even better than 17-WT?

In his essay "The 17-tone Puzzle -- And the Neo-medieval Key That Unlocks It" George Secor wrote:

"Is 17-WT, then, the final step in this alternate history of tuning and temperament? At this point I think not. Once the resources of the 17-tone system were fully exploited, we could expect that other options with better intonation would be sought. I have tried a number of the progressions that we have discovered in 17-WT in other tuning systems, and there is a near-just 13-limit system (that includes rations of 5) into which virtually everything that we have tried can be transferred; the progressions not only work, but they sound even better than in 17-WT! Hopefully, this will be the topic for a follow-up article."

George, or anyone here, can you say more now about near-just 13-limit temperaments that sound better than 17-WT?

Also, for any such "better" temperament, can you devise a keyboard or buttonboard layout (or layouts) for concertina, accordion, bayan, bandoneon, symphonetta or some other acoustic free reed instrument?

Just curious!
==
Manu

--- In tuning-math@yahoogroups.com, "manuphonic" <manuphonic@...> wrote:
>
> In his essay "The 17-tone Puzzle -- And the Neo-medieval Key That Unlocks It" George Secor wrote:
>
> "Is 17-WT, then, the final step in this alternate history of tuning and temperament? At this point I think not. Once the resources of the 17-tone system were fully exploited, we could expect that other options with better intonation would be sought. I have tried a number of the progressions that we have discovered in 17-WT in other tuning systems, and there is a near-just 13-limit system (that includes rations of 5) into which virtually everything that we have tried can be transferred; the progressions not only work, but they sound even better than in 17-WT! Hopefully, this will be the topic for a follow-up article."
>
> George, or anyone here, can you say more now about near-just 13-limit temperaments that sound better than 17-WT?
>
> Also, for any such "better" temperament, can you devise a keyboard or buttonboard layout (or layouts) for concertina, accordion, bayan, bandoneon, symphonetta or some other acoustic free reed instrument?
>
> Just curious!
> ==
> Manu

Aha! This message was posted nearly 2 months ago and just showed up today!

"Manu" & I have been discussing this off-list, and I'm now in the process of working out several buttonboard designs for microtonal concertinas. For the benefit of any others who may be curious, the following is the reply I gave regarding the question in the subject line:

<< I intended to write the follow-up article for the next issue of Xenharmonikon, but unfortunately there won't be any more. I wrote to John Chalmers in October 2006 suggesting that a Xenharmonikon website could be set up so that future articles could be published online (and possibly some past articles made available), but nothing has materialized. ...

But to answer your question: the near-just tuning is my 29-tone high-tolerance temperament. It was first described in XH3, but I mentioned it a couple of times on the tuning lists. See:
/makemicromusic/topicId_6820.html#6889
which references an earlier message (with .scl data) and contains a link (no longer good) to an mp3 file that you can now temporarily download from here:
/tuning-math/files/secor/improv29.mp3

The 29-HTT basically consists of 3 open chains of tempered fifths (such that 9 fifths stacked exactly equal 63/52 plus 5 octaves); one chain of fifths (8 tones) contains C=1/1, the second (7 tones) contains an exact E\!=5/4, and the third (13 tones) contains an exact B!!!)=7/4. The first chain has prime 3 relationships; the second chain has prime 5 relationships (relative to chain 1), and the third chain has primes 7, 11, & 13 (with 9:13 exact, and 9:11 almost exact). Thus (with octave-equivalence) it's a 28-tone 4-D tuning that maps to the 29-division of the octave. The hole at Eb is filled by adding a tone that makes fifths of equal size with Bb and Ab, almost exactly 19/16 relative to C. The result is 16 harmonics in 6 different keys with maximum error <3.25 cents; at the 7-odd limit the max error is half of that.

Listen to the above sound file and tell me if it doesn't sound like JI. >>

The sound file is still there -- if anyone else is still curious.

--George