Message from Dave Keenan on Blackjack subsets

Here are the URLs for my posts on Blackjack subsets.

/tuning/topicId_22431.html#22431
/tuning/topicId_22431.html#22441
/tuning/topicId_27122.html#27162
/tuning/topicId_27122.html#27164
/tuning/topicId_27122.html#27183

Note that Manuel Op de Coul found about half of them. Manuel has made it
possible to reproduce his results in Scala version 18, by using SET MAXDIFF
before COMPARE /SUPERSET. However, this considers the accuracy of _all_
intervals, and cannot be restricted to consonant ones. To put it crudely,
it finds "melodic" approximations rather than "harmonic" ones.

The others that I found, were exact subsets of particular rationalisations
of Blackjack, whose consonances are of course approximated within 3.3c by
Blackjack, and they are therefore "harmonic" approximations.

I didn't repeat any that I found by my methods, if Manuel had already found
them by his, so many of those listed by Manuel are both melodic and
harmonic approximations. Both kinds of approximation are of course valuable.

Here's one more harmonic subset I found only recently, using Blackjack
rationalisations that you posted recently:

erlich11.scl
Canonical JI interpretation of the Symmetrical decatonic mode of 22-tET

Paul, you credited me with suggesting some Scala modification relating to
finding chords. I don't believe I had anything to do with that. I did
however supply Manuel with an algorithm for computing the Constant
Structure margin of a scale. This is now given by SHOW DATA. CS "margin" is
the much better name that Manuel came up with for what I called CS "level"
in the tuning-math list. The approximate subset search was my suggestion
too, but its algorithm is entirely Manuel's. What would we do without
Marvelous Manuel!

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com