Fwd: [ATL] Re: What's so Super about Superparticularity?

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

> Hello J . . .
>
> I'd _really_ like to try to answer your questions here, but I'm
> having trouble following you at the moment. It seems that there is
a
> huge amount of infomation and knowledge behind them, and you have a
> great number of things to express that you're trying to get across
> here . . .

JG: You are too kind. "Just" making some observations...

> Could I ask you to try to expand on these things in as slow and
clear
> language as you can? The problem is that we all come at this stuff
as
> near-isolates so have all come up with our own languages . . . I'd
> really like to get a chance to really talk with you about your
ideas.
>
> -P

JG: With the "new-fangled" brute-force solution to the Yahoo "de-
formatting-machine" below, perhaps my (modified) text will make more
sense:
----------------------3/2
---------------------/--\
--------------------/----\
-------------------/------\
------------------/--------\
-----------------/----------\
----------------/------------\
---------------/--------------\
--------------/----------------\
-------------/------------------\
------------/--------------------\
-----------4/3------------------5/3
----------/---\----------------/---\
---------/-----\--------------/-----\
--------/-------\------------/-------\
-------/---------\----------/---------\
------5/4--------7/5-------8/5--------7/4
-----/--\-------/--\------/--\-------/--\
---6/5--9/7--11/8-10/7-11/7--13/8-12/7--9/5

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> JG: In the segment of the Stern-Brocot tree branching (upwards,
> generally) into the 3/2 node (then following on upwards to the 2/1
> node, and the 1/1 node), the 6/5 and 9/7 nodes have a mediant of
> 5/4,
> the 5/4 and 7/5 nodes have a mediant of 4/3, and the 4/3 and 5/3
> nodes have a mediant of 3/2. THE NODAL RATIOS 6/5, 5/4, 4/3, AND
3/2 FORM A "SUPERPARTICULAR CHAIN" OF NODAL RATIOS ALONG THE EDGE OF
THIS SUB-BRANCH.

> However, in a "mirror-image" pattern
> (centered about the 3/2 node), the "Farey adjacent" but
> not "superparticular" 9/5 and 12/7 nodes have a mediant of 7/4, the
> 7/4 and 8/5 nodes have a mediant of 5/3, and (reduntantly), the 5/3
> and the 4/3 nodes also have a mediant of 3/2. THE NODAL RATIOS 9/5,
7/4, 5/3, AND 3/2 DO *NOT* FORM A "SUPERPARTICULAR CHAIN" OF NODAL
RATIOS ALONG THE EDGE OF THIS SUB-BRANCH.

> Can these two "mirror-
> image" groups (where BOTH groups contain nodal ratio values which
> are "Farey adjacent" to each other traveling upwards or downwards
> along the branches involved, but only the *FIRST* group cited above
> contains nodal ratio values which are "superparticular") be
> considered musically EQUIVALENT (FROM THE PERSPECTIVE OF
DESIRABILITY AS CHOICES OF VALUES OF "SCALE INTERVALS" THEMSELVES)
> when combined with a 1/1, or other ratios present in a given
scale),
> or does the superparticularity of such ratios impart a PREFERABLE
> quality as compared to the other non-superparticular "SCALE
INTERVAL RATIOS" which one
> might select to include within a given scale.

Or (along the lines of - WHAT I INTERPRETED TO BE KRAIG'S -

original thought), would (KRAIG) refrain from judging the
desirability of a given superparticular ratio in a scale until KRAIG
had evaluated its use in conjunction with all *other* scale ratios?

PAUL - DOES THE ABOVE HELP IN CLARIFYING THIS TEXT?

J Gill
--- End forwarded message ---