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It may be asked, Why may not the Pipes be so ordered, as to have their Sounds in just Proportion, as well as thus Bearing?I answer, It might very well be so, if all Musick were Composed to the same Key or (as the Greeks call it) the same Mode. As, for instance, if in all Compositions, Mi were alwaies placed in B fa b mi. For then the Pipes might be ordered in such proportions as I have now designed.
But Musical Compositions are made in great variety of Modes or with great diversity in the Pitch. Mi is not always placed in B fa b mi; but sometimes in E la mi; sometimes in A la mi re, &c. And (in summe) there is none of these 12 or 13 Pipes but may be made the Seat of Mi. And if they were exactly fitted to any one of these cases, they would be quite out of order for all the rest.
As, for instance; If M be removed from B fa b mi (by a Flat in B) to E la mi: Instead of the Proportions but now designed, they must be thus ordered;
| B | # | C | # | D | # | E | F | # | G | # | a | b | ||||||||||||
| fa | # | sol | # | la | # | mi | fa | # | sol | # | la | fa | ||||||||||||
| 1817 | 1716 | 2019 | 1918 | 1817 | 1716 | 1615 | 1817 | 1716 | 2019 | 1918 | 1615 |
Where 'tis manifest, that the removal of mi doth quite disorder the whole series of Proportions. And the same would again happen, if mi be removed from E to A (by another Flat in E.) And again if removed from A to D. And so perpetually.
But the Hemitones being made all Equal; they do indifferently answer all the positions of Mi (though not exactly to any:) Yet nearer to some than to others. 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
