The ratio which expresses the value of the _diesis_ is that of 128 to
125. If, therefore, the octaves are to remain perfect, which they must
do, _each major third must be tuned sharper than perfect by one-third
part of the diesis_.

The foregoing demonstration may be made still clearer by the following
diagram which represents the length of string necessary to produce
these tones. (This diagram is exact in the various proportional
lengths, being about one twenty-fifth the actual length represented.)

Middle C (2C) 60 inches.
--------------------------------------------------
O O

E (4/5 of 60) 48 inches.
--------------------------------------------
O O

G♯ (A♭) (4/5 of 48) 38-2/5 inches.
--------------------------------------
O O

3C (4/5 of 38-2/5) 30-18/25 inches.
--------------------------------
O O

This diagram clearly demonstrates that the last C obtained by the
succession of thirds covers a segment of the string which is 18/25
longer than an exact half; nearly three-fourths of an inch too long,
30 inches being the exact half.