Page:A Letter of Dr. John Wallis to Samuel Pepys Esquire, Relating to Some Supposed Imperfections in an Organ.djvu/5

253

Thus, by the help of Flats and Sharps (dividing each Whole Note, be it the Greater or the Lesser, into two Half-notes or what we call so,) the whole Octave is divided into Twelve Parts or Intervals (contained between Thirteen Pipes) which are commonly called Hemitones or Half-notes. Not, that each is precisely Half a Note, but somewhat near it, and so called. And I say, by Flats and Sharps; For sometime the one, sometime the other, is used. As, for instance, a Flat in D, or a Sharp in C, do either of them denote a Midling Sound (tho' not precisely in the Midst) between C and D; Sharper than C, and Flatter than D

Accordingly; supposing Mi to stand in B fa b mi (which is accounted its Natural seat) the Sounds of each Pipe are to bear these proportions to each other, viz,

B

C

#

D

#

E

F

#

G

#

a

#

b

mi

fa

#

sol

#

la

fa

#

sol

#

la

#

mi

16/15

18/17

17/16

20/19

19/18

16/15

18/17

17/16

20/19

19/18

18/17

17/16

$\scriptstyle {\underbrace {\quad \quad \quad } }$

$\scriptstyle {\underbrace {\quad \quad \quad } }$

$\scriptstyle {\underbrace {\quad \quad \quad } }$

$\scriptstyle {\underbrace {\quad \quad \quad } }$

$\scriptstyle {\underbrace {\quad \quad \quad } }$

9/8

10/9

9/8

10/9

9/8

$\scriptstyle {\underbrace {\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } }$

$\scriptstyle {\underbrace {\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } }$

4/3

4/3

$\scriptstyle {\underbrace {\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } }$

3/2

$\scriptstyle {\underbrace {\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } }$

2/1

And so in each Octave successively following. And if the Pipes in each Octave be fitted to sounds in these proportions of Gravity & Acuteness; it will be supposed (according to this Hypothesis) to be perfectly proportioned.

But, instead of these successive proportions for each Hemitone; it is found necessary (if I do not mistake the practise) so to order the 13 Pipes (containing 12 Intervals which they call Hemitones) as that their Sounds (as to Gravity & Acuteness) be in Continual Proportion, (each to its next following, in one and the same Proportion;) which, all together, shall compleat that of an 0ctave or Dia-pason, as 2 to 1. Whereby it comes to pass, that each Pipe doth not express its proper Sound, but very near it, yet somewhat varying from it, Which they call Bearing. Which is somewhat of Imperfection in this Noble Instrument, the Top of all.

It