Mailing list post
From: genewardsmith (2012-03-08)
Subject: Fokkerization
Among the scales one finds in the Scala collection is the following:
! mandelbaum7.scl
!
Mandelbaum's 7-limit 19-tone scale
19
!
25/24
15/14
9/8
7/6
6/5
5/4
9/7
4/3
7/5
36/25
3/2
14/9
8/5
5/3
7/4
9/5
15/8
27/14
2/1
If we investigate the possibility that this might be a Fokker block, we find that the scale has Graham complexity 18 in both meantone and magic, but the lowest value we get next is 24, for MODMOS of keemun and negri. The keemun MODMOS has a generator chain -9, -6, -5, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15 and the negri MODMOS has a chain -10, -7, -6, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14 (in both cases using the interior product to define the chain.)
Both of these can be tweaked in the obvious way to a -6 to 12, and -7 to 11, MOS. However, negri will not work with meantone and magic to produce Fokker blocks, as the matrix [<1 0 0 0|, meantone v 2, magic v 2, negri v 2] is singular. But we can produce a Fokker block using keemun. I propose "Fokkerization" as a name for this process.
! mandelbaum7keemun.scl
!
Keemun Fokkerization of mandelbaum7
!
19
! meantone: -8 to 10; magic: -6 to 12; keemun: -6 to 12
25/24
15/14
9/8
7/6
6/5
5/4
9/7
4/3
7/5
36/25
3/2
25/16
8/5
5/3
7/4
9/5
15/8
48/25
2/1
Full thread (2 messages)
From: genewardsmith (2012-03-08)
Subject: Fokkerization
Among the scales one finds in the Scala collection is the following:
! mandelbaum7.scl
!
Mandelbaum's 7-limit 19-tone scale
19
!
25/24
15/14
9/8
7/6
6/5
5/4
9/7
4/3
7/5
36/25
3/2
14/9
8/5
5/3
7/4
9/5
15/8
27/14
2/1
If we investigate the possibility that this might be a Fokker block, we find that the scale has Graham complexity 18 in both meantone and magic, but the lowest value we get next is 24, for MODMOS of keemun and negri. The keemun MODMOS has a generator chain -9, -6, -5, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15 and the negri MODMOS has a chain -10, -7, -6, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14 (in both cases using the interior product to define the chain.)
Both of these can be tweaked in the obvious way to a -6 to 12, and -7 to 11, MOS. However, negri will not work with meantone and magic to produce Fokker blocks, as the matrix [<1 0 0 0|, meantone v 2, magic v 2, negri v 2] is singular. But we can produce a Fokker block using keemun. I propose "Fokkerization" as a name for this process.
! mandelbaum7keemun.scl
!
Keemun Fokkerization of mandelbaum7
!
19
! meantone: -8 to 10; magic: -6 to 12; keemun: -6 to 12
25/24
15/14
9/8
7/6
6/5
5/4
9/7
4/3
7/5
36/25
3/2
25/16
8/5
5/3
7/4
9/5
15/8
48/25
2/1
From: Chris Vaisvil (2012-03-12)
Subject: Re: [tuning] Fokkerization
got it - gonna try it.
On Wed, Mar 7, 2012 at 8:14 PM, genewardsmith
<genewardsmith@...>wrote:
> **
>
>
> Among the scales one finds in the Scala collection is the following:
>
> ! mandelbaum7.scl
> !
> Mandelbaum's 7-limit 19-tone scale
> 19
> !
> 25/24
> 15/14
> 9/8
> 7/6
> 6/5
> 5/4
> 9/7
> 4/3
> 7/5
> 36/25
> 3/2
> 14/9
> 8/5
> 5/3
> 7/4
> 9/5
> 15/8
> 27/14
> 2/1
>
> If we investigate the possibility that this might be a Fokker block, we
> find that the scale has Graham complexity 18 in both meantone and magic,
> but the lowest value we get next is 24, for MODMOS of keemun and negri. The
> keemun MODMOS has a generator chain -9, -6, -5, -3, -2, -1, 0, 1, 2, 3, 4,
> 5, 6, 7, 8, 9, 11, 12, 15 and the negri MODMOS has a chain -10, -7, -6, -4,
> -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14 (in both cases using the
> interior product to define the chain.)
> Both of these can be tweaked in the obvious way to a -6 to 12, and -7 to
> 11, MOS. However, negri will not work with meantone and magic to produce
> Fokker blocks, as the matrix [<1 0 0 0|, meantone v 2, magic v 2, negri v
> 2] is singular. But we can produce a Fokker block using keemun. I propose
> "Fokkerization" as a name for this process.
>
> ! mandelbaum7keemun.scl
> !
> Keemun Fokkerization of mandelbaum7
> !
> 19
> ! meantone: -8 to 10; magic: -6 to 12; keemun: -6 to 12
> 25/24
> 15/14
> 9/8
> 7/6
> 6/5
> 5/4
> 9/7
> 4/3
> 7/5
> 36/25
> 3/2
> 25/16
> 8/5
> 5/3
> 7/4
> 9/5
> 15/8
> 48/25
> 2/1
>
>
>