19-tone JI SCALA files now available

Hello tuners!

I've made simple SCALA files of the 19-tone JI scales that Paul
Erlich has recently posted.

They are available in the FILES section of Yahoo egroups.

/tuning/files/Pehrson/

Of course, Graham Breed's MIDI RELAY should be a great way to hear
these scales... It plays SCALA files DIRECTLY and you don't even
have to "tune anything up..."

________ ______ _____ _
Joseph Pehrson

Hello,

Being new to the world of microtonality I am curious as to how some
composer manage to deal with the complexity of some scales... Set-theory
has come up quite a bit on the list, but nothing that directly links it to
one's composing. I was hoping that some composers out there could tell me
how they have used the principles of set-theory in their compositions. I
also hope that the information that I gather here may help me in my research
into the uses of set-theoretic ideas in all composition. I am very curious
as to how a composer who may use set-theory deals with the vast number of
sets in larger ET's. Also, are there any resources that list all possible
sets for scales other than 12TET? Thank you,

Steven Kallstrom
skallstr@sun.iwu.edu

>Being new to the world of microtonality I am curious as to how some
>composer manage to deal with the complexity of some scales... Set-theory
>has come up quite a bit on the list, but nothing that directly links it
>to
>one's composing. I was hoping that some composers out there could tell
>me
>how they have used the principles of set-theory in their compositions. I
>also hope that the information that I gather here may help me in my
>research
>into the uses of set-theoretic ideas in all composition. I am very
>curious
>as to how a composer who may use set-theory deals with the vast number
>of
>sets in larger ET's. Also, are there any resources that list all
>possible
>sets for scales other than 12TET? Thank you,

Well,my approach to harmony has always been based on chords as sets of pitches,although i haven�t been able to use any lists of all possible n-note sets for a given tuning-only because of the trouble with making or finding one-but it has been more intuitive.It wouldn�t be that hard as long as you keep to a moderate number of notes in the sets.Fact is,it�s time i start to sort at least the lower number ETs out for sets...

-=-=-=-=-=-=-
MATS �LJARE
http://www.angelfire.com/mo/oljare
_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

Hello again,

I have yet another question... I am really itching to write a microtonal
piece of music for a retuned synthesizer. I have a great computer lab here
at my school, but access is limited and I would really like to start this
project here in my room. The only equipment that I have is an old Roland
U-20 RS-PCM Keyboard, which I have no documentation for since I got it
virtually for free. I doubt that this is re-tunable, but I figured someone
here may have some answers. My other question involves Finale. I was
wondering if it would be possible to play back music directly from Finale in
a different temperament through the internal MIDI... that would be really
great... I was hoping that I could get some good answers, or suggestions on
how to quickly get up and working with microtones...

Steven Kallstrom
skallstr@sun.iwu.edu

--- In tuning@y..., "Steven Kallstrom" <skallstr@s...> wrote:
> Hello again,
>
> I have yet another question... I am really itching to write
a microtonal
> piece of music for a retuned synthesizer. I have a great computer
lab here
> at my school, but access is limited and I would really like to
start this
> project here in my room. The only equipment that I have is an old
Roland
> U-20 RS-PCM Keyboard, which I have no documentation for since I got
it
> virtually for free. I doubt that this is re-tunable, but I figured
someone
> here may have some answers.

Steven,

The U-20 can be microtuned, but the only way to do it is with the
Rhythm Part - and this is full-keyboard retunabilty. You have to
assign musical timbres, where the drums are then individually tune
each key.

JL

Steven,

If you haven't already seen it check out the thread on Polya's counting
theorem from Dec. 2000/Jan 2001. I discussed how to count the number of
sets. If you are interested, I could cook up a short computer program to
actually produce a table of sets for a given ET. I'll have to think about
set tables for Margo's "two manuals offset by a comma" tunings. Polya's
theorem can give us the number of sets of various sizes, but the tables
could be tricky to generate. Write me off list if you are interested.

David Bowen
dmb@sgi.com

On 8 Mar 2001 tuning@yahoogroups.com wrote:

> From: "Steven Kallstrom" <skallstr@sun.iwu.edu>
> Subject: Set-theory and composition
>
> Being new to the world of microtonality I am curious as to how
> some composer manage to deal with the complexity of some scales...
> Set-theory has come up quite a bit on the list, but nothing that
> directly links it to one's composing. I was hoping that some
> composers out there could tell me how they have used the principles of
> set-theory in their compositions. I also hope that the information
> that I gather here may help me in my research into the uses of
> set-theoretic ideas in all composition. I am very curious as to how a
> composer who may use set-theory deals with the vast number of sets in
> larger ET's. Also, are there any resources that list all possible
> sets for scales other than 12TET? Thank you,

Hi Steven - I notice someone already answered you about Polya's counting
theorem. By hand, cranking out the numbers is a pain in the neck, but you
can get Maple or Mathematica to do it quite easily. If you want to
actually see an example of a chord from each set-class, you can write a
little code. I did it once for 19-tET and could probably dig up the
C code if you're really interested. Anyway, here are the raw numbers for
an example tuning, 31-tET, so you can get an idea of the magnitudes:

cardinality number of set-classes
0, 31 1
1, 30 1
2, 29 15
3, 28 80
4, 27 560
5, 26 2793
6, 25 12103
7, 24 42640
8, 23 127920
9, 22 325845
10, 21 716859
11, 20 1367184
12, 19 2278640
13, 18 3329165
14, 17 4280355
15, 16 4850640

And I'll just add that I calculated the number of scales/chords of 26
notes in 53-tet to be: 9183681736376. That's 9 trillion, 183 billion, 681
million, 736 thousand and 376. I doubt we'll be seeing a 53-tet sequel to
Slominsky's compendium of scales...

By the way, this question comes up periodically, and I suggest a FAQ
entry: HOW MANY SCALES OR CHORDS ARE THERE IN A GIVEN EQUAL TEMPERAMENT?

The answer would contain a brief introduction to the notion of a
set-class in an arbitrary tuning system, a description of the way you can
count the scales/chords, and finally a table with the "answers", i.e.
numbers of set-classes of each cardinality, for all ETs up to some upper
limit.

I don't post to the tuning list very often, but I'd still be glad to
contribute this FAQ entry if it's thought to be a good idea.

By the way, when I did a study of set-classes in 19-tET, I found it useful
to group them in multiplicative classes. I.e., [0,1,2,3,4] <-> [0,2,4,6,8]
<-> [0,3,6,9,12] <-> [0,4,8,12,16] <-> [0,1,5,10,15] <-> [0,5,6,12,18] <->
[0,2,7,9,14] <-> [0,5,8,13,16] <-> [0,8,9,17,18]. This reduces the number
of distinct classes by a factor of almost 9, and makes it considerably
easier to account for things.

As to the other question, of approaches to composition with set-classes, I
would say that the approaches in books like Robert Morris's "Composition
with Pitch-classes" are based on general principles, not tied to 12-tET.
As for me, I'm fascinated with the numbers of set-classes that come up,
and the combinational principles, but I don't intentionally "compose with
set-classes" and neither, I think, do most composers whose music gets
analysed using set-classes.

Cheers --Jon Wild

Hi Jon,

Jon Wild:
> By the way, this question comes up periodically, and I suggest a
> FAQ entry: HOW MANY SCALES OR CHORDS ARE THERE IN A GIVEN EQUAL
> TEMPERAMENT?

> I don't post to the tuning list very often, but I'd still be
> glad to contribute this FAQ entry if it's thought to be a good
> idea.

Yes, please do!

- Jeff