A description of a tuning recently used -- better late than never

Hi tuners,

First and foremost, I apologize for the long delay in this post which I promised to send some time ago. As some of you already know, a few weeks ago, I made a "semi-improvized" recording called simply "11-limit Something Without 7s". The tuning used is a 3D temperament whose aim is to temper out the "11-limit kleisma" (if I can call it that way) of 4000/3993. This kleisma is what you get when you stack three 11/10s falling and a 4/3 rising (or, I should say, three 10/11s and one 4/3). Because we want to have a possibility to play not only the 11th and 10th harmonics but also an octave equivalent to the 1st, we can use a 3D tuning which has a period of 2/1, then a tempered 8/11 is used once in one dimmension, and then a tempered 10/11 is used at least three times in the other dimmension - actually, I used it five times so that I could retune my 12-tone keyboard with it. If the 11/8s are widened by 1/6 of the kleisma and the 11/10s are widened by its 1/3, then you can get to a pure fourth by going "8/11, 5/4, 8/11, 5/4, 8/11, 5/4", where each of the intervals will be tempered by 1/6 of the kleisma, including even the resulting 3/5.

Okay, well, that's just about it. :-)

Petr