Comma names

Manuel's list is closing in on listing and having a name for every
11-limit superparticular, which t seems to me an excellent thing.

We have

9/8 major whole tone
10/9 minor whole tone
11/10 Ptolemy's second
12/11 unidecimal neutral second
15/14 major diatonic semitone (should be septimal diatonic semitone)
16/15 minor diatonic semitone (should be diatonic semitone)
21/20 minor semitone
22/21 no name--unidecimal minor semitone?
25/24 classic chromatic semitone, minor chroma
28/27 Archytas' 1/3-tone
33/32 unidecimal comma (bad name! Schoenberg's diesis?)
36/35 septimal diesis, 1/4-tone
45/44 1/5-tone (needs improvement)
49/48 slendro diesis, 1/6-tone
50/49 Erlich's decatonic comma, tritonic diesis, jubilee comma
55/54 major unidecimal comma?
56/55 minor unidecimal comma?
64/63 septimal comma
81/80 syntonic comma, Didymus comma
99/98 small unidecimal comma
100/99 Ptolemy's comma
121/120
126/125 small septimal comma (is this the best we can do?)
176/175
225/224 septimal kleisma (is this the best we can do?)
243/242 neutral third comma
385/384 unidecimal kleisma
441/440
540/539 Swets' comma (who is Swet?)
2401/2400 breedsma
3025/3024 lehmerisma
4375/4374 ragisma
9801/9800 kalisma (Gauss' comma)

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> 121/120

Naming it after linear temperaments, this could be the undecimal
schrutar-orwell-valentine comma, or unisov for short.

> 126/125 small septimal comma (is this the best we can do?)

This is the starling comma if named after a planar temperament, or
meantone-nonkleismic if we use linear temperaments

> 176/175

Unidecimal nonkleismic-orwell-valentine comma, or uninov for short.

> 225/224 septimal kleisma (is this the best we can do?)

The marvel comma (not to be confused with Marvel Comics) or the
miracle-orwell comma.

> 441/440

It's a comma of miracle and unidec, but there are other linear
temperaments involved here which are pretty good but not yet named.

Gene Ward Smith wrote:

>>121/120
> > Naming it after linear temperaments, this could be the undecimal
> schrutar-orwell-valentine comma, or unisov for short.

That's the neutral second comma, because it's between 12:11 and 11:10.

>>225/224 septimal kleisma (is this the best we can do?)
> > The marvel comma (not to be confused with Marvel Comics) or the
> miracle-orwell comma.

I though it was already established as a kleisma. The only reason the name "marvel" had to be thought up is that there's already a "kleismic". Of course, it is the marvel comma, but it's mostly the septimal kleisma. What's wrong with that name?

If it does need a new one, how about some permutation of "secor"? It's the comma between 16:15 and 15:14, the two simple rationalizations of a secor. And George doesn't have a comma yet.

>>441/440
> > It's a comma of miracle and unidec, but there are other linear
> temperaments involved here which are pretty good but not yet named.

I don't see a "Wilson's comma" either. Surely Erv must have run into this somwhere.

Graham

Gene wrote:

>15/14 major diatonic semitone (should be septimal diatonic semitone)

I wouldn't say "should be", it's another possibility. This list
wasn't intended to be systematic but more as a list of historical
usage.

>22/21 no name--unidecimal minor semitone?

You mean "undecimal", looks ok to me.

>33/32 unidecimal comma (bad name! Schoenberg's diesis?)

Why Schönberg's diesis and not undecimal 1/4-tone for example?

>540/539 Swets' comma (who is Swet?)

Wouter Swets is a Dutch ethnomusicologist. He mentioned this
comma to me personally. I can't say more about it since he
still has to publish his results.

Manuel

--- In tuning-math@yahoogroups.com, Graham Breed <graham@m...> wrote:
> Gene Ward Smith wrote:
>
> >>121/120
> >
> > Naming it after linear temperaments, this could be the undecimal
> > schrutar-orwell-valentine comma, or unisov for short.
>
> That's the neutral second comma, because it's between 12:11 and
11:10.

Sounds good, except for the part about "between". I'd call it a ratio.

> >>225/224 septimal kleisma (is this the best we can do?)

> If it does need a new one, how about some permutation of "secor"?
It's
> the comma between 16:15 and 15:14, the two simple rationalizations
of a
> secor. And George doesn't have a comma yet.

Again, sounds good. Secorisma?

> >>441/440
> >
> > It's a comma of miracle and unidec, but there are other linear
> > temperaments involved here which are pretty good but not yet
named.
>
> I don't see a "Wilson's comma" either. Surely Erv must have run
into
> this somwhere.

Kind of hard not to, which is the point of naming all the 11-limit
superparticulars. It would be nice to have a better excuse than this
for naming this particular comma after Erv, but we are running out of
11-limit commas, and that may do as a reason.

Where did the names "ragisma" and "kalisma" come from, and why?

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
>
> Gene wrote:
>
> >15/14 major diatonic semitone (should be septimal diatonic
semitone)
>
> I wouldn't say "should be", it's another possibility. This list
> wasn't intended to be systematic but more as a list of historical
> usage.

Which is why I was objecting--isn't diatonic semitone the
historically established name for 16/15?

> >22/21 no name--unidecimal minor semitone?
>
> You mean "undecimal", looks ok to me.
>
> >33/32 unidecimal comma (bad name! Schoenberg's diesis?)
>
> Why Schönberg's diesis and not undecimal 1/4-tone for example?

Because "undecimal 1/4-tone" is kind of ugly, and Schoenberg seems to
have considered this comma according to Monzo's analysis.

> >540/539 Swets' comma (who is Swet?)
>
> Wouter Swets is a Dutch ethnomusicologist. He mentioned this
> comma to me personally. I can't say more about it since he
> still has to publish his results.

Ah. Surprising if this makes an ethnomusicological appearance.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Manuel's list is closing in on listing and having a name for every
> 11-limit superparticular, which t seems to me an excellent thing.
>
> We have
>
> 28/27 Archytas' 1/3-tone

Nice, or perhaps Archytas' diesis, since Dave Keenan's work in
defining small-interval categories resulted in an upper boundary of
~68.57c for a diesis.

> 33/32 unidecimal comma (bad name! Schoenberg's diesis?)

Unidecimal diesis. Dave's comma/diesis boundary is ~35.19c.

> 64/63 septimal comma
> 81/80 syntonic comma, Didymus comma
> 100/99 Ptolemy's comma

What about:
64/63 septimal comma, Archytas' comma

Margo, Dave, and I have been using this term for a couple of years.
The comma is the difference between the largest intervals (7:8 and
8:9) in Archytas' diatonic tetrachord, in exact analogy to those (8:9
and 9:10) in Didymus' diatonic tetrachord.

Besides, in a very short time it will be revealed that the ancients
(at the direction of the gods) have already named 63:64 after
Archytas, so you would merely be recognizing a _fait accompli_. ;-)

> 2401/2400 breedsma
> 3025/3024 lehmerisma
> 4375/4374 ragisma
> 9801/9800 kalisma (Gauss' comma)

Conspicuous by its absence is:

4096/4095 tridecimal schisma or schismina

When Dave and I went about devising the Sagittal symbols, the schisma
(or schismina) 4095:4096 (which we are presently calling the
tridecimal schismina) was the first to be discovered (about 2/3 of
the way through the following message):

/tuning-math/message/3679

This is the difference between the sum (product) of the 5 and 7
commas (80:81 and 63:64) and the 13 diesis (1024:1053), three of the
principal commas that define the semantics of the notation. (The
large 13 diesis, 26:27, is also symbolized in the notation, being the
apotome complement of 1024:1053.)

Perhaps you will want to suggest another name for 4095:4096 that
would acknowledge it as the linchpin of the Sagittal symbol-flag
economy.

--George

P.S. - I'm not really back on the lists yet (not reading everything),
only peeking in from time to time to scan the subject lines.

--- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> Conspicuous by its absence is:
>
> 4096/4095 tridecimal schisma or schismina

That's because it is 13-limit, of course, but Manuel does have it
listed as "tridecimal schisma". There are no names for a lot of other
13-limit supers, such as 2080/2079, 4225/4224, 6656/6655, and
123201/123200, but he has 10648/10647 down as the "harmonisma".

> Perhaps you will want to suggest another name for 4095:4096 that
> would acknowledge it as the linchpin of the Sagittal symbol-flag
> economy.

I think you should do that, if you wish. Of course "sagittal schisma"
suggests itself.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "George D. Secor"
<gdsecor@y...>
> wrote:
> > Conspicuous by its absence is:
> >
> > 4096/4095 tridecimal schisma or schismina
>
> That's because it is 13-limit, of course, but Manuel does have it
> listed as "tridecimal schisma". There are no names for a lot of
other
> 13-limit supers, such as 2080/2079, 4225/4224, 6656/6655, and
> 123201/123200, but he has 10648/10647 down as the "harmonisma".
>
> > Perhaps you will want to suggest another name for 4095:4096 that
> > would acknowledge it as the linchpin of the Sagittal symbol-flag
> > economy.
>
> I think you should do that, if you wish. Of course "sagittal
schisma"
> suggests itself.

Looks as if that's the name to go with. A 13-limit schisma would be
very appropriate to associate with Sagittal, because all of the 11-
limit consonances (relative to a Pythagorean chain of fifths) are
notated *exactly*. Hence, 11-limit schismas enter into the picture
only when primes 5, 7, and/or 11 have exponent > 1.

Two other small schismas that figure prominently in the notation are:
4374:4375 (2*3^7:5^4*7), ~0.396 cents (ragisma)
184528125:184549376 (3^10*5^5:2^24*11), ~0.199 cents
But the second one is not superparticular.

--George

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > Conspicuous by its absence is:
> >
> > 4096/4095 tridecimal schisma or schismina
>
> That's because it is 13-limit, of course, but Manuel does have it
> listed as "tridecimal schisma". There are no names for a lot of other
> 13-limit supers, such as 2080/2079, 4225/4224, 6656/6655, and
> 123201/123200, but he has 10648/10647 down as the "harmonisma".
>
> > Perhaps you will want to suggest another name for 4095:4096 that
> > would acknowledge it as the linchpin of the Sagittal symbol-flag
> > economy.
>
> I think you should do that, if you wish. Of course "sagittal schisma"
> suggests itself.

Please don't rename 225/224. There's nothing wrong with "septimal
kleisma" and it's been in use for a long time.

If you want to name a comma after George then I suggest that 4096/4095
could be Secor's schismina, although I am generally no longer in
favour of naming things after people, since that gives you no clue as
to what the things are or what they are good for, and makes it likely
that you'll only have to rename them again later when an earlier
mention comes to light.

Haven't you got something better to work on George. :-)

I'm not here either.

I'll add the name Sagittal schismina to 4096/4095.

>Which is why I was objecting--isn't diatonic semitone the
>historically established name for 16/15?

Yes but 15/14 also has been named major diatonic semitone.

>Because "undecimal 1/4-tone" is kind of ugly, and Schoenberg seems to
>have considered this comma according to Monzo's analysis.

I'll make it al-Farabi's 1/4-tone.

Manuel

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> > --- In tuning-math@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
> > > Conspicuous by its absence is:
> > >
> > > 4096/4095 tridecimal schisma or schismina
> >
> > That's because it is 13-limit, of course, but Manuel does have it
> > listed as "tridecimal schisma". There are no names for a lot of
other
> > 13-limit supers, such as 2080/2079, 4225/4224, 6656/6655, and
> > 123201/123200, but he has 10648/10647 down as the "harmonisma".
> >
> > > Perhaps you will want to suggest another name for 4095:4096
that
> > > would acknowledge it as the linchpin of the Sagittal symbol-
flag
> > > economy.
> >
> > I think you should do that, if you wish. Of course "sagittal
schisma"
> > suggests itself.
>
> Please don't rename 225/224. There's nothing wrong with "septimal
> kleisma" and it's been in use for a long time.
>
> If you want to name a comma after George then I suggest that
4096/4095
> could be Secor's schismina,

Please don't. There is already the Miracle "sec(ond, min)or".
Having two intervals named after anyone would be too much (as well as
potentially confusing), unless one interval is clearly related to the
other.

> although I am generally no longer in
> favour of naming things after people, since that gives you no clue
as
> to what the things are or what they are good for,

"Sagittal schismina" will do nicely, then, because disregarding it
results in an economical use of symbol-elements in the notation. (We
don't refer to 4095:4096 as a schisma, because there are a couple of
schismas, 32768:32805 and 512:513, that _are_ symbolized in the
notation. A schismina is small enough that it may be disregarded
when notating JI.)

> and makes it likely
> that you'll only have to rename them again later when an earlier
> mention comes to light.

Even then I would not be too hasty to name an interval after somebody
simply because they happened to mention it in passing (without
drawing attention to its special significance) or apparently happened
to be the first to list it (along with a bunch of other intervals).
If you're in doubt as to whether it would be appropriate to attach
someone's name to a comma or schisma, then don't do it unless you are
reasonably sure that that person recognized something of practical or
theoretical value that is associated with that interval.

> Haven't you got something better to work on George. :-)

Yes, and I'm continuing to make good progress on it. 8-}

I just need a break from time to time to see what's going on in the
outside world, and I responded to this because I thought my good
friend Archytas hasn't been getting the recognition he deserves for
his advocacy of ratios of 7 in a musical scale.

> I'm not here either.

Then I guess I'll need to copy you off-list with the above. ;-)

--George

I'm still not here. But it seems a good time to post this.

http://dkeenan.com/Music/CommaNamer.zip (181 KB)

It's an Excel spreadsheet that automatically generates a unique
systematic name for any 31-limit comma (almost). It includes over 200
commas. It has the commas from Scala's intnam.par with their common
names (although some may be out of date) and it has all the commas
smaller than an apotome which can be represented exactly in Sagittal
notation, with their symbols (in the ASCII longhand representation).

The "almost" above, is because I have not properly implemented the
"complexity level" calculation, but instead used a quick and dirty
heuristic that works for all the commas listed (and probably any that
anyone is likely to want to add in the near future).

I did most of this spreadsheet months ago, but it was waiting for me
to code the "complexity level" algorithm. So I added the heuristic
today, just so I could release it.

Regards,
-- Dave Keenan