--- 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 ---