Comma size categories extended

I'm sorry, but I can't stop playing with the idea of systematic comma
names. But please note that these are intended to be _in_addition_to_
(not replacing) common or historical names in the case of well known
commas - just like in the naming of chemical compounds or biological
organisms.

Here's a proposal to extend the systematic comma size categories out
to 115 cents. And again I would like to acknowledge Joe Monzo's
pioneering work in this area.

The following tables will be much easier to read in email. If you're
reading on Yahoo's web interface, you can "Forward" it to yourself.

Size category name Boundary Alternative name
----------------------------------------------------------
0 c
schismina
[-84 53]/2 ~= 1.81 c
schisma
[317 -200]/2 ~= 4.50 c
kleisma
[-19 12]/2 ~= 11.73 c
comma
[-57 36]/2 ~= 35.19 c
minor-diesis or small-diesis
[8 -5]/2 ~= 45.11 c
diesis or medium-diesis
[-11 7]/2 ~= 56.84 c
major-diesis or large-diesis
[-30 19]/2 ~= 68.57 c
chromatic-semitone or small-semitone
[35 -22]/2 ~= 78.49 c
limma or medium-semitone
[-3 2]/2 ~= 101.96 c
diatonic-semitone or large-semitone
[62 -39]/2 ~= 111.88 c
apotome
[-106 67]/2 ~= 115.49 c

These will give many systematic names that are the same as the
historical or common names used in Scala (with the substitution of
"Pythagorean" for 3, "classic" for 5, "septimal" for 7, etc.)

They also have the useful property that each category has an exact
apotome-complement category, except for schisma and kleisma which must
be combined to give a complement to the diatonic-semitone category.
But that's all right because the distinction between schisma and
kleisma isn't necessary for making names unique, but only for matching
historical usage.

Category Complementary category
---------------------------------------
schismina apotome
schisma/kleisma diatonic-semitone
comma limma
minor-diesis chromatic-semitone
diesis major-diesis

In case anyone has just joined the discussion: The purpose of these
precise boundaries is to make it possible to uniquely and
unambiguously name many commas without having to refer to the power of
3 (or 2) contained in the comma, since this is effectively encoded in
the size category.

George,
Please remind me why we didn't use the terms minor-diesis, diesis,
major-diesis?

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> I'm sorry, but I can't stop playing with the idea of systematic
comma
> names. ...

I see that you've finalized the boundaries (below), so least I'm
getting something out of this.

> Here's a proposal to extend the systematic comma size categories out
> to 115 cents. ...
>
> ...
> Size category name Boundary Alternative name
> ----------------------------------------------------------
> 0 c
> schismina
> [-84 53]/2 ~= 1.81 c
> schisma
> [317 -200]/2 ~= 4.50 c
> kleisma
> [-19 12]/2 ~= 11.73 c
> comma
> [-57 36]/2 ~= 35.19 c
> minor-diesis or small-diesis
> [8 -5]/2 ~= 45.11 c
> diesis or medium-diesis
> [-11 7]/2 ~= 56.84 c
> major-diesis or large-diesis
> [-30 19]/2 ~= 68.57 c
> chromatic-semitone or small-semitone
> [35 -22]/2 ~= 78.49 c
> limma or medium-semitone
> [-3 2]/2 ~= 101.96 c
> diatonic-semitone or large-semitone
> [62 -39]/2 ~= 111.88 c
> apotome
> [-106 67]/2 ~= 115.49 c

I was under the impression that "chromatic semitone" and "apotome"
were alternate names for the same thing (at least in JI),
likewise "diatonic semitone" and "limma". I think that "limma"
and "apotome" are okay, but I would prefer to see different names for
the other 2 categories.
> ...
> George,
> Please remind me why we didn't use the terms minor-diesis, diesis,
> major-diesis?

We spent a lot of time looking for meaningful terms that would result
in abbreviations that would require different letters and would also
be easy to remember. Small, medium, and large ("S", "M", and "L")
was by far the best thing we could come up with (all in upper case).
("Schisma" is also abbreviated with "s", but that one, along with
kleisma, is lower case.)

--George