9toner inside 22EDO

Hi Paul, everyone,

below is a brief exposition of a 9-tone pentatonic inside 22 Equal,
after rereading the PEs article on the Decatonic scale and 22EDO/22UDO
(UDO unequal divisions of the octave?)

someone's bound to have seen it before, but this just comes out of
the dreaded Balzano stuff I bang on about...

1. Generator circle representation
----------------------------------

Generator of difference 5 in C22 group

0 5 10 15 20 3 8 13 18 1 6 11 16 21 4 9 14 19 2 7 12 17 (0...

segment of generator which has transposition properties T+5,
exchanges one pitch-class for adjacent one +1 higher:

... 0 5 10 15 20 3 8 13 8 ....

2. Presentation on a 2d grid
----------------------------

(3
20 (1 <--- replaces 0 at T+5

15 18

10 13

5 8

0 3

20

3. Scale
--------

If 0 chosen as starting pitch class, at 0 cents:

0 3 5 8 10 13 15 18 20 (0
L s L s L s L s s

(looks like a "pentatonic", no?)

in cents (to nearest cent for convenience, actual values from 22EDO)

0 164 272 436 545 709 818 982 1090 (1200=0

JI form (some ratios doubtful, 982=7/4???)

1/1 11/10 7/6 9/7 11/8 3/2 8/5 7/4 15/8

4. AOB
------

is the generator a sequence of 7/6s?

can anyone knock up a 3,5,7,11 lattice with this mode in?

--------------------------------------

Anyone want to play with this and let me know what they think?

For me, it has a nice wide 9/7, and a lovely 11/8ish. A dynamic mode?

Mark

Mark Gould wrote:

> someone's bound to have seen it before, but this just comes out of
> the dreaded Balzano stuff I bang on about...

It's called Orwell. Gene's got a web page about it

http://x31eq.com/genewardsmith/orwell.htm

> JI form (some ratios doubtful, 982=7/4???)
> > 1/1 11/10 7/6 9/7 11/8 3/2 8/5 7/4 15/8

All those are correct. You can also have 12/11 as well as 11/10, 14/11 at the same position as 9/7, and there must be other equivalences I didn't spot as I was going through.

> 4. AOB
> ------
> > is the generator a sequence of 7/6s?

Yes.

> can anyone knock up a 3,5,7,11 lattice with this mode in?

I can use a neutral second lattice. But I'd better wait until lunch time. How do you want it labelled?

> Anyone want to play with this and let me know what they think?

Fortunately, as Gene's sufficiently deluded as to think that he can make microtonal music with MIDI and electronics, you can hear an example, tuned to 53-equal. Follow the link I gave above.

> For me, it has a nice wide 9/7, and a lovely 11/8ish. A dynamic mode?

A lot of that depends on the tuning. Gene prefers more accuracy than 22-equal.

Graham

--- In tuning@yahoogroups.com, "Mark Gould" <mark.gould@a...> wrote:
> Hi Paul, everyone,
>
> below is a brief exposition of a 9-tone pentatonic inside 22 Equal,
> after rereading the PEs article on the Decatonic scale and
22EDO/22UDO
> (UDO unequal divisions of the octave?)

thanks for taking the time to read my paper, and to respond with your
own thoughts. i value them highly. could i humbly suggest that it
could be confusing to refer to a 9-tone scale as pentatonic?

> someone's bound to have seen it before,

it's in the famous mode list
http://www.xs4all.nl/~huygensf/doc/modename.html
in one rotation as "rezsutek's percussion scale" and in another
rotation as "twenty-two tone orwell".

> but this just comes out of
> the dreaded Balzano stuff I bang on about...
>
> 1. Generator circle representation
> ----------------------------------
>
> Generator of difference 5 in C22 group
>
> 0 5 10 15 20 3 8 13 18 1 6 11 16 21 4 9 14 19 2 7 12 17 (0...
>
> segment of generator which has transposition properties T+5,
> exchanges one pitch-class for adjacent one +1 higher:
>
> ... 0 5 10 15 20 3 8 13 8 ....

in other words, this 9-toner is a distributionally even scale, and in
particular, one in which the period (of repetition) is the octave
(just like the traditional pentatonic and diatonic scales).

in my distributionally even decatonic, the period is the half-octave;
in *both* of my decatonic scales, transposition changes, by 1/22
oct., at a minimum *two* pitch-classes per octave, while moving from
one kind of decatonic to the other can involve only *one* pitch class
changing per octave).

in my paper, i did not derive distributional evenness from any deeper
properties, but i can -- namely, a fokker periodicity block with all
but one of its defining unison vectors tempered out yields a
distributionally even scale (in which the period can turn out to be
an octave, a half-octave, a third-octave, a quarter-octave, etc.)

>
> 3. Scale
> --------
>
>
> If 0 chosen as starting pitch class, at 0 cents:
>
> 0 3 5 8 10 13 15 18 20 (0
> L s L s L s L s s
>
> (looks like a "pentatonic", no?)

i don't get it. why does it look like a "pentatonic"? it has more
small steps than large ones, so isn't it more like a "diatonic"?
obviously i have no idea what you mean by "pentatonic".

> in cents (to nearest cent for convenience, actual values from 22EDO)
>
> 0 164 272 436 545 709 818 982 1090 (1200=0
>
> JI form (some ratios doubtful, 982=7/4???)
>
> 1/1 11/10 7/6 9/7 11/8 3/2 8/5 7/4 15/8

>
> 4. AOB
> ------

meaning?

>
> is the generator a sequence of 7/6s?

sure, that's a great way to view it. this system, with all the
approximations through the 11-limit that you've indicated, is known
on tuning-math as "orwell", since gene found that the optimal
generator (to minimize the overall error of all the approximations,
including the approximation 1 generator = 7:6) is very nearly 19/84
octave (1984 -> george orwell). gene has a webpage about it somewhere.

> can anyone knock up a 3,5,7,11 lattice with this mode in?

that would be 4-dimensional, so kind of difficult . . . i could do it
without the 11 dimension though, if anyone's interested . . .

hope the theory-talk isn't too disconcerting for anyone . . .
-paul

tuning@yahoogroups.com wrote:

>
>

Hello Mark!

The keyboard pattern i use for my 22 tone pascal eikasany uses a keyboard that treat the scale as a chain of 7/6
like intervals which appealed to me cause of it being one way to generate pelog. I have used this alot.

>
> From: "Mark Gould" <mark.gould@argonet.co.uk>
> Subject: 9toner inside 22EDO
>
> Hi Paul, everyone,
>
> below is a brief exposition of a 9-tone pentatonic inside 22 Equal,
> after rereading the PEs article on the Decatonic scale and 22EDO/22UDO
> (UDO unequal divisions of the octave?)
>
> someone's bound to have seen it before, but this just comes out of
> the dreaded Balzano stuff I bang on about...
>
> 1. Generator circle representation
> ----------------------------------
>
> Generator of difference 5 in C22 group
>
> 0 5 10 15 20 3 8 13 18 1 6 11 16 21 4 9 14 19 2 7 12 17 (0...
>
> segment of generator which has transposition properties T+5,
> exchanges one pitch-class for adjacent one +1 higher:
>
> ... 0 5 10 15 20 3 8 13 8 ....
>
> 2. Presentation on a 2d grid
> ----------------------------
>
> (3
> 20 (1 <--- replaces 0 at T+5
>
> 15 18
>
> 10 13
>
> 5 8
>
> 0 3
>
> 20
>
> 3. Scale
> --------
>
> If 0 chosen as starting pitch class, at 0 cents:
>
> 0 3 5 8 10 13 15 18 20 (0
> L s L s L s L s s
>
> (looks like a "pentatonic", no?)
>
> in cents (to nearest cent for convenience, actual values from 22EDO)
>
> 0 164 272 436 545 709 818 982 1090 (1200=0
>
> JI form (some ratios doubtful, 982=7/4???)
>
> 1/1 11/10 7/6 9/7 11/8 3/2 8/5 7/4 15/8
>
> 4. AOB
> ------
>
> is the generator a sequence of 7/6s?
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM 8-9PM PST

Mark Gould wrote:

> If 0 chosen as starting pitch class, at 0 cents:
> > 0 3 5 8 10 13 15 18 20 (0
> L s L s L s L s s

I'll name the notes using numerals

0 3 5 8 10 13 15 18 20 (0
L s L s L s L s s
1 2 3 4 5 6 7 8 9 (1

> can anyone knock up a 3,5,7,11 lattice with this mode in?

Using a neutral second lattice, with template

5----------15
/ \ / \
/ \ / \
/ 11 / \
/ 7 \ / \
/ \ / \
1-----------3-----------9

I make it

' 9
' / 9
' / 7 / 9
' 5 / / \ / 7 /
'8 \ / / \ 5 / / \ /
' \ / 3-----------8 / \ / / \ 5 /
' 6 \ / / \ / 3-----------8 / \ /
' \ / 1-----------6 \ / / \ / 3
' 4 / \ / \ / 1-----------6 \
' / \ / 4 / \ / \
' / 2 / \ / 4
' 9 / / / 2
' / / 9 / /
' 7 / / / / 9
' / \ / / 7 / /
' / \ / 5 / / \ / / 7
'3-----------8 / \ / / \ / 5 / / \
' \ / / \ / 3-----------8 / \ / / \
' \ / 1-----------6 \ / / \ / 3-----------8
' 4 \ / \ / 1-----------6 \ /
' \ / 4 \ / \ / 1
' 2 \ / 4
' 2

(Remember to view source and set a fixed width font, or whatever it is you do.)

Graham

--- In tuning@yahoogroups.com, "Mark Gould" <mark.gould@a...> wrote:

> Hi Paul, everyone,
>
> below is a brief exposition of a 9-tone pentatonic inside 22 Equal,

> 0 3 5 8 10 13 15 18 20 (0
> L s L s L s L s s

hi mark, in case you haven't seen it yet, there's gene's page on, and
piece in, this scale:

http://x31eq.com/genewardsmith/orwell.htm

http://artists.mp3s.com/artist_song/2145/2145780.html

i'd like to hear your feedback to gene's mode of thinking (especially
if i can help explain anything to you), and also hope for your snail-
mail address (in case the offlist e-mail didn't get through).

7-limit lattice coming up (stay tuned)!

best,
paul

--- In tuning@yahoogroups.com, "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Mark Gould" <mark.gould@a...> wrote:
>
> > Hi Paul, everyone,
> >
> > below is a brief exposition of a 9-tone pentatonic inside 22
Equal,
>
> > 0 3 5 8 10 13 15 18 20 (0
> > L s L s L s L s s

> 7-limit lattice coming up (stay tuned)!
>
> best,
> paul

in order to view these properly, click on "message index" and
then "expand messages".

here's the original scale:

/ `. / 3 / /
/ 15 / `. / /
/ / `. / 20 /
. / / 10 / / `. /
-13 / / `. / / 15
`. / / 5--------18 / / `.
8 / / `. ,' `. / / 10 /
`. / / 0--------13 / / `. /
3 / / `. / / 5--------18
/ `. / / 8 / / `. ,' `
/ 20 / `. / / 0-------
/ / `. / 3 / /
/ / 15 / `. / /
------18 / / `. / 20 /
. ,' `. / / 10 / / `. /
0--------13 / / `. / / 15
/ `. / / 5--------18 / / `.
/ 8 / / `. .' `. / / 10
`. / / 0--------13 / / `.
3 / / `. / / 5-

as you can see, there are no complete 7-limit tetrads. thus
the "chromatically altered" scales that gene proposed on his page
(analogous to melodic or harmonic minor in the diatonic scale or
symmetrical in the decatonic scale, but actually *adding* to the
number of complete chords). if there's any interest, i'll try to
lattice these out too, but for at least some of them, thinking in
terms of a 22-equal mapping will produce a different (more intricate)
lattice than thinking in terms of an orwell mapping . . .

--- In tuning@yahoogroups.com, "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> http://x31eq.com/genewardsmith/orwell.htm
>
> http://artists.mp3s.com/artist_song/2145/2145780.html

I was planning on doing a whole series of these, but it didn't work
out. Would anyone be willing to host it without trying to micromanage
me?

>I was planning on doing a whole series of these, but it didn't work
>out. Would anyone be willing to host it without trying to micromanage
>me?

I would. Write me off-list.

-Carl