Question on Pythagorean tuning

> Hmm . . . I wouldn't say they exploited the comma, only that they exploited
> the dissonance of the Pythagorean thirds, not knowing that future
> generations would use the just thirds only a comma away as consonances.
>
> In the 1400s, when the latter were introduced, composers did exploit the
> felicitous closeness of the Pythagorean comma to the syntonic comma, in
> order to get quasi-just thirds out of Pythagorean tuning. In other words,
> they exploited the schisma.

Hi Paul Erlich!

I have a short question for you... If the C-E interval in Pythagorean
is 81:80, or 408 cents and the E# a "comma" away resulting from a fifth
down from the Pythagorean comma B# is HIGHER... then how can it be a
"pure" ratio, since the just third a SYNTONIC comma away from the
Pythagorean third would have to be SMALLER... by 22 cents... wouldn't
make it more a D#... or am I getting totally confused...

_________ ____ __ _ _
Joseph Pehrson

Joseph,

The note in Pythagorean tuning that approximates a just major third
above C is Dx (D double-sharp), not E#.

-Paul