To make this proposition still better understood, we give the
comparison of the actual vibration numbers as follows:--

Perfect thirds in ratio
4/5 have these vibration
numbers: =

1st third 2d third 3d third
(C 256 - E 320) (E 320 - G♯ 400) (G♯ 400 - C 500)
--------------- ----------------- -----------------
no beats no beats no beats

Tempered thirds qualified
to produce true
octave: =

(C 256 - E 322 5/10) (E 322 5/10 - G♯ 406 4/10) (G♯ 406 4/10 - C 512)
-------------------- -------------------------- ----------------------
10 beats 13-1/10 beats 16 beats

We think the foregoing elucidation of Proposition I sufficient to
establish a thorough understanding of the facts set forth therein, if
they are studied over carefully a few times. If everything is not
clear at the first reading, go over it several times, as this matter
is of value to you.


QUESTIONS ON LESSON XII.