Topic: Doing 12-equal within 133-et

1 scales

Thread (16 messages)

From: Gene Ward Smith (2003-04-13)
Subject: Doing 12-equal within 133-et

Since 133 = 11*12+1, it might seem I am one off here. However, let's
consider the dominant sevenths temperament, which more or less
characterizes Western common-practice music in the 17-19th centuries. 

Dominant sevenths is defined by the wedgie [1, 4, -2, 4, -6, -16] or
the comma basis [36/35, 64/63]. The canonical map is given by
[245^(1/8), 6125^(1/8), 5, 7]
or in terms of generators 2 and 3/2, by
[245^(1/8), 5^(1/4)].

This, of course, has pure 5's and 7's, with flat 2's and 3's. We can
get something related to this by finding the least squares x for
(28*x - cents(5))^2 + (34*x - cents(7))^2, which turns out to be
99.25611588 cents. This is reasonably close to 2^(11/133), which is 
99.24812030 cents. The mapping to primes using this step value is
11 * [12, 19, 28, 34] = [132, 209, 308, 374]; here we take these as
133-equal values. In comparison the standard val for 133-equal would
be [133, 211, 309, 373].

Retuning any 12-et piece into this tuning is a straightforward task,
and I hope to get around to actually doing it soon. (I've either got
to boot up DOS, which I seldom do now, or get my Linux up to speed.)

From: Carl Lumma (2003-04-25)
Subject: Re: [tuning-math] Doing 12-equal within 133-et

>Retuning any 12-et piece into this tuning is a straightforward task,
>and I hope to get around to actually doing it soon. (I've either got
>to boot up DOS, which I seldom do now, or get my Linux up to speed.)

Any progress on this?

I can't say I see how applying a temperament to any 12-et piece would
be "straightforward"?  Do you do this in maple?

-Carl

From: Gene Ward Smith (2003-04-26)
Subject: Re: Doing 12-equal within 133-et

--- In [email protected], Carl Lumma <ekin@l...> wrote:

> >Retuning any 12-et piece into this tuning is a straightforward task,
> >and I hope to get around to actually doing it soon. (I've either got
> >to boot up DOS, which I seldom do now, or get my Linux up to speed.)
> 
> Any progress on this?

I'm still not happy about how Scala works under Linux for me, but I
don't really need it. 

> I can't say I see how applying a temperament to any 12-et piece would
> be "straightforward"?  Do you do this in maple?

Eh? Wasn't this exactly what you were doing with the shootout?

Maple is what I'd use for my example though, and calling it
straightforward is a stretch, since I'd take a midi file, turn it into
a Csound score file, edit that into a Maple file, then work with the
Maple file and then create a Scala file using Maple. Since Scala under
Linux seems very fussy about what files it will read, and I can't get
Maple to work on my chip under Windows, I'll probably need to copy the
.seq file over to the DOS part of the disk under Linux, and then
reboot to finish in Windows.

Like I said, straightforward.

From: Gene Ward Smith (2003-04-26)
Subject: Re: Doing 12-equal within 133-et

--- In [email protected], "Gene Ward Smith" <gwsmith@s...>
wrote:

> Maple is what I'd use for my example though, and calling it
> straightforward is a stretch, since I'd take a midi file, turn it into
> a Csound score file, edit that into a Maple file, then work with the
> Maple file and then create a Scala file using Maple. Since Scala under
> Linux seems very fussy about what files it will read, and I can't get
> Maple to work on my chip under Windows, I'll probably need to copy the
> .seq file over to the DOS part of the disk under Linux, and then
> reboot to finish in Windows.
> 
> Like I said, straightforward.

I converted the 4th movement of the Brahms string quartet #2 to a
Scala seq file in 132 (which is to say, 12) et, and Scala rendered it
as a midi file with no trouble. When I changed "0 equal 132" to "0
equal 133" it told me there were not enough midi channels; depite it
being a quartet Brahms uses a lot of double stops.

Drat midi. When is someone going to fix it? Isn't the midi tuning
standard supposed to deal with this stuff?

From: Manuel Op de Coul (2003-04-26)
Subject: Re: [tuning-math] Re: Doing 12-equal within 133-et

Gene wrote:

>Since Scala under
> Linux seems very fussy about what files it will read,

The scale files? Then see readme.txt. I could save the archive
in Unix format, but then there'll be Windows editors to
become fussy.

>Drat midi. When is someone going to fix it? Isn't the midi tuning
>standard supposed to deal with this stuff?

You could use Audio Compositor as Carl did with his temperament
exercise. AC has been fixed recently. Convert the seq file to
a midi file first, then use example/midi/mts.
Or use a tunable softsynth with a MIDI loopback, only that will affect
the timing a bit.
In 133-tET there are two fifths you can use.

Manuel

From: Carl Lumma (2003-04-26)
Subject: Re: [tuning-math] Re: Doing 12-equal within 133-et

>> I can't say I see how applying a temperament to any 12-et piece would
>> be "straightforward"?  Do you do this in maple?
>
>Eh? Wasn't this exactly what you were doing with the shootout?

I'm mapping 12 pitches to 12 other pitches.  I was under the impression
this conversion required mapping intervals to intervals.

-Carl

From: Gene Ward Smith (2003-04-26)
Subject: Re: Doing 12-equal within 133-et

--- In [email protected], "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
> 
> Gene wrote:
> 
> >Since Scala under
> > Linux seems very fussy about what files it will read,
> 
> The scale files? Then see readme.txt. I could save the archive
> in Unix format, but then there'll be Windows editors to
> become fussy.

They both seem fussy. I'm finding the Linux version works fine as long
as everything is created in a native Linux environment, with *no*
cutting and pasting of anything taken from a Windows file. The midi
files for my examples were created on the Linux side.

> >Drat midi. When is someone going to fix it? Isn't the midi tuning
> >standard supposed to deal with this stuff?
> 
> You could use Audio Compositor as Carl did with his temperament
> exercise. AC has been fixed recently. Convert the seq file to
> a midi file first, then use example/midi/mts.

It's the conversion of a seq to a midi file which is the problem. 

> In 133-tET there are two fifths you can use.

For this canonical map business, I must use the meantone fifth.

From: Manuel Op de Coul (2003-04-28)
Subject: Re: [tuning-math] Re: Doing 12-equal within 133-et

Gene, I don't understand why you're using 132-et note numbers
in the seq file. Why not use 12-et note numbers and change
the current scale to whatever temperament you want to produce?

>It's the conversion of a seq to a midi file which is the problem.

Not if you convert it to a 12-tet midi file first.

Manuel

From: Gene Ward Smith (2003-04-28)
Subject: Re: Doing 12-equal within 133-et

--- In [email protected], "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:

> Gene, I don't understand why you're using 132-et note numbers
> in the seq file. Why not use 12-et note numbers and change
> the current scale to whatever temperament you want to produce?

Because I've never gotten that to work.

From: Gene Ward Smith (2003-04-28)
Subject: Re: Doing 12-equal within 133-et

--- In [email protected], "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In [email protected], "Manuel Op de Coul"
> <manuel.op.de.coul@e...> wrote:
> 
> > Gene, I don't understand why you're using 132-et note numbers
> > in the seq file. Why not use 12-et note numbers and change
> > the current scale to whatever temperament you want to produce?

> Because I've never gotten that to work.

One addition to Scala you might want to consider would be to allow
non-integer values for "n" in the "equal" command of Scala; for
instance along with

0 equal 12

we could do instead

0 equal 12.023

This would address the whole matter nicely.

From: Manuel Op de Coul (2003-04-28)
Subject: Re: [tuning-math] Re: Doing 12-equal within 133-et

Gene wrote:
>Because I've never gotten that to work.

Maybe you gave up too quickly. If you send me the file that
doesn't work I could tell you what's wrong with it.

>0 equal 12

>we could do instead

>0 equal 12.023

You can do instead

0 equal 12 1197.7

Manuel

From: Gene Ward Smith (2003-04-28)
Subject: Re: Doing 12-equal within 133-et

--- In [email protected], "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
> 
> Gene wrote:
> >Because I've never gotten that to work.
> 
> Maybe you gave up too quickly. If you send me the file that
> doesn't work I could tell you what's wrong with it.

Evidently. I just managed to get it to work!

This file retuned the Brahms example I had trouble with before with no
problem:

! zeta12.scl
!
12 equal zeta tuning
 12
!
99.807
199.614
299.422
399.229
499.036
598.843
698.650
798.457
898.265
998.072
1097.879
1197.686

> >0 equal 12
> 
> >we could do instead
> 
> >0 equal 12.023
> 
> You can do instead
> 
> 0 equal 12 1197.7

Yow. Who would have guessed? Thanks!

From: Carl Lumma (2003-05-02)
Subject: Re: [tuning-math] Re: Doing 12-equal within 133-et

Manuel,

>>0 equal 12
>
>>we could do instead
>
>>0 equal 12.023
>
>You can do instead
>
>0 equal 12 1197.7

Does the .scl format support stretch/compression?
IIRC the last pitch line is taken as the interval
of equivalence, so instead of 2/1, we could give
a cents value of 1197?

-Carl

From: Manuel Op de Coul (2003-05-06)
Subject: Re: [tuning-math] Re: Doing 12-equal within 133-et

Carl asked:
>Does the .scl format support stretch/compression?
>IIRC the last pitch line is taken as the interval
>of equivalence, so instead of 2/1, we could give
>a cents value of 1197?

Yes indeed!

Manuel

From: Gene Ward Smith (2003-05-08)
Subject: Re: Doing 12-equal within 133-et

--- In [email protected], "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
> 
> Carl asked:
> >Does the .scl format support stretch/compression?
> >IIRC the last pitch line is taken as the interval
> >of equivalence, so instead of 2/1, we could give
> >a cents value of 1197?
> 
> Yes indeed!

What would be really interesting would be allowing the cents values to
occur in any order.

By the way, I read somewhere that Scala can produce Csound score
files. How is that done?

From: Manuel Op de Coul (2003-05-08)
Subject: Re: [tuning-math] Re: Doing 12-equal within 133-et

Gene wrote:
>What would be really interesting would be allowing the cents values to
>occur in any order.

Doesn't it?

>By the way, I read somewhere that Scala can produce Csound score
>files. How is that done?

There's an example in cmd\cs-demo.cmd.
Or maybe easier if you have a midi file that you want to
convert to a tuned Csound score is to use midi2cs by
Rüdiger Borrmann. There's a tip about it in tips.par.

Manuel