( 705 )

exactly fitted to any one os thefe Cases, they would be quite out of order forait thc rest.

As for Instance; If mi, be removed from B-fa-b-mi (by a Flat in B) toE-la-mi: Instead of the Proportions but now designed, they must be thus or-tkred.,

B.äg.-C.Sfi.D.gg.E.F'. Sg.G.Sg.a.b

/4 - 88 . /«/ . 88 . /4 . 88 . . /4 . 38 . /0/ . 88 . /4 . /4..

,8 \j_ 20 i£ 18^ YL i£ 18 17 20 ij9_ 16

17 16 18 >7 15 17 Ü I? 18 -r

* Where ’tis manifest, , that the removal of mi doth quite disorder the whole

Series of Proportions. And the- fame would- again happen, if »ii be removedfrom E to A ( by another Flat in E .) And again if remov’d from A to D.And fo perpetually. But the JIemitoncs being made all equal; they do indit-fercntly answer all the Position; of wh ( though not exactly toany:) Yecnearer to forne than to others. VVhence it is - ,, that the serae T 'une Sounds bet-tet at one K& than at another.

It is asked, Whether this may not be Remedy’d ; by Interpol mg more Pipes ;and thereby dividing a Note , not only (as now) in tu Ihtif Notes, but imoQuarter-Notes or Half-Quarter-Notcs , &c.

I answer; It may be thus Remedy’d in part; ( that is, thc Imperfection 'might thus be sömewhat liess, and the Sounds somewhar nearer to the JustProportions :) but it can never be exactly true, so long as thsir Sounds (be-they never so many ) be in continual Proportion ; that is, each to the nextSubsequent in the fame Proportion.

For it hath been long since Demonstrated, that there is no such thing asa. just' Hcmi-tonc practicab|e in Musicis, (and the like for the Division of aTone into any Number of Equal parts; three, four or more.) For, fuppolingthe Proportion of a Tone or Füll Note, to be f'(or, as 9 to 8;) that of the

Hals-Note must be as V 9, to V 8 ; that is' as 3 to v/ 8. or 3 to 2 V 2 ) ^

4-

which are Incommcnsurablc Quantitics. And that of a Quart er Note, as 9 to8, which is yet more Incommensumtc. And the like for any orber Num-ber of Equal parts, which will therefore never fall in with the Proportions ofNumber to Number.

So that this can never be perfectly Adjusted fdrnll Keys (without somewhatof Bearing ) by Multiplying Pipes ; unless we would for every Key or every dif-ferent Seat of mi ) ha ve a different Sct of Pipes, es which this or that is tobe used, according as ( in the Cotnpositivn ) mi is liippesed to stand in thisor that Seat, Which vast Number of Pipes ( for every OH/iuc) would vustlyiricrease the Charge : And (when ali is done make the whole ImpeatlN ■cablc* -

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