Page:A Letter of Dr. John Wallis to Samuel Pepys Esquire, Relating to Some Supposed Imperfections in an Organ.djvu/8

 And thus it is necessary to suppose in the Pipes of an Organ; which have each their determinate Sound and not to be corrected, in their little Inequalities, as the Voice may be by the guidance of the Ear.

But Pythagoras, and those who follow him found (by the Ear) that this Equality of Intervals would not exactly answer the Musical Appearances, in Concords and Discords: just as our Organists and Organ-makers be now aware; that their Pipes at equal Intervals do not give the just desired Harmony, without somewhat of Bearing that is, of some little variation from the just Sound.

The Pythagorians to help this, changed the notion of Equal Intervals into that of due Proportions. And this is followed by Zarline, Keppler, Cartes, and others who treat of Speculative Musick in this and the last Age. And though they speak of Notes and Half notes (in a more gross way) much as others do, yet declare themselves to be understood more nicely.

And though our present Gam-ut take no notice of this little diversity; yet, in Vocal Musick, the Ear directs the Voice to a more just proportion. And, in String Musick, it may in like manner be helped by straining and slackening the Strings, or moving the Frets. But in Wind Musick the Pipes are not capable of such correction; and therefore we must be content with some little irregularity therein; that so they may tolerably answer (though not exactly) the different Compositions according to the different placing of Mi in the Gam-ut.

Now the Design of Mr. Harris seems to be this; either (by multiplying intermediate Pipes) to bring the Organ to a just Perfection: Or else (if that cannot be done) to rest content with the little Imperfection that is; which though, by more Pipes, it may be somewhat abated, yet cannot be perfectly remedied. And in this I think we must acquiesce,

I am

SIR

Yours to serve you

Oxford June 27. 1698.