Small 7 limit adaptive tuning puzzle

Hi John,

Here's the smaller adaptive tuning puzzle.

http://members.tripod.com/~robertinventor/tunes/tunes.htm#7_equal_trio

It turned out to be 7 limit. (I expect that will please
you :-)).

Has an Ab and a G#, but both turn out to be 49/32!

Uses David Canright's 7-limit j.i. scale.

If real time adaptive tuning program chose
8/5 each time instead, it would end up
over a tone sharp at the end of the piece.

So, will be a fine challenge for your program I hope.

Robert

Hi John,

Sorry, should be
http://members.tripod.com/~robertinventor/tunes/tunes.htm#7_limit_adaptive_puzzle

Robert

[Robert wrote:]
>Here's the smaller adaptive tuning puzzle.

>http://members.tripod.com/~robertinventor/tunes/tunes.htm#7_limit_adaptive_puzzle

Hi, Robert! Sorry this took me so long.

>It turned out to be 7 limit. (I expect that will please you :-)).

Interesting! I'll try attacking it both in 5-lim and 7-lim, & see
what happens.

>Has an Ab and a G#, but both turn out to be 49/32!

Now I'm confused! There's only one Ab/G# in the piece, at 18.002
seconds, and it's tuned +27.88 cents relative to 12-tET. Lessee: 49/32
would be 737.65 cents from root. I'll bet you're using a G note for
this, are you not? That's a serious problem for my program, because I
begin by stripping out your bends, then evaluate the scale degrees.
(I don't yet have code to recognize input bends as _tuning_. But in
any case, for purposes of this "puzzle", that would be cheating, yes?)

>Uses David Canright's 7-limit j.i. scale.

Which I'm sure I ought to be familiar with, but I'm not. However, I
can guess that Bb is 7/4, if Ab is 49/32. Wow, then I'd expect D to
be 35/32, and F to be 21/16; can _that_ be right???

>If real time adaptive tuning program chose
>8/5 each time instead, it would end up
>over a tone sharp at the end of the piece.

>So, will be a fine challenge for your program I hope.

As it stands, a bit _too_ much of a challenge, I'm afraid! Could you
possibly redo it using scale degree 8 for Ab/G#? The bend of -62.35
cents is still very workable for a MIDI module.

JdL