Alternative names for Paul's paper -- 5-limit LTs

This is an update of a table I sent to Paul. I've only done the 5-
limit ones so far. Did I miss any? Did I get any wrong?

Erlich name Other names used in discussions Descriptive name in
terms of generators as fractions of just intervals Descriptive
name in terms of ETs

Dicot Neutral thirds Minor major thirds 7&10-LT

Meantone 'Diatonic' Wide fourths, Narrow fifths
12&19-LT

Augmented Diesic Triple minor thirds 12&27-LT

Mavila Pelogic Extra-wide fourths 7&16-LT

Porcupine Semi minor thirds 15&22-LT

Blackwood Quintuple (major) thirds 15&25-LT

Dimipent Diminished, 'Octatonic' Quadruple (major) thirds
12&28-LT

Srutal Diaschismic, 5-limit Pajara Twin narrow fourths, Twin
wide fifths 22&46-LT

Magic 5-limit Magic, Major thirds (Simple) (major) thirds
19&22-LT

Superchrome Superchrome Tri(sect) minor thirds 12&35-LT

Hanson Kleismic (Simple) minor thirds 19&34-LT

Negripent Negri Tri(sect) (major) thirds 19&29-LT

Tetracot Quartafifths, Minimal diesic Quarter fifths
34&41-LT

Superpyth Superpythagorean Narrow fourths, Wide fifths
22&27-LT

Helmholtz Schismic, Helmholz/Groven Complex fourths,
Complex fifths 12&41-LT

Sensipent Semisixths, Tiny diesic Semi (major) sixths
19&46-LT

Subchrome Quarter (major) thirds 12&37-LT

Würschmidt Wuerschmidt Complex (major) thirds 31&34-LT

Compton Aristoxenean 12-fold 15 cents 12&72-LT

Amity AMT, Acute minor thirds 5-part elevenths, 339 cents
46&53-LT

Orson 5-limit Orwell Tri(sect) minor sixths 22&31-LT

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> This is an update of a table I sent to Paul. I've only done the 5-
> limit ones so far. Did I miss any? Did I get any wrong?

Things seem to be getting more and more complicated.

>This is an update of a table I sent to Paul. I've only done the 5-
>limit ones so far. Did I miss any? Did I get any wrong?

Are you aware that the e-mail RFC calls for hard reterns
every 76 chars? Some servers put them in. Anyway, your
table came wrapped. Why not upload it to the web?

-Carl

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> > This is an update of a table I sent to Paul. I've only done the
5-
> > limit ones so far. Did I miss any? Did I get any wrong?
>
> Things seem to be getting more and more complicated.

Yes. When people decide to use musically-meaningless names for
musical objects, the uninitiated tend to need tables they can look
up to find more meaningful ones. And when people keep changing those
musically-meaningless names, things get even more complicated.

Here it is on the web (17 kB Excel spreadsheet). Thanks Carl.

http://dkeenan.com/Music/Alternative%205-lim%20LT%
20names.xls

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Here it is on the web (17 kB Excel spreadsheet). Thanks Carl.
>
> http://dkeenan.com/Music/Alternative%205-lim%20LT%
> 20names.xls

You can use this instead:

http://tinyurl.com/4kzuo

Dave Keenan wrote:

> This is an update of a table I sent to Paul. I've only done the 5-
> limit ones so far. Did I miss any? Did I get any wrong?

Strictly speaking, "diatonic" and "octatonic" are names of MOS scales, not temperaments; you could talk about the "diatonic" (5L+2s) scale in schismic or injera temperaments, for instance (another name for injera is "double diatonic"). But diatonic is typically associated with meantone, and octatonic almost exclusively (?) with diminished temperament (usually 12-ET).

> Augmented Diesic Triple minor thirds 12&27-LT

12&15-LT. It would be nice to include 21-ET somehow, but it's not consistent. (The simplest would be "3&9", but I'm assuming you don't want to include these oddball ET's.)

> Mavila Pelogic Extra-wide fourths 7&16-LT

Since pelog is occasionally described as an approximation of 9-ET (more so than 16, AFAIK), this one might be better named 7&9-LT.

> Helmholtz Schismic, Helmholz/Groven Complex fourths, > Complex fifths 12&41-LT

I almost want to say 12&29. But 29 isn't that much better than 12 in this case.

> Compton Aristoxenean 12-fold 15 cents 12&72-LT

12&60. Maybe even 12&48, but 48-ET's thirds aren't much better than 12-ET's.

> Here it is on the web (17 kB Excel spreadsheet). Thanks Carl.
>
> http://dkeenan.com/Music/Alternative%205-lim%20LT%
> 20names.xls

Thanks Dave!!

Some more random thoughts:

() Best to avoid spaces in file names when publishing
to the web. Try underscores.

() Conisdered trying to import this into the database section
of the Tuning list? It could live alongside Paul's...

-Carl

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...>
wrote:
> Dave Keenan wrote:
>
> > This is an update of a table I sent to Paul. I've only done the
5-
> > limit ones so far. Did I miss any? Did I get any wrong?
>
> Strictly speaking, "diatonic" and "octatonic" are names of MOS
scales,
> not temperaments;

Yes. That's why they are in quotes. I lifted them that way from
Paul's database over on "tuning".
/tuning/database?
method=reportRows&tbl=10
I still think it's a good idea to include them.

. you could talk about the "diatonic" (5L+2s) scale in
> schismic or injera temperaments, for instance (another name for
injera
> is "double diatonic").

Yes. Alternative (non-systematic but musically meaningful) names I
have listed for Injera are: Twin meantone, "Double diatonic".

> But diatonic is typically associated with
> meantone,

Right. I've never seen it used as an alternative name for schismic
temperament, although of course you're correct in saying that
diatonic scales exist in schismic.

> and octatonic almost exclusively (?) with diminished
> temperament (usually 12-ET).

Yes.

>
> > Augmented Diesic Triple minor thirds 12&27-LT
>
> 12&15-LT.

Yes. Now that I look at it again, I don't know why I picked 27
instead of 15.

My criterion was loosely that the generator in the ET that is the
sum of those two ETs should be near optimum, or that the two ET's
should have errors approximately the same, but on opposite sides of
the optimum. I'm not sure what kind of optimum I was using, as I was
just eyeballing it off Paul's chart here (zoom 10):
http://www.tonalsoft.com/enc/eqtemp.htm

The other thing I did was to plug the TOP generator and period from
Paul's paper into this:
http://dkeenan.com/Music/MyhillCalculator.xls
(54kB Excel spreadsheet)
to get the convergents and semiconvergents.

> It would be nice to include 21-ET somehow, but it's not
> consistent. (The simplest would be "3&9", but I'm assuming you
don't
> want to include these oddball ET's.)

You assume correctly.

> > Mavila Pelogic Extra-wide fourths 7&16-LT
>
> Since pelog is occasionally described as an approximation of 9-ET
(more
> so than 16, AFAIK), this one might be better named 7&9-LT.

That's fine by me.

> > Helmholtz Schismic, Helmholz/Groven Complex fourths,
> > Complex fifths 12&41-LT
>
> I almost want to say 12&29. But 29 isn't that much better than 12
in
> this case.

In my way of thinking that makes 12&29-LT quite acceptable. This is
a case where having equal errors in opposite directions conflicts
somewhat with getting a near-optimum by adding. I'll go with 12&29.

> > Compton Aristoxenean 12-fold 15 cents 12&72-LT
>
> 12&60. Maybe even 12&48, but 48-ET's thirds aren't much better
than 12-ET's.

Same problem as with schismic, 12&48 sounds fine to me.

So if we agree on at least one of the ETs then we can choose the
other one as the one with closest to equal error, having a generator
on the _other_ side of optimum. That narrows the problem down a bit.
How do others feel about that?

Can we then agree that the octave-fraction form of systematic name
will have a denominator that is the sum of the two ETs in the pair-
of-ETs form of systematic name?

--- In tuning-math@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> > Here it is on the web (17 kB Excel spreadsheet). Thanks Carl.
> >
> > http://dkeenan.com/Music/Alternative%205-lim%
20LT%
> > 20names.xls
>
> Thanks Dave!!
>
> Some more random thoughts:
>
> () Best to avoid spaces in file names when publishing
> to the web. Try underscores.

Sorry.

> () Conisdered trying to import this into the database section
> of the Tuning list? It could live alongside Paul's...

No. Ideally Paul's would just include extra columns.

>> () Conisdered trying to import this into the database section
>> of the Tuning list? It could live alongside Paul's...
>
>No. Ideally Paul's would just include extra columns.

Good point. Have you tried adding them?

Note. You can always download Paul's database, import into
Excel, add the columns you want, reimport to Yahoo. I think.

-Carl

Dave Keenan wrote:

> So if we agree on at least one of the ETs then we can choose the > other one as the one with closest to equal error, having a generator > on the _other_ side of optimum. That narrows the problem down a bit. > How do others feel about that?
> > Can we then agree that the octave-fraction form of systematic name > will have a denominator that is the sum of the two ETs in the pair-
> of-ETs form of systematic name?

These sound reasonable.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> Dave Keenan wrote:

> > Can we then agree that the octave-fraction form of systematic name
> > will have a denominator that is the sum of the two ETs in the pair-
> > of-ETs form of systematic name?
>
> These sound reasonable.

It also means each can easily be computed from the other, which is a
major plus.