--- In tuning@y..., kalleaho@m... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > I'm assuming you're familiar with my solution for 22-tET, which
> > omits the "E" keys on the keyboard, thus placing the "naturals"
> > my decatonic system on the black keys, with the white keys
> > acting as "sharps" and "flats" . . . yes?
> Yes indeed. In fact I was just rereading your paper "Tuning,
> Tonality, and Twenty-Two-Tone Temperament" and I'm going to tune my
> system that way today and give it a try.
> I have to ask what is your relation to JI?
A love-hate relationship :) Seriously, as you can see in the paper, I
think consonance has a huge amount to do with approximating simple JI
ratios, but when it comes to tuning systems, I agree with Dave Keenan
that some form of temperament (not necessarily equal temperament) can
usually have more benefits than costs. We study these matters quite a
bit on <email@example.com
> This far I myself have been interested in both the temperaments and
> just intonation.
Hopefully, by "temperaments" you don't just mean equal temperaments.
> Personally I find it wise to tune scales derived
> from Combination Product Sets or Tonality Diamonds in Just
> since it is not particularly important to be able to modulate in
> these systems.
That makes absolutely perfect sense. However, many composers who have
used these JI structures, such as Harry Partch and Kraig Grady, have
embedded them in larger JI scales which "fill the holes" in a way
that allows for many more consonant relationships, as well as a sort
of full melodic flexibility. These scales generally conform to
Fokker's conception of "periodicity blocks" in the lattice. Dave
Keenan has shown convincingly that certain very fine temperings (NOT
ETs -- think meantone as a simple example) of these larger JI scales
can _greatly_ increase the number of consonant relationships, while
(to our ears) not materially decreasing the consonance of each of
these intervals. The details, and general principles, of all this are
being discussed mainly on <firstname.lastname@example.org
>, but much is
to be found in the archives of this list. Dave Keenan has also
constructed "microtemperaments" for JI scales that are not
periodicity blocks, for example Dean Drummond's "zoomoozophone" scale.
> Strictly pure intervals give these scales an eerie
> edge. I don't find justly tuned intervals boring at all as some
> people do.
I would at least try out some of Dave Keenan's microtemperaments, to
see if the quality of the slightly-tempered intervals is
aesthetically useful to you.
> I am also interested in synthetic scales (which do not have any
> prototypes in Just Intonation) because I'm a fan of Olivier
> and Iannis Xenakis.
You might be surprised how synthetic scales can often be related to
just intonation scales with certain "commas" tempered out . . .