Yahoo Tuning Groups Ultimate Backup mills-tuning-list Small miscellany

Apologies, my tuning friends: I've left several responses to my messages
(both on the list and privately) hanging; somehow I didn't seem to get
any less busy when the summer began, but am just as busy with different
things. But here are a couple of drive-by comments:

I've generated a couple more consistency tables, and the best candidates
I've spotted so far for synthesizers are probably 1224 (2^3 * 3^2 * 17)
and 1848 (2^3 * 3 * 7 * 11). You can see their consistency levels at
various limits at .

It's diameter, not radius, please, and yes, an ET having a diameter less
than or equal to its consistency level is a desirable property in my
book. I think of it being "quasi-JI-like", in a way.

It's kind of hard to represent on a 2D screen with ASCII characters what
I would do with a 4D 9-limit lattice, but here's a go:

10/9 --- 5/3 --- 5/4
/ \ / \10/7 / \
/ \ / \ / \
/14/9 \ / 7/6 \ / 7/4 \
16/9 --- 4/3 --- 1/1 --- 3/2 --- 9/8
\ 8/7 / \12/7 / \ 9/7 /
\ / \ / \ /
\ / 7/5 \ / \ /
8/5 --- 6/5 --- 9/5

This is a projection of part of the 3D 7-limit lattice into a plane.
The triangles are in the 3-5 plane, and the ratios inside the triads are
either one layer above or below depending on whether they're inside
major or minor triads. This shows all pitches separated from the 1/1 by
intervals I consider consonant or primary within the 9-limit; however,
without drawing lines which intersect and become confusing I can't
draw lines for all those intervals, even when I'm not restricted to
ASCII art. Several of the 9-limit intervals look like secondaries
instead of primaries when represented this way. In 4 dimensions it
would look like this:

5/3 --- 5/4
/ \10/7 / \
10/9 / \ / \ 3/2 --- 9/8
/ \ / 7/6 \ / 7/4 \ \ 9/7 /
/ \ 4/3 --- 1/1 --- 3/2 \ /
/14/9 \ \ 8/7 / \12/7 / \ /
16/9 --- 4/3 \ / \ / 9/5
\ / 7/5 \ /
8/5 --- 6/5

The tetrad on the left would be the 3D layer "below" the middle one in
4D space, and the one on the right the layer "above". All primary
9-limit intervals could then be seen as being one step away from the
origin. If, as I said, we were 5-dimensional beings who could use
4-dimensional paper.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

>However, I had a mail recently saying that they are stopping
>production because it doesn't sell. : (
>Did you hear anything along those lines?

I didn't ask how they were selling, or whether they were continuing to
produce them or not. They definitely didn't volunteer comments to that
effect, but that probably doesn't mean much. It definitely does appear in
the brochure they had at the flute convention, but I don't know for sure
how new or old that brochure is.

Small miscellany

🔗Paul Hahn <Paul-Hahn@...>

🔗mr88cet@texas.net (Gary Morrison)

🔗"Patrick Ozzard-Low" <patrick.ozzard-low.itex@...>