( ; 
do together make-up jDia-pa/bn ; that is ( as we now fpeak ) a 
Fourth and Fifth do together make an Eighth or Ofiave : And, 
the T>iff'erence of thofe two (of a Fourth and Fifth ) they agreed 
to call a Tone ; which we now call a IV hole note. 
• Such is that, ( in our prelent Mufick, ) of La Mi , ( or as it 
was wont to be called, Re Mi. ) For La fa j'ol la^ or Mi fa fol 
Jay is a perfed Fourth : And fa Jol la mi^ or La mi fa jol la^ 
IS a perfe6t Fifth : The 'Difference of which, is La m. Which 
is, what the Greeks call, the "DiazmSiick Tone \ which doth 
2)is'join two Fourths ( on each fide of it ; ) and, being added 
to either of them, doth make a Fifth. Which was, in their 
Mufick, that from Mefe to Tarameje ; that is in our Muiick, 
from A to B : fuppoiing Mi to fland in B^i b w/, which is 
accounted its Natural pofition. 
Now, in order to this, Arijloxenus and his Followers, did 
take, that of a Fourth ^ as a Known Interval^ by the judgement 
of the Ear ; and, that of a Fifths likewife ; And confequently, 
that of an OSfave^ as the Aggregate of both • and that of a 
Toney as the 'Difference of thole Two. 
And this of a Tone ( as a kliown Interval ) they took as a 
common Meafure^ by which they did citimate other Intervals. 
And accordingly they accounted a Fourth to contain Two Tones 
and an half a Fifth to contain Three Tones and an half and con- 
fequently an Eighth to contain Six Tones^ or Five Tones and 
two Half-tones, And it is very near the matter, though not ex- 
€xa6Uy fba 
^nd at this rate we commonly fpeak at this day ; fuppofing 
an 05iave to confift of Twelve Hemitones^ox Half notes. (Mean- 
ing thereby, fomewhat near fo many half-notes:) But, when 
we would fpeak more Nicely, we do not take thofe fuppofed 
Half-notes to be exa£Hy E^ua% or each of them juft the Half of 
a Full-note fuch as is that of La-mi. 
T/thagoras SLud thofe who follow him, not taking the Ear 
alone to be a competent Judge in a cafe fo nice ; chofe to diftin- 
guifh thefe, not by Intervals^ but by Troportions. And accord- 
ingly they accounted that of an OSiavCy to be, when the degree 
of Gravity or Acutenefs of the one Sound to that of the other, is 
T>ouhkj or as 2 to i ; that of a Fifthy when it is Sefqui-diery or 
as 3 to 2. ; that of a Fourth when Sefqui-tertiafty or as 4 to Ac- 
counting That, the Sweetefl proportion, which is expreffed in 
the SmaUefl Numbers ^ and therefore ( next to the Unijone ) that 
