Monz lattice diagram for neo-Gothic JI -- it's fantastic

Hello, there, and I would just like to share my excitement over the
artful representation of my recent neo-Gothic multi-prime JI tuning by
that master latticemaker, the Monz, at

http://www.ixpres.com/interval/td/schulter/hi-primeJI.htm

The commentary and the visual dimensionality of the graphical lattice
diagram available as part of this Web page give some very interesting
angles on the structure of the tuning, based as it is on pure 3:2
fifths and complex integer ratios of 14:11 for some of the major
thirds. The Monz draws a parallel with other tuning situations where
two "cross-exponent" prime factors (here the 11 and 7 of 14:11)
consistently occur together rather than separately.

There's also a curious comment I added about the topic of fifths and
fourths in tunings, and the question of octave affinity (not
necessarily synonymous with absolute "identity" or "equivalence," as
we've seen in the harmonic entropy discussions).

Finally, taking a look this evening at Partch's _Genesis of a Music_,
I'd like to comment on a certain "cosmic humor" in this tuning.

In his book, Partch is not especially enthusiastic about Pythagorean
tuning, and specifically does _not_ endorse its use of high integer
ratios based in powers of 3 ("threeness") to define the gamut, with
medieval European practice and theory taken as an example.

Further, Partch presents an 11-odd-limit system including the ratio
14:11, but at least from what I quickly read, this may ratio may be of
somewhat peripheral importance in his system -- comments from
followers and interpreters of Partch being warmly invited.

Now along I come, from a strongly medieval European and Pythagorean
perspective, and likely in good part because of Partch, who did make
it part of his system, hear about the 14:11. My response is: "That's
an interesting proportion for a large major third, it might expand
very nicely to a fifth -- and the numbers somehow are very pleasing to
me."

One of the results is a "JI" system which has a major third at D-F# --
which I wasn't even specifically considering when designing the system
-- at 12544:9801. Of course, my reaction was: "What a neat and
unexpected bonus!" Yes, I find this interval musically very pleasing
also, especially in a couple of common Gothic-style cadences, a topic
for another post.

At least until someone corrects me, may I share my impression that
maybe the 14:11 is the not the most clearly defined and recognizable
of all the intervals I could have chosen from Partch's 43-note system,
and maybe my choice is quite in character.

The moral of all this: maybe that "JI" can mean very different things
to different people, and that some very creative cross-fertilization
can occur even between radically divergent theories and musics.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:
> http://www.egroups.com/message/tuning/13435
>
> Hello, there, and I would just like to share my excitement over
> the artful representation of my recent neo-Gothic multi-prime JI
> tuning by that master latticemaker, the Monz, at
>
> http://www.ixpres.com/interval/td/schulter/hi-primeJI.htm

Thank you, Margo, for your compliments both in your post and
in the commentary you sent me as an addendum to the webpage.

I've added another version of my lattice, drawn in ASCII format,
in which one can click on the lattice-points to play a short
MIDI-file of that note.

I hope to get around to making a similar table of clickable MIDI
links in the form of the interval (dyad) matrix of this tuning,
and perhaps even a table of all possible triads.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:
> http://www.egroups.com/message/tuning/13435
>
> Hello, there, and I would just like to share my excitement over
> the artful representation of my recent neo-Gothic multi-prime JI
> tuning by that master latticemaker, the Monz, at
>
> http://www.ixpres.com/interval/td/schulter/hi-primeJI.htm

I thought I'd add a comment about two 3==11 'xenharmonic bridges'
that relate this tuning to the linear Pythagorean tuning that
underlies most of Margo's work.

One is the bridge spanning one exponent each of prime-factors
7 and 11, separating 14/11 (= ~418 cents) and 81/64 (== [3^4]
= ~408 cents). This has the ratio 896/891, which is
[3^-4 * 7^1 * 11^-1] in prime-factor notation, and is ~9.688
cents.

The other is the bridge spanning two exponents each of
prime-factors 7 and 11, separating 12544:9801 (==
[3^-4 * 7^2 * 11^-2] = ~427 cents) and 3^16 (= ~431 cents,
and a ratio with numbers too large for me to bother with).
This bridge is [3^20* 7^-2 * 11^2] in prime-factor notation,
and is ~4.084 cents.

If I were to revise my lattice to show these bridges, they
would be dotted lines, one connecting 14/11 with 81/64, and
the other connecting 12544/9801 with [3^16].

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:

http://www.egroups.com/message/tuning/13435

> The moral of all this: maybe that "JI" can mean very different
things to different people, and that some very creative
cross-fertilization can occur even between radically divergent
theories and musics.
>

Well, Margo Schulter really succinctly "sums this up" again... but,
of course, if everybody keeps leaving the list in a "huff" such
interchange isn't about to happen...

Here's to "open mindedness." As I have repeatedly said, *MY* mind is
"totally open..."

OH... BTW really enjoyed Monzo's ascii lattice with the AUDIBLE
PITCHES... This is a development going in the direction of his
wonderful "Just Music Software" and I don't believe I've seen it on
the list before (??)
___________ _____ __ __ _
Joseph Pehrson