Is this scale known?

! unknown.scl
!
Is this scale known?
7
!
12/11
6/5
4/3
3/2
5/3
11/6
2/1

It seems to have some interesting properties. For one, the neutral seconds on either side of C; I like scales that divide the minor third into roughly equal parts. The scale is strictly proper, a Constant Structure, and all intervals are superparticular. It has harmonics 8-12 starting on F, or subharmonics going down from G (symmetrical around C). It seems like the sort of thing that ought to have been found before; it's a subset of many larger scales, but no exact match in the Scala archive.

Restatement of the "untitled" scale

12/11  (harmonic series in reverse (smaller to larger IE 12/11 * 11/10 * 10/9))
12/10
12/9  
--------
9/6     (x/6 harmonic series, not in reverse)
10/6
11/6
-----------
2/1 (octave)

************************
   Again, the above scale seems to prove my suspicion that splitting a scale into two different harmonic series (one from 1 to 1.5....the other from 1.5 to 2) is a good way to make a tetra-chordal scale.  My scale
9/8   (harmonic series x/8)
10/8
11/8
12/8(3/2) 
30/18  (harmonic series x/18)
33/18
36/18
.............is created in a similar fashion to your scale.

     It makes sense as well...that no one had made your "untitled scale"...as I've seen very few scales that essentially use two completely different harmonic series (IE 2 different o-tonalities) to create a scale

.  My hunch...the method of using two different o-tonallities, one before the 5th and one after, seems to be a great way to make very beautiful and unique scales.  Agreed?

-Michael
                          

--- On Mon, 2/9/09, Herman Miller <hmiller@...> wrote:

From: Herman Miller <hmiller@...>
Subject: [tuning] Is this scale known?
To: tuning@yahoogroups.com
Date: Monday, February 9, 2009, 9:13 PM

! unknown.scl

!

Is this scale known?

7

!

12/11

6/5

4/3

3/2

5/3

11/6

2/1

It seems to have some interesting properties. For one, the neutral

seconds on either side of C; I like scales that divide the minor third

into roughly equal parts. The scale is strictly proper, a Constant

Structure, and all intervals are superparticular. It has harmonics 8-12

starting on F, or subharmonics going down from G (symmetrical around C).

It seems like the sort of thing that ought to have been found before;

it's a subset of many larger scales, but no exact match in the Scala

archive.

What about dividing octave in exact half, which is tritone, and make 6, 8 or 10 tones symmetric scales (similar to Messiaen's, but microtonal)? It would be different kind of symmetry.

Daniel Forro

On 10 Feb 2009, at 2:27 PM, Michael Sheiman wrote:

>
> Restatement of the "untitled" scale
>
> 12/11 (harmonic series in reverse (smaller to larger IE 12/11 * > 11/10 * 10/9))
> 12/10
> 12/9
> --------
> 9/6 (x/6 harmonic series, not in reverse)
> 10/6
> 11/6
> -----------
> 2/1 (octave)
>
> ************************
> Again, the above scale seems to prove my suspicion that > splitting a scale into two different harmonic series (one from 1 to > 1.5....the other from 1.5 to 2) is a good way to make a tetra-> chordal scale. My scale
> 9/8 (harmonic series x/8)
> 10/8
> 11/8
> 12/8(3/2)
> 30/18 (harmonic series x/18)
> 33/18
> 36/18
> .............is created in a similar fashion to your scale.
>
> It makes sense as well...that no one had made your "untitled > scale"...as I've seen ver y few scales that essentially use two > completely different harmonic series (IE 2 different o-tonalities) > to create a scale
>
> . My hunch...the method of using two different o-tonallities, one > before the 5th and one after, seems to be a great way to make very > beautiful and unique scales. Agreed?
>
> -Michael

   Tritone as is...sqrt(2)/1?   Interesting idea...my only question is what ratios and/or generators would enable intersection with the tri-tone?

-Michael

--- On Mon, 2/9/09, Daniel Forro <dan.for@...> wrote:

From: Daniel Forro <dan.for@...>
Subject: Re: [tuning] Is this scale known?
To: tuning@yahoogroups.com
Date: Monday, February 9, 2009, 9:55 PM

What about dividing octave in exact half, which is tritone, and make

6, 8 or 10 tones symmetric scales (similar to Messiaen's, but

microtonal)? It would be different kind of symmetry.

Daniel Forro

On 10 Feb 2009, at 2:27 PM, Michael Sheiman wrote:

>

> Restatement of the "untitled" scale

>

> 12/11 (harmonic series in reverse (smaller to larger IE 12/11 *

> 11/10 * 10/9))

> 12/10

> 12/9

> --------

> 9/6 (x/6 harmonic series, not in reverse)

> 10/6

> 11/6

> -----------

> 2/1 (octave)

>

> ************ ********* ***

> Again, the above scale seems to prove my suspicion that

> splitting a scale into two different harmonic series (one from 1 to

> 1.5....the other from 1.5 to 2) is a good way to make a tetra-

> chordal scale. My scale

> 9/8 (harmonic series x/8)

> 10/8

> 11/8

> 12/8(3/2)

> 30/18 (harmonic series x/18)

> 33/18

> 36/18

> ............ .is created in a similar fashion to your scale.

>

> It makes sense as well...that no one had made your "untitled

> scale"...as I've seen ver y few scales that essentially use two

> completely different harmonic series (IE 2 different o-tonalities)

> to create a scale

>

> . My hunch...the method of using two different o-tonallities, one

> before the 5th and one after, seems to be a great way to make very

> beautiful and unique scales. Agreed?

>

> -Michael

This is for me high math. I just thought about something simple like for example (Cents):

0
133.3
300
466.6
600
733.3
900
1066.6
(1200)

Daniel Forro

On 10 Feb 2009, at 3:14 PM, Michael Sheiman wrote:

>
> Tritone as is...sqrt(2)/1? Interesting idea...my only question > is what ratios and/or generators would enable intersection with the > tri-tone?
>
> -Michael

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> ! unknown.scl
> !
> Is this scale known?
> 7
> !
> 12/11
> 6/5
> 4/3
> 3/2
> 5/3
> 11/6
> 2/1

Funny thing, I have

!
Michael Sheiman's 7-tone just scale, TL 79656.
7
!
12/11
6/5
4/3
3/2
5/3
11/6
2/1
!

-Carl

Carl said...
--Funny thing, I have
--!
--Michael Sheiman's 7-tone just scale, TL 79656.

To Carl,
    Hehehe...doh!

    That's an old version of the scale I just posted...before I figured out that putting it in forward harmonic order IE 9/8 10/8 11/8...sounds better than 12/11 6/5 4/3  (because it sounds more "major" than "minor" and major triads sound more consonant than minor ones).  I hadn't looked at my old version in a while and I forgot it existed.
***************************************************************************************

Herman,

    Glad to see someone is (you are) enjoying my "freak" scales. :-)
   Well, ok, maybe not so "freak", since it is really two "overlapping" JI scales,
but at least it's not pure JI. :-)

--It seems to have some interesting properties. For one, the neutral
--seconds on either side of C;
   Indeed, I was going for a sense of symmetry in as many directions as possible with the intervals.  Glad to see I'm not the only one who has found a use for that. :-)

    Also, still, I think my 9-tone scale under the pre-existing "golden ratio" tuning is far superior to either of those "split JI" scales.  It contains the 9 notes:

------Mike's PHI scale-------------
 198.515
 297.708
 397.038 *
 466.095
 664.664
 833.024 ("octave" IE the repeating interval even though it technically is 1.618033 and not 2/1)

   Note that 397.038 sounds significantly more tense than the other notes and, despite being based on an irrational generator, the entire scale (at least to me) sounds far more pleasing
so far as chords and harmony than either of my JI scales. 

   So if you are enjoying my old "best efforts" to make an ultra-symmetrical scale, I'd highly recommend playing around with that one as well. :-)

-Michael

--- On Mon, 2/9/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: Is this scale known?
To: tuning@yahoogroups.com
Date: Monday, February 9, 2009, 10:55 PM

--- In tuning@yahoogroups. com, Herman Miller <hmiller@... > wrote:

>

> ! unknown.scl

> !

> Is this scale known?

> 7

> !

> 12/11

> 6/5

> 4/3

> 3/2

> 5/3

> 11/6

> 2/1

Funny thing, I have

!

Michael Sheiman's 7-tone just scale, TL 79656.

7

!

12/11

6/5

4/3

3/2

5/3

11/6

2/1

!

-Carl

Herman.
Wasn't there someone who did quite a bit of investigating of self mirroring scales? Jacky Ligon? for one, but someone else some years back?
This does seem like a good one though.

Michael. examples of your dual harmonic series have been referred to again and again. it is Ptolemy equal diatonic i believe. Found also in Ethiopia. maybe used by Landini according to Doug Leedy. Also in the mideast.
http://anaphoria.com/xen9mar.PDF
The last chart on page 15 has the scale in the middle and it also shows how it can be developed by a chain of modulations.
I am sure the exact scale is also in Chalmers, Division of a tetrachord. all outside of all the people who use it everyday.

--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>> ! unknown.scl
>> !
>> Is this scale known?
>> 7
>> !
>> 12/11
>> 6/5
>> 4/3
>> 3/2
>> 5/3
>> 11/6
>> 2/1
> > Funny thing, I have
> > !
> Michael Sheiman's 7-tone just scale, TL 79656.
> 7
> !
> 12/11
> 6/5
> 4/3
> 3/2
> 5/3 > 11/6
> 2/1
> !

Hmm, I thought I had a fairly recent copy of the Scala archive. Oh, I see this message was from December. I guess I need to keep up to date with the Scala files! And now I do remember that thread. I probably even tried out the scale in Scala, which could be why it sounded familiar. Thanks for the info!

> > !
> > Michael Sheiman's 7-tone just scale, TL 79656.
> > 7
> > !
> > 12/11
> > 6/5
> > 4/3
> > 3/2
> > 5/3
> > 11/6
> > 2/1
> > !
>
> Hmm, I thought I had a fairly recent copy of the Scala archive.
> Oh, I see this message was from December. I guess I need to keep
> up to date with the Scala files! And now I do remember that
> thread. I probably even tried out the scale in Scala, which
> could be why it sounded familiar.
> Thanks for the info!

It may be in the archive, I don't know. I forked it back
in 1999, you could say.

-Carl