John Wallis

“ But, in common disourse (when we do not pretend to speak nicely, nor intend to be so understood) it is usual to call it an Hemitone or Half-Note (as being very near it ) and, the other, two Whole-Notes. And this is what Ptolemy calls Diatonum Ditonum, (of the Diatonick kind with Two full Tones.)
Against this, it is objected (as not the most convenient Division,) that the Numbers of 81 to 64, are too great for that of a Ditone or Greater Third: Which is not Harsh to the Ear; but is rather Sweeter than that of a single Tone who's proportion is 9 to 8. ”

“ Whence it is, that the same Tune sounds better at one Key than at another.
It is asked, Whether this may not be remedied; by interposing more Pipes; and thereby dividing a Note, not only (as now) into Half-Notes, but into Quarter-notes or Half quarter-notes &c.
I answer; It may be thus remedied in part; (that is the Imperfection might thus be somewhat Less, and the Sounds somewhat nearer to the just Proportions:) but it can never be exactly true, so long as their Sounds (be they never so many) be in continual proportion; that is, each to the next subsequent in the same Proportion. ”

“ And accordingly they accounted a Fourth to contain Two Tones and an half; a Fifth to contain Three Tones and an half and consequently an Eighth to contain Six Tones or Five Tones and two Half-tones, And it is very near the matter, though not exexactly so.
And at this rate we commonly speak at this day; supposing an Octave to consist of Twelve Hemitones, or Half-notes. (Meaning thereby, somewhat near so many half-notes:) But, when we would speak more Nicely, we do not take those supposed Half-notes to be exactly Equal or each of them just the Half of a Full-note such as is that of La-mi. ”