Yahoo Tuning Groups Ultimate Backup tuning-math different way of thinking about the 9lim diamond

Hey just an update of what I have been doing â"

Noticed that the 9 lim diamond can be achieved by the addition of the
five different linear arrangements of the pentatonic 6/5, 7/6, 8/7,
9/8, 10/9

Since they are the superparticular harmonics, each arrangement results
in a linear scale of division of the first member. This is the same
as taking each line of the xlim tonality diamond from x to 2x.

So the 9lim diamond can be viewed as 5 different pentatonic scales,
(since the lines for 7 and 14 are the same)

This process can be applied of course with a higher prime lim and u
will end up with a set of equal length linear scales that ad up to the
diamond.

Mapping this to a keyboard is pretty straightforward. It takes
improvisation to a whole new level of ease. Ive been having lots fun
jamming on it. Just have to get better at playing the keyboard!

🔗tfllt <nasos.eo@gmail.com>

--- In tuning-math@yahoogroups.com, "tfllt" <nasos.eo@...> wrote:
>
> Hey just an update of what I have been doing ï¿½"
>
> Noticed that the 9 lim diamond can be achieved by the addition of the
> five different linear arrangements of the pentatonic 6/5, 7/6, 8/7,
> 9/8, 10/9
>
> Since they are the superparticular harmonics, each arrangement results
> in a linear scale of division of the first member. This is the same
> as taking each line of the xlim tonality diamond from x to 2x.
>
> So the 9lim diamond can be viewed as 5 different pentatonic scales,
> (since the lines for 7 and 14 are the same)
>
> This process can be applied of course with a higher prime lim and u
> will end up with a set of equal length linear scales that ad up to the
> diamond.
>
> Mapping this to a keyboard is pretty straightforward. It takes
> improvisation to a whole new level of ease. Ive been having lots fun
> jamming on it. Just have to get better at playing the keyboard!
>

here is a .scl file note u may need to tweak depending on how much
range ur keyboard has! it has 2 octaves for each harmonic space and
goes backward from 14 to 7

! D:\TUN\d\big.scl
!

72
!
8/7
9/7
10/7
12/7
2/1
16/7
18/7
20/7
24/7
4/1
4/1
1/1
7/6
4/3
3/2
5/3
2/1
7/3
8/3
3/1
10/3
4/1
4/1
1/1
6/5
7/5
8/5
9/5
2/1
12/5
14/5
16/5
18/5
4/1
4/1
1/1
10/9
4/3
14/9
16/9
2/1
20/9
8/3
28/9
32/9
4/1
4/1
1/1
9/8
5/4
3/2
7/4
2/1
9/4
5/2
3/1
7/2
4/1
4/1
1/1
8/7
9/7
10/7
12/7
2/1
16/7
18/7
20/7
24/7
4/1
4/1
4/1

🔗Kraig Grady <kraiggrady@anaphoria.com>

this is cheating - any diamond made of 5 elements you can call a pentatonic.
although i see no reason not just to take pentatonics and make diamonds out of them

tfllt wrote:
>
> Hey just an update of what I have been doing ï¿½"
>
> Noticed that the 9 lim diamond can be achieved by the addition of the
> five different linear arrangements of the pentatonic 6/5, 7/6, 8/7,
> 9/8, 10/9
>
> Since they are the superparticular harmonics, each arrangement results
> in a linear scale of division of the first member. This is the same
> as taking each line of the xlim tonality diamond from x to 2x.
>
> So the 9lim diamond can be viewed as 5 different pentatonic scales,
> (since the lines for 7 and 14 are the same)
>
> This process can be applied of course with a higher prime lim and u
> will end up with a set of equal length linear scales that ad up to the
> diamond.
>
> Mapping this to a keyboard is pretty straightforward. It takes
> improvisation to a whole new level of ease. Ive been having lots fun
> jamming on it. Just have to get better at playing the keyboard!
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗tfllt <nasos.eo@gmail.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

you say that you have a pentatonic scale generating a diamond. well a pentatonic by definition has 5 notes, how is this significant.
couldn't this be said of any diamond made of 5 elements?
Also anytime you have the common tone modulations/rotation of any set you have a diamond.
this is how Partch formed it.
BTW this set was used by Stockhausen in his piece "Sirius" and by 'coincidence' was centered on the pitch G like Partch

tfllt wrote:
>
> i dont understand what u are saying?
>
> the diamond has 19 tones, not 5
>
> how is it cheating? who is it cheating?
>
> i am trying to say the 9lim diamond can be expressed as all the
> rotations of the pentatonic 6/5, n+1/n ... 10/9
>
> can u please explain better what u r saying?
>
> --- In tuning-math@yahoogroups.com > <mailto:tuning-math%40yahoogroups.com>, Kraig Grady <kraiggrady@...> > wrote:
> >
> > this is cheating - any diamond made of 5 elements you can call a
> pentatonic.
>
> i dont udnerstand - the diamond is made of 19 tones
> > although i see no reason not just to take pentatonics and make diamonds
> > out of them
> >
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗tfllt <nasos.eo@gmail.com>

--- In tuning-math@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> you say that you have a pentatonic scale generating a diamond. well a
> pentatonic by definition has 5 notes, how is this significant.
> couldn't this be said of any diamond made of 5 elements?

what do you mean by diamond made of 5 elements?

> Also anytime you have the common tone modulations/rotation of any set
> you have a diamond.

yes of course

> this is how Partch formed it.

i didnt realise this was how partch formed it but it makes sense if u
rotate a series of superparticular intervals it will make a diamond.

all i was trying to say, is that i rearranged the 9lim 19 tone diamond
into 5 pentatonic scales so that it can actually be played. it seems
to be the most complete way i have found without involving 11, the
9lim diamond to me seems like a good choice.

🔗Kraig Grady <kraiggrady@anaphoria.com>

by 5 elements in the sense that you can have you can make a diamond out of any 5 harmonics or interval one chooses or likes the sound of.
they needn't be superparicular
some people like 13s more than 11 and i agree that the 9 limit diamond has allot of material in it.
there is the 1-3-5-7-9 double dekany of 14 notes that i like quite a bit too. which is formed by taking the 2 out of 5 set and the 3 out of 5 set as in
1x3
1x5
1x7
1x9
3x5
3x7
3x9
5x7
5x9
7x9
1x3x5
1x3x7
1x3x9
1x5x7
1x5x9
1x7x9
3x5x7
3x5x9
3x7x9
5x7x9
i can't seem to find a picture of it off hand

tfllt wrote:
>
> --- In tuning-math@yahoogroups.com > <mailto:tuning-math%40yahoogroups.com>, Kraig Grady <kraiggrady@...> > wrote:
> >
> > you say that you have a pentatonic scale generating a diamond. well a
> > pentatonic by definition has 5 notes, how is this significant.
> > couldn't this be said of any diamond made of 5 elements?
>
> what do you mean by diamond made of 5 elements?
>
> > Also anytime you have the common tone modulations/rotation of any set
> > you have a diamond.
>
> yes of course
>
> > this is how Partch formed it.
>
> i didnt realise this was how partch formed it but it makes sense if u
> rotate a series of superparticular intervals it will make a diamond.
>
> all i was trying to say, is that i rearranged the 9lim 19 tone diamond
> into 5 pentatonic scales so that it can actually be played. it seems
> to be the most complete way i have found without involving 11, the
> 9lim diamond to me seems like a good choice.
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗tfllt <nasos.eo@gmail.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

I get 40 such pentatonic scales, as follows:

[9/8, 10/9, 6/5, 8/7, 7/6] [9/8, 5/4, 3/2, 12/7, 2]
[10/9, 6/5, 7/6, 8/7, 9/8] [10/9, 4/3, 14/9, 16/9, 2]
[10/9, 6/5, 7/6, 9/8, 8/7] [10/9, 4/3, 14/9, 7/4, 2]
[9/8, 10/9, 8/7, 7/6, 6/5] [9/8, 5/4, 10/7, 5/3, 2]
[9/8, 10/9, 8/7, 6/5, 7/6] [9/8, 5/4, 10/7, 12/7, 2]
[6/5, 7/6, 8/7, 9/8, 10/9] [6/5, 7/5, 8/5, 9/5, 2]
[10/9, 6/5, 9/8, 7/6, 8/7] [10/9, 4/3, 3/2, 7/4, 2]
[10/9, 6/5, 9/8, 8/7, 7/6] [10/9, 4/3, 3/2, 12/7, 2]
[10/9, 9/8, 6/5, 8/7, 7/6] [10/9, 5/4, 3/2, 12/7, 2]
[10/9, 9/8, 8/7, 6/5, 7/6] [10/9, 5/4, 10/7, 12/7, 2]
[10/9, 9/8, 6/5, 7/6, 8/7] [10/9, 5/4, 3/2, 7/4, 2]
[10/9, 9/8, 8/7, 7/6, 6/5] [10/9, 5/4, 10/7, 5/3, 2]
[9/8, 8/7, 7/6, 10/9, 6/5] [9/8, 9/7, 3/2, 5/3, 2]
[9/8, 8/7, 10/9, 6/5, 7/6] [9/8, 9/7, 10/7, 12/7, 2]
[9/8, 8/7, 10/9, 7/6, 6/5] [9/8, 9/7, 10/7, 5/3, 2]
[9/8, 10/9, 6/5, 7/6, 8/7] [9/8, 5/4, 3/2, 7/4, 2]
[9/8, 8/7, 7/6, 6/5, 10/9] [9/8, 9/7, 3/2, 9/5, 2]
[6/5, 7/6, 8/7, 10/9, 9/8] [6/5, 7/5, 8/5, 16/9, 2]
[6/5, 7/6, 10/9, 8/7, 9/8] [6/5, 7/5, 14/9, 16/9, 2]
[6/5, 7/6, 10/9, 9/8, 8/7] [6/5, 7/5, 14/9, 7/4, 2]
[6/5, 10/9, 7/6, 8/7, 9/8] [6/5, 4/3, 14/9, 16/9, 2]
[6/5, 10/9, 7/6, 9/8, 8/7] [6/5, 4/3, 14/9, 7/4, 2]
[6/5, 10/9, 9/8, 7/6, 8/7] [6/5, 4/3, 3/2, 7/4, 2]
[6/5, 10/9, 9/8, 8/7, 7/6] [6/5, 4/3, 3/2, 12/7, 2]
[7/6, 6/5, 8/7, 9/8, 10/9] [7/6, 7/5, 8/5, 9/5, 2]
[7/6, 6/5, 8/7, 10/9, 9/8] [7/6, 7/5, 8/5, 16/9, 2]
[7/6, 6/5, 10/9, 8/7, 9/8] [7/6, 7/5, 14/9, 16/9, 2]
[7/6, 6/5, 10/9, 9/8, 8/7] [7/6, 7/5, 14/9, 7/4, 2]
[7/6, 8/7, 6/5, 9/8, 10/9] [7/6, 4/3, 8/5, 9/5, 2]
[7/6, 8/7, 6/5, 10/9, 9/8] [7/6, 4/3, 8/5, 16/9, 2]
[7/6, 8/7, 9/8, 6/5, 10/9] [7/6, 4/3, 3/2, 9/5, 2]
[7/6, 8/7, 9/8, 10/9, 6/5] [7/6, 4/3, 3/2, 5/3, 2]
[8/7, 7/6, 6/5, 9/8, 10/9] [8/7, 4/3, 8/5, 9/5, 2]
[8/7, 7/6, 6/5, 10/9, 9/8] [8/7, 4/3, 8/5, 16/9, 2]
[8/7, 7/6, 9/8, 6/5, 10/9] [8/7, 4/3, 3/2, 9/5, 2]
[8/7, 7/6, 9/8, 10/9, 6/5] [8/7, 4/3, 3/2, 5/3, 2]
[8/7, 9/8, 7/6, 6/5, 10/9] [8/7, 9/7, 3/2, 9/5, 2]
[8/7, 9/8, 7/6, 10/9, 6/5] [8/7, 9/7, 3/2, 5/3, 2]
[8/7, 9/8, 10/9, 6/5, 7/6] [8/7, 9/7, 10/7, 12/7, 2]
[8/7, 9/8, 10/9, 7/6, 6/5] [8/7, 9/7, 10/7, 5/3, 2]

Getting rid of rotations reduces it down to 22 scales.

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗tfllt <nasos.eo@gmail.com>

hey gene what i meant by linear rotations,
was if u take the 6/5, 7/6, 8/7, 9/8, 10/9 as a circle and take each
from a different starting point; that gives u 5 linear pentatonics
(going one way around th ecircle)

6/5, 7/6, 8/7, 9/8, 10/9 -> 6/5, 7/5, 8/5, 9/5, 2
7/6, 8/7, 9/8, 10/9, 6/5 -> 7/6, 4/3, 3/2, 5/3, 2
8/7, 9/8, 10/9, 6/5, 7/6 -> 8/7, 9/7, 10/7, 12/7, 2
9/8, 10/9, 6/5, 7/6, 8/7 -> 9/8, 5/4, 3/2, 7/4, 2
10/9, 6/5, 7/6, 8/7, 9/8 -> 10/9, 4/3, 14/9, 16/9, 2

if you add up those 5 scales u have the 9lim diamond

-- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "tfllt" <nasos.eo@> wrote:
> >
> > Hey just an update of what I have been doing ï¿½"
> >
> > Noticed that the 9 lim diamond can be achieved by the addition of the
> > five different linear arrangements of the pentatonic 6/5, 7/6, 8/7,
> > 9/8, 10/9
>
> I get 40 such pentatonic scales, as follows:
>
> [9/8, 10/9, 6/5, 8/7, 7/6] [9/8, 5/4, 3/2, 12/7, 2]
> [10/9, 6/5, 7/6, 8/7, 9/8] [10/9, 4/3, 14/9, 16/9, 2]
> [10/9, 6/5, 7/6, 9/8, 8/7] [10/9, 4/3, 14/9, 7/4, 2]
> [9/8, 10/9, 8/7, 7/6, 6/5] [9/8, 5/4, 10/7, 5/3, 2]
> [9/8, 10/9, 8/7, 6/5, 7/6] [9/8, 5/4, 10/7, 12/7, 2]
> [6/5, 7/6, 8/7, 9/8, 10/9] [6/5, 7/5, 8/5, 9/5, 2]
> [10/9, 6/5, 9/8, 7/6, 8/7] [10/9, 4/3, 3/2, 7/4, 2]
> [10/9, 6/5, 9/8, 8/7, 7/6] [10/9, 4/3, 3/2, 12/7, 2]
> [10/9, 9/8, 6/5, 8/7, 7/6] [10/9, 5/4, 3/2, 12/7, 2]
> [10/9, 9/8, 8/7, 6/5, 7/6] [10/9, 5/4, 10/7, 12/7, 2]
> [10/9, 9/8, 6/5, 7/6, 8/7] [10/9, 5/4, 3/2, 7/4, 2]
> [10/9, 9/8, 8/7, 7/6, 6/5] [10/9, 5/4, 10/7, 5/3, 2]
> [9/8, 8/7, 7/6, 10/9, 6/5] [9/8, 9/7, 3/2, 5/3, 2]
> [9/8, 8/7, 10/9, 6/5, 7/6] [9/8, 9/7, 10/7, 12/7, 2]
> [9/8, 8/7, 10/9, 7/6, 6/5] [9/8, 9/7, 10/7, 5/3, 2]
> [9/8, 10/9, 6/5, 7/6, 8/7] [9/8, 5/4, 3/2, 7/4, 2]
> [9/8, 8/7, 7/6, 6/5, 10/9] [9/8, 9/7, 3/2, 9/5, 2]
> [6/5, 7/6, 8/7, 10/9, 9/8] [6/5, 7/5, 8/5, 16/9, 2]
> [6/5, 7/6, 10/9, 8/7, 9/8] [6/5, 7/5, 14/9, 16/9, 2]
> [6/5, 7/6, 10/9, 9/8, 8/7] [6/5, 7/5, 14/9, 7/4, 2]
> [6/5, 10/9, 7/6, 8/7, 9/8] [6/5, 4/3, 14/9, 16/9, 2]
> [6/5, 10/9, 7/6, 9/8, 8/7] [6/5, 4/3, 14/9, 7/4, 2]
> [6/5, 10/9, 9/8, 7/6, 8/7] [6/5, 4/3, 3/2, 7/4, 2]
> [6/5, 10/9, 9/8, 8/7, 7/6] [6/5, 4/3, 3/2, 12/7, 2]
> [7/6, 6/5, 8/7, 9/8, 10/9] [7/6, 7/5, 8/5, 9/5, 2]
> [7/6, 6/5, 8/7, 10/9, 9/8] [7/6, 7/5, 8/5, 16/9, 2]
> [7/6, 6/5, 10/9, 8/7, 9/8] [7/6, 7/5, 14/9, 16/9, 2]
> [7/6, 6/5, 10/9, 9/8, 8/7] [7/6, 7/5, 14/9, 7/4, 2]
> [7/6, 8/7, 6/5, 9/8, 10/9] [7/6, 4/3, 8/5, 9/5, 2]
> [7/6, 8/7, 6/5, 10/9, 9/8] [7/6, 4/3, 8/5, 16/9, 2]
> [7/6, 8/7, 9/8, 6/5, 10/9] [7/6, 4/3, 3/2, 9/5, 2]
> [7/6, 8/7, 9/8, 10/9, 6/5] [7/6, 4/3, 3/2, 5/3, 2]
> [8/7, 7/6, 6/5, 9/8, 10/9] [8/7, 4/3, 8/5, 9/5, 2]
> [8/7, 7/6, 6/5, 10/9, 9/8] [8/7, 4/3, 8/5, 16/9, 2]
> [8/7, 7/6, 9/8, 6/5, 10/9] [8/7, 4/3, 3/2, 9/5, 2]
> [8/7, 7/6, 9/8, 10/9, 6/5] [8/7, 4/3, 3/2, 5/3, 2]
> [8/7, 9/8, 7/6, 6/5, 10/9] [8/7, 9/7, 3/2, 9/5, 2]
> [8/7, 9/8, 7/6, 10/9, 6/5] [8/7, 9/7, 3/2, 5/3, 2]
> [8/7, 9/8, 10/9, 6/5, 7/6] [8/7, 9/7, 10/7, 12/7, 2]
> [8/7, 9/8, 10/9, 7/6, 6/5] [8/7, 9/7, 10/7, 5/3, 2]
>
> Getting rid of rotations reduces it down to 22 scales.
>

🔗tfllt <nasos.eo@gmail.com>

🔗Carl Lumma <ekin@lumma.org>

🔗tfllt <nasos.eo@gmail.com>

--- In tuning-math@yahoogroups.com, "Carl Lumma" <ekin@...> wrote:
>
> > Mapping this to a keyboard is pretty straightforward.
>
> Oh? How's that done, exactly? I saw your .scl file, which
> looked a little bit odd to me.
>
> -Carl
>

hi there carl

the keyboard mapping works like this, for each octave of the piano
there is two octaves of a pentatonic scale

they go in this order

8/7 * 9/8 * 10/9 * 6/5 * 7/6
7/6 * 8/7 * 9/8 * 10/9 * 6/5
6/5 * 7/6 * 8/7 * 9/8 * 10/9
10/9 * 6/5 * 7/6 * 8/7 * 9/8
9/8 * 10/9 * 6/5 * 7/6 * 8/7

The Keys B and C are the same.

so for instance, my midi keyboard has 4 octaves range so if i want to
jam, i know the octave on the utmost left is a linear septimal scale,
the one next to it is /6, then /5, then /4, then i have to press the
octave shift button to get to the octagonal.

you might like to make your own mapping to suit your equipment better.
if you had a larger keyboard you may want to dedicate two octaves key
range to 4 octaves of the pentatonic.

so basically, the advantage is, rather than thinking about the
tonality diamond as a continuous 1 dimensional line that goes from
lowest to highest (being difficult to map to an instrument, and even
more difficult to play), u can think of it as 5 different 'modes',
each of these modes being a linear (all tones have a common
denominator) scale, or a chord.

u can breakdown any tonality diamond into such "modes" of ascending
superparticular intervals of equal length.

i printed the .scl file below again, but with spaces between the
pentatonics so u can see whats going on. the final one in the
original scale was just the septimal again for ease of access, only a
60tone scale is really necessary though.

if i get some free time and motivation i am hoping to try and
implement this in a real instrument.. maybe a bass guitar or some bell
thing..

60
!

8/7
9/7
10/7
12/7
2/1
16/7
18/7
20/7
24/7
4/1
4/1

1/1
7/6
4/3
3/2
5/3
2/1
7/3
8/3
3/1
10/3
4/1
4/1

1/1
6/5
7/5
8/5
9/5
2/1
12/5
14/5
16/5
18/5
4/1
4/1

1/1
10/9
4/3
14/9
16/9
2/1
20/9
8/3
28/9
32/9
4/1
4/1

1/1
9/8
5/4
3/2
7/4
2/1
9/4
5/2
3/1
7/2
4/1
4/1

🔗Carl Lumma <ekin@lumma.org>

>hi there carl
>
>the keyboard mapping works like this, for each octave of the piano
>there is two octaves of a pentatonic scale

You lost me. Are all four octaves the same, and if so can you
show one of them?

>they go in this order
>
>8/7 * 9/8 * 10/9 * 6/5 * 7/6
>7/6 * 8/7 * 9/8 * 10/9 * 6/5
>6/5 * 7/6 * 8/7 * 9/8 * 10/9
>10/9 * 6/5 * 7/6 * 8/7 * 9/8
>9/8 * 10/9 * 6/5 * 7/6 * 8/7
>
>The Keys B and C are the same.

Which keys are those?

>so for instance, my midi keyboard has 4 octaves range so if i want to
>jam, i know the octave on the utmost left is a linear septimal scale,
>the one next to it is /6, then /5, then /4, then i have to press the
>octave shift button to get to the octagonal.

Huh?

>so basically, the advantage is, rather than thinking about the
>tonality diamond as a continuous 1 dimensional line that goes from
>lowest to highest

I don't typically think of them this way, and neither did Partch.
He thought of them as collections of otonal and utonal scales.

>(being difficult to map to an instrument, and even
>more difficult to play), u can think of it as 5 different 'modes',
>each of these modes being a linear (all tones have a common
>denominator) scale, or a chord.

The 9-limit diamond has 10 normal tonalities, which are pentatonic;
5 otonal (common denominator) and 5 utonal (common numerator).
This is the main way in Partch, Wilson, Prent Rodgers, etc., view
the diamond.

>i printed the .scl file below again, but with spaces between the
>pentatonics so u can see whats going on. the final one in the
>original scale was just the septimal again for ease of access, only a
>60tone scale is really necessary though.

That looks like a strangely-formed .scl file. There are duplicate
pitches (like 4/1), and the pitches are not monotonically ascending.

>if i get some free time and motivation i am hoping to try and
>implement this in a real instrument.. maybe a bass guitar or some bell
>thing..

I'd like to try it on my MIDI keyboard, if I could figure out what
it is you're doing.

-Carl

🔗tfllt <nasos.eo@gmail.com>

there are *five* distinct pentatonic modes to the 9lim diamond, each
is achieved by multiplying the fifth to tenth harmonic like below

>
> >they go in this order
> >
> >8/7 * 9/8 * 10/9 * 6/5 * 7/6
> >7/6 * 8/7 * 9/8 * 10/9 * 6/5
> >6/5 * 7/6 * 8/7 * 9/8 * 10/9
> >10/9 * 6/5 * 7/6 * 8/7 * 9/8
> >9/8 * 10/9 * 6/5 * 7/6 * 8/7
> >

this gives us the scales

1 8/7 9/7 10/7 12/7 2
1 7/6 4/3 3/2 5/3 2
1 6/5 7/5 8/5 9/5 2
1 10/9 12/9 14/9 16/9 2
1 9/8 5/4 3/2 14/9 2

there are 20 non octave tones in these 5 pentatonics but since two of
them have simplified to the perfect fifth, we are left with the 9lim
diamond

> >The Keys B and C are the same.
>
> Which keys are those?
>

actually i made a mistake, Bb and B are the same, these are white and
black keys immediately to the left of C.

for the sake of ease, i was trying to map two octaves of each of the
scales above to once octave of the 12tet keyboard, just because it
fits best that way.

> >so for instance, my midi keyboard has 4 octaves range so if i want to
> >jam, i know the octave on the utmost left is a linear septimal scale,
> >the one next to it is /6, then /5, then /4, then i have to press the
> >octave shift button to get to the octagonal.
>
> Huh?
>
> >so basically, the advantage is, rather than thinking about the
> >tonality diamond as a continuous 1 dimensional line that goes from
> >lowest to highest
>
> I don't typically think of them this way, and neither did Partch.
> He thought of them as collections of otonal and utonal scales.
>

sure thats how the diamond is defined but the structure of the diamond
in itself is not really an accessible way to use the scale since.

it is more rational to break it into several linear scales, of which
the diamond structure is made up of in repeating patterns, each of
these linear scales defines a unique chord/mood of the scale.

in any of those pentatonics u can play the whole infinite scale and
the period of the waveform will be the same, since it is a linear
scale. (look at the other post i made)

> >(being difficult to map to an instrument, and even
> >more difficult to play), u can think of it as 5 different 'modes',
> >each of these modes being a linear (all tones have a common
> >denominator) scale, or a chord.
>
> The 9-limit diamond has 10 normal tonalities, which are pentatonic;
> 5 otonal (common denominator) and 5 utonal (common numerator).
> This is the main way in Partch, Wilson, Prent Rodgers, etc., view
> the diamond.
>
> >i printed the .scl file below again, but with spaces between the
> >pentatonics so u can see whats going on. the final one in the
> >original scale was just the septimal again for ease of access, only a
> >60tone scale is really necessary though.
>
> That looks like a strangely-formed .scl file. There are duplicate
> pitches (like 4/1), and the pitches are not monotonically ascending.
>
> >if i get some free time and motivation i am hoping to try and
> >implement this in a real instrument.. maybe a bass guitar or some bell
> >thing..
>
> I'd like to try it on my MIDI keyboard, if I could figure out what
> it is you're doing.
>
> -Carl
>

u will understand why i mapped it this way when u play it.

just load this into ur synth and muck around on it.

ur ref key will start at
1 8/7 9/7 10/7 12/7 2

and the modes will descend up the keyboard

a proper implementation of this arrangement would be in the form of 5
immediately accessable surfaces with as much range as u needed up and
down.

note these 5 linear scales are the otonal elements of the diamond in a
one octave range from the prime lim /p to /2p

here is th e.scl again just trying bashing each octave with both hands
and u wil see what i mean

! D:\TUN\9lim Diamond\19t.scl
!

60
!
8/7
9/7
10/7
12/7
2/1
16/7
18/7
20/7
24/7
4/1
4/1
1/1
7/6
4/3
3/2
5/3
2/1
7/3
8/3
3/1
10/3
4/1
4/1
1/1
6/5
7/5
8/5
9/5
2/1
12/5
14/5
16/5
18/5
4/1
4/1
1/1
10/9
4/3
14/9
16/9
2/1
20/9
8/3
28/9
32/9
4/1
4/1
1/1
9/8
5/4
3/2
7/4
2/1
9/4
5/2
3/1
7/2
4/1
4/1
4/1