Dear Andreas,

Thank you for posting your temperament with one wide fifth based on
complex integer ratios, a technique that fascinates me, and which I
have used in rather different stylistic settings.

There is one small revision that might appeal to me, and I would be
very curious as to your opinion on what I might propose.

Looking at the sizes of fifths, I noticed that at D-A there is a fifth
considerably narrower than any other, at only about 694.1 cents, or
almost 8 cents smaller than pure, with a ratio of 884/592. This is a
bit more than 1/3 Pythagorean comma of tempering, and I wondered if
the step A (Scala step 9) might be raised slightly to make this fifth
a bit closer to pure without seriously compromising any other
interval.

In this proposed variation on your tuning, A is raised to 885/529 with
respect to C, or 885/592 with respect to D, forming a fifth D-A which
is narrow by almost exactly 1/4 Pythagorean comma -- indeed, the
accuracy of 885/592 in approximating this common degree of temperament
is amazing! The main complication I would see, if you like the result,
is that your pitch standard would then become a4 = 442.5.

! ProposedVariationOnSparschuh442wideFrench5th.scl
!
Proposed revision: step 9 (A) at 885/529, 890.9 cents -- Margo Schulter
12
!
558/529
592/529
628/529
662/529
706/529
744/529
792/529
837/529
885/529
942/529
992/529
2/1



0: 1/1 0.000 unison, perfect prime
1: 558/529 92.397
2: 592/529 194.795
3: 628/529 296.996
4: 662/529 388.276
5: 706/529 499.681
6: 744/529 590.442
7: 792/529 698.679
8: 837/529 794.352
9: 885/529 890.892
10: 942/529 998.951
11: 992/529 1088.487
12: 2/1 1200.000 octave

Most appreciatively,

Margo Schulter
mschulter@...