is, the Proportion of 9 to 8 Six Times repeated) 
is fomewhat more than that of an Odave (or the Proportion 
of 2 to i:) And, confeqaently, fuch an Hemi-tone, is fbme- 
what more than the Twelfth Part of an Eighth, or Octave, or 
Dia-pafon, But the Difference is fo little, that che Ear can 
hardly diftinguiOi it : And therefore Cin common Speechj it 
is ufu^l fb to fpeak. 
And,accordingIy,when we are direded to take the Lengths - 
(for what are called the 12 Hemi-tones} in Geometrical Pro- 
portion : it is to be underflood (nor, to be fo in the utmoft 
Scri&iefij but) to be accurate enough for common Ufe ; for 
placing-. 
