comma and chroma

A question pertaining, particularly to Ben Johnston's music:

Why is it that the interval 25/24 is called the diatonic COMMA, the
interval 81/80 is called the syntonic COMMA,

but, then when we get into the higher partial ratios, the seventh
partial 36/35 is called the seventh partial CHROMA, and likewise,
33/32 is the eleventh partial CHROMA...

What's the difference between a COMMA and a CHROMA??

Thanks!

________ _______ ________
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> A question pertaining, particularly to Ben Johnston's music:
>
> Why is it that the interval 25/24 is called the diatonic COMMA,

No, it isn't. You'd better go back and check. A CHROMA, perhaps.

the
> interval 81/80 is called the syntonic COMMA,
>
> but, then when we get into the higher partial ratios, the seventh
> partial 36/35 is called the seventh partial CHROMA, and likewise,
> 33/32 is the eleventh partial CHROMA...
>
> What's the difference between a COMMA and a CHROMA??

The size? About 35 cents might be the dividing line.

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

/tuning/topicId_26308.html#26325

> --- In tuning@y..., jpehrson@r... wrote:
> > A question pertaining, particularly to Ben Johnston's music:
> >
> > Why is it that the interval 25/24 is called the diatonic COMMA,
>
> No, it isn't. You'd better go back and check. A CHROMA, perhaps.
>

Hi Paul!

This is why I was confused. Perhaps it's just sloppy editing in the
introduction to the Ben Johnston _String Quartet #6_. Probably the
editors are so "befuddled" by all this stuff they let typos and
mislabels go by... (??)

It *definitely* says right at the beginning of the score that the:

DIATONIC COMMA
# = +70c (x 25/24)
b = -70c (- 25/24)

then

SYNTONIC COMMA
+ = +22c (x 81/80)
- = -22c (- 81/80)

(Well, at least *this* one looks OK... :) )

SEVENTH PARTIAL CHROMA
(x 36/35)
(- 36/35)

(Can't replicate the symbols, a "7" and an "upside down" one...)

ELEVENTH PARTIAL CHROMA
(uses arrows)
(x 33/32)
(- 33/32)
_______________________________

Could the terminology for the chromatic semitone just be a mistake??

_________ ______ _____
Joseph Pehrson

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., jpehrson@r... wrote:
> > A question pertaining, particularly to Ben Johnston's music:
> >
> > Why is it that the interval 25/24 is called the diatonic COMMA,
>
> No, it isn't. You'd better go back and check. A CHROMA, perhaps.
...
> > What's the difference between a COMMA and a CHROMA??
>
> The size? About 35 cents might be the dividing line.

Nope. It's nothing to do with size. See Scala's intnam.par.

But I can't see why anyone would call 24:25 anything but a DIATONIC
SEMITONE.

--- In tuning@y..., jpehrson@r... wrote:

> Could the terminology for the chromatic semitone just be a mistake??

I think so!

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> I wrote,
>
> <<which would be the uniquely articulated scale step analogous to
the
> diatonic semitone in the syntonic major model>>
>
> I meant to write something more on the order of "singly uniquely
> articulated scale step", so:
>
> The [4,3] scale, i.e., the 7-tone scale with 4 small steps and 3
large
> steps can be seen in one possible interpretation as a 2D periodicity
> block using 7 and 13 instead of 3 and 5.
>
> So in this interpretation the generalized participants are... 8/7,
> which would be the singly uniquely articulated scale step analogous
to
> the diatonic semitone in the syntonic major model; 52/49 and
> 16384/15309, which would be the two (so-called minor and major)
> chromas; and 28672/28561, which would be the 2D comma.
>
> Perhaps replacing minor and major here with more generalized terms
> like primary and secondary and identifying them by their dimension
> (i.e., in the above example 52/49 would be the primary 2D chroma,
> 16384/15309 the secondary 2D chroma, and 28672/28561 the 2D
comma)...
> ?

Your terminology seems perfectly reasonable to me, although I'd
probably use the term "remapped" rather than "generalised".

Of course why anyone would want to remap primes 3 and 5 to 7 and 13 is
another question. But each to their own. :-)

-- Dave Keenan