Re: [tuning] Re: Apology on ~17.095-tet confusion (Dan Stearns, Paul Erlich)

Margo Schulter wrote,

> If I translate "17.095-tet" to a Gary Morrison style "~70.196-cet,"
then the obvious difference becomes more clear: a Pythagorean diatonic
semitone is around 90 cents, not 70 cents!

Yes that's right. I had mentioned this tuning specifically only
because the thread had converged on Pythagorean, 17-tET, and
consistency, and this tuning is oh so close to 17-tET, sets the 3/2
pure, and (somewhat dramatically) increases consistency when compared
to 17-tET proper.

> Interestingly, ten steps make a pure 3:2 fifth

Yes, the way I look at this is as an equal division of the 3/2, i.e.,
(LOG(2)-LOG(1))*(n/LOG(3/2)) where "n" in this case is 10. I've posted
quite a few of these types of scales in the past.

> That augmented sixth in the first example has an effect similar and
quite different -- one of the attractions of 17-tet.

Nice. Agreed!

Dan