CPS on a standard keyboard

Tuners, (maybe Kraig Grady is the expert on this?):

Are there any known precedents for 12-pitch-to-the-octave CPS's that would
work on a standard keyboard...I'm interested in exploring them in a live
improvisational setting.....

Best,
Aaron.

>Tuners, (maybe Kraig Grady is the expert on this?):
>
>Are there any known precedents for 12-pitch-to-the-octave CPS's that
>would work on a standard keyboard...I'm interested in exploring them
>in a live improvisational setting.....

Hi Aaron,

Pascal's triangle gives the cards of the CPS scales...

______________________________________________________________________
|
0..................................0 |
1...............................1 1 |
2............................1 2 1 |
3.........................1 3 3 1 |
4......................1 4 6 4 1 |
5...................1 5 10 10 5 1 |
6................1 6 15 20 15 6 1 |
7.............1 7 21 35 35 21 7 1 |
8..........1 8 28 56 70 56 28 8 1 |
9.......1 9 36 84 126 126 84 36 9 1 |
10....1 10 45 120 210 252 210 120 45 10 1 |
______________________________________________________________________|

As you can see, the only 12s will appear along the edges. These are
trivial Partchian o- or utonalities. The most interesting CPS are
usually closer to the center. One could take 2 hexanies and superpose
them to get 12 notes. Or if you're clever you could perhaps overlap
two dekanies and find 8 notes that overlap. Erv has a superposed
dekany scale, which alas has 14 notes...

!
Union of 2|5 and 3|5 [1 3 5 7 9] dekanies.
14
!
21/20
9/8
7/6
5/4
21/16
7/5
35/24
3/2
63/40
5/3
7/4
9/5
15/8
2/1
!

...but remember you're free to choose the harmonic identities, and
with this choice you may find a case with more overlaps.

You could also leave out 3 tones of a 15-tone CPS from the 6th row.

Last but not least, here is a very uneven 12-tone scale of mine
which is derived from the 7-limit stellated hexany (hexany with
its triads completed to 7-limit o- and utonalities). Specifically,
the st. hexany has 14 tones, and this simply omits 2 of them...

!
12-out-of [4 5 6 7] stellated hexany.
12
!
21/20
7/6
6/5
5/4
21/16
7/5
3/2
8/5
42/25
7/4
9/5
2/1
!
! Carl Lumma, 1998.
!
! e(7-limit)=30, tetrads(7-limit)=6.
! Scale is not proper.
!
! 5/4
! /|\
! / | \
! / | \
! 7/6---------7/4--------21/16
! \'-. /.-'/ \'-.\ .-'/
! \ 1/1--/---\--3/2 /
! \ /|\ / \ /|\ /
! \ | / \ | /
! / \|/ \ / \|/ \
! / 7/5--------21/20 \
! /.-' \'-.\ /.-'/ '-. \
! 8/5------\--6/5--/------9/5
! \ | /
! \ | /
! \|/
! 42/25

Have fun!

-Carl

Thanks, Carl-BTW, what was your logic for figuring which 2 pitches to remove?

I also notice that there are a lot of similarities to Paul Hahn's 32
consonance scale...a coincidence?

BTW, what is the precise definition of a proper scale? Is it a scale that is
too uneven to be approximated by an equal temperament?

Best,
Aaron.

On Saturday 27 December 2003 04:11 pm, Carl Lumma wrote:
> >Tuners, (maybe Kraig Grady is the expert on this?):
> >
> >Are there any known precedents for 12-pitch-to-the-octave CPS's that
> >would work on a standard keyboard...I'm interested in exploring them
> >in a live improvisational setting.....
>
> Hi Aaron,
>
> Pascal's triangle gives the cards of the CPS scales...
>
> ______________________________________________________________________
>
> 0..................................0 |
> 1...............................1 1 |
> 2............................1 2 1 |
> 3.........................1 3 3 1 |
> 4......................1 4 6 4 1 |
> 5...................1 5 10 10 5 1 |
> 6................1 6 15 20 15 6 1 |
> 7.............1 7 21 35 35 21 7 1 |
> 8..........1 8 28 56 70 56 28 8 1 |
> 9.......1 9 36 84 126 126 84 36 9 1 |
> 10....1 10 45 120 210 252 210 120 45 10 1 |
> ______________________________________________________________________|
>
>
> As you can see, the only 12s will appear along the edges. These are
> trivial Partchian o- or utonalities. The most interesting CPS are
> usually closer to the center. One could take 2 hexanies and superpose
> them to get 12 notes. Or if you're clever you could perhaps overlap
> two dekanies and find 8 notes that overlap. Erv has a superposed
> dekany scale, which alas has 14 notes...
>
> !
> Union of 2|5 and 3|5 [1 3 5 7 9] dekanies.
> 14
> !
> 21/20
> 9/8
> 7/6
> 5/4
> 21/16
> 7/5
> 35/24
> 3/2
> 63/40
> 5/3
> 7/4
> 9/5
> 15/8
> 2/1
> !
>
> ...but remember you're free to choose the harmonic identities, and
> with this choice you may find a case with more overlaps.
>
> You could also leave out 3 tones of a 15-tone CPS from the 6th row.
>
> Last but not least, here is a very uneven 12-tone scale of mine
> which is derived from the 7-limit stellated hexany (hexany with
> its triads completed to 7-limit o- and utonalities). Specifically,
> the st. hexany has 14 tones, and this simply omits 2 of them...
>
> !
> 12-out-of [4 5 6 7] stellated hexany.
> 12
> !
> 21/20
> 7/6
> 6/5
> 5/4
> 21/16
> 7/5
> 3/2
> 8/5
> 42/25
> 7/4
> 9/5
> 2/1
> !
> ! Carl Lumma, 1998.
> !
> ! e(7-limit)=30, tetrads(7-limit)=6.
> ! Scale is not proper.
> !
> ! 5/4
> ! /|\
> ! / | \
> ! / | \
> ! 7/6---------7/4--------21/16
> ! \'-. /.-'/ \'-.\ .-'/
> ! \ 1/1--/---\--3/2 /
> ! \ /|\ / \ /|\ /
> ! \ | / \ | /
> ! / \|/ \ / \|/ \
> ! / 7/5--------21/20 \
> ! /.-' \'-.\ /.-'/ '-. \
> ! 8/5------\--6/5--/------9/5
> ! \ | /
> ! \ | /
> ! \|/
> ! 42/25
>
> Have fun!
>
> -Carl
>
>
> [MMM info]------------------------------------------------------
> More MMM music files are at http://www.microtonal.org/music.html
> ------------------------------------------------------[MMM info]
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>
> From: Carl Lumma <ekin@...>
> Subject:

Hi Carl!
I am afraid i was the one who figured out this 14 tone MOS.
Although the double dekany is of course his invention/discovery.

> Re: CPS on a standard keyboard
> Erv has a superposed
> dekany scale, which alas has 14 notes...
>
> !
> Union of 2|5 and 3|5 [1 3 5 7 9] dekanies.
> 14
> !
> 21/20
> 9/8
> 7/6
> 5/4
> 21/16
> 7/5
> 35/24
> 3/2
> 63/40
> 5/3
> 7/4
> 9/5
> 15/8
> 2/1
> !
>
>

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

--- In MakeMicroMusic@yahoogroups.com, kraig grady <kraiggrady@a...>
wrote:
>
>
> >
> > From: Carl Lumma <ekin@l...>
> > Subject:
>
> Hi Carl!
> I am afraid i was the one who figured out this 14 tone MOS.
> Although the double dekany is of course his invention/discovery.

This 14 tone MOS? What 14 tone MOS?

>
>
> > Re: CPS on a standard keyboard
> > Erv has a superposed
> > dekany scale, which alas has 14 notes...
> >
> > !
> > Union of 2|5 and 3|5 [1 3 5 7 9] dekanies.
> > 14
> > !
> > 21/20
> > 9/8
> > 7/6
> > 5/4
> > 21/16
> > 7/5
> > 35/24
> > 3/2
> > 63/40
> > 5/3
> > 7/4
> > 9/5
> > 15/8
> > 2/1
> > !
> >
> >
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

>
> From: "Paul Erlich" <perlich@...>
>
>
> This 14 tone MOS? What 14 tone MOS?

Actually that is not right , it is a 14 tone 'constant structure'. He had
mapped out other Double Dekanies but not this one . It is possiibly trivial
compared to the actual structure itself. i happen to have a 'run' of 14 tone
scales for a bit and used this one (which you can find on the dallessandro
tuning/layout) in my film- Mystery without Clews. I think you can lay it out
in a chain of variable 6-7-8 with one 'wolf' I believe.
This also overlaps with my centaur tuning quite a bit.

As far as the opposing hexanies are concern i will put a diagram which for
me is always worth a thousand words.
http://anaphoria.com/hexanies.GIF

>
>
> >
> >
> > > Re: CPS on a standard keyboard
> > > Erv has a superposed
> > > dekany scale, which alas has 14 notes...
> > >
> > > !
> > > Union of 2|5 and 3|5 [1 3 5 7 9] dekanies.
> > > 14
> > > !
> > > 21/20
> > > 9/8
> > > 7/6
> > > 5/4
> > > 21/16
> > > 7/5
> > > 35/24
> > > 3/2
> > > 63/40
> > > 5/3
> > > 7/4
> > > 9/5
> > > 15/8
> > > 2/1
> > > !
> > >
> > >
> >
> > -- -Kraig Grady
> > North American Embassy of Anaphoria Island
> > http://www.anaphoria.com
> > The Wandering Medicine Show
> > KXLU 88.9 FM WED 8-9PM PST
>
> ________________________________________________________________________
> ________________________________________________________________________
>
> Message: 2
> Date: Tue, 30 Dec 2003 08:42:34 -0000
> From: "Paul Erlich" <perlich@...>
> Subject: Re: [tuning] CPS on a standard keyboard
>
> --- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
> <akjmicro@c...> wrote:
> > On Sunday 28 December 2003 01:15 am, kraig grady wrote:
> > > Hi Aaron!
> > > There is none
>
> I agree with Kraig, but why is this posted of his deleted from the
> archives?
>
> > By 'tuning hexanies opposite' I assume you mean 1-3-5-7, and 1-1/3-
> 1/5-1/7 and
> > octave normalized, no?
>
> No, Kraig means as far apart as possible from one another in the
> eikosany -- I'll let him explain, though I've found I can sometimes
> help people understand this stuff.

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