Mailing list post
From: Gene Ward Smith (2004-04-06)
Subject: Re: Six more {2,3,7} Fokker blocks
--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> These are, up to transposition, all the Fokker blocks with 64/63 and
> 6561/6272 as commas.
>
> [1 28/27 9/8 7/6 81/64 21/16 112/81 3/2 14/9 27/16 7/4 49/27]
> [1 28/27 9/8 7/6 9/7 4/3 81/56 3/2 14/9 27/16 16/9 27/14]
> [1 28/27 9/8 7/6 81/64 21/16 112/81 3/2 14/9 27/16 7/4 243/128]
> [1 28/27 9/8 7/6 81/64 4/3 112/81 3/2 14/9 27/16 7/4 27/14]
> [1 54/49 8/7 32/27 9/7 4/3 81/56 32/21 81/49 12/7 16/9 27/14]
> [1 28/27 9/8 32/27 9/7 4/3 81/56 3/2 14/9 12/7 16/9 27/14]
The best of these scales seem clearly to be the second listed, which
has five each of subminor and supermajor triads, and four each of
chords of type 1-3/2-7/4 and 1-7/6-7/4. I called the best of the
64/63 and 729/686 blocks "aaron", so I think I'll call this "akj". It
has a ratio of largest to smallest scale step of 2.67, and a Lumma
stability of 0.223924. Once again, we have an improper scale but of
course epimorphic. As expected, the scale is more 3-oriented than
aaron.scl, with 3 exponents ranging from -3 to 4, and 7 exponents
only from -1 to 1, and with nine fifths this time. Aaron.scl seems to
be more what Aaron was looking for, but this also is an interesting
scale, and should be excellent for making Michael Harrison style
music.
! akj.scl
64/63 6561/6272 Fokker block 5,5,4,4
12
!
28/27
9/8
7/6
9/7
4/3
81/56
3/2
14/9
27/16
16/9
27/14
2
Full thread (6 messages)
From: Gene Ward Smith (2004-04-06)
Subject: Six more {2,3,7} Fokker blocks
These are, up to transposition, all the Fokker blocks with 64/63 and
6561/6272 as commas.
[1 28/27 9/8 7/6 81/64 21/16 112/81 3/2 14/9 27/16 7/4 49/27]
[1 28/27 9/8 7/6 9/7 4/3 81/56 3/2 14/9 27/16 16/9 27/14]
[1 28/27 9/8 7/6 81/64 21/16 112/81 3/2 14/9 27/16 7/4 243/128]
[1 28/27 9/8 7/6 81/64 4/3 112/81 3/2 14/9 27/16 7/4 27/14]
[1 54/49 8/7 32/27 9/7 4/3 81/56 32/21 81/49 12/7 16/9 27/14]
[1 28/27 9/8 32/27 9/7 4/3 81/56 3/2 14/9 12/7 16/9 27/14]
From: Gene Ward Smith (2004-04-06)
Subject: Re: Six more {2,3,7} Fokker blocks
--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> These are, up to transposition, all the Fokker blocks with 64/63 and
> 6561/6272 as commas.
>
> [1 28/27 9/8 7/6 81/64 21/16 112/81 3/2 14/9 27/16 7/4 49/27]
> [1 28/27 9/8 7/6 9/7 4/3 81/56 3/2 14/9 27/16 16/9 27/14]
> [1 28/27 9/8 7/6 81/64 21/16 112/81 3/2 14/9 27/16 7/4 243/128]
> [1 28/27 9/8 7/6 81/64 4/3 112/81 3/2 14/9 27/16 7/4 27/14]
> [1 54/49 8/7 32/27 9/7 4/3 81/56 32/21 81/49 12/7 16/9 27/14]
> [1 28/27 9/8 32/27 9/7 4/3 81/56 3/2 14/9 12/7 16/9 27/14]
The best of these scales seem clearly to be the second listed, which
has five each of subminor and supermajor triads, and four each of
chords of type 1-3/2-7/4 and 1-7/6-7/4. I called the best of the
64/63 and 729/686 blocks "aaron", so I think I'll call this "akj". It
has a ratio of largest to smallest scale step of 2.67, and a Lumma
stability of 0.223924. Once again, we have an improper scale but of
course epimorphic. As expected, the scale is more 3-oriented than
aaron.scl, with 3 exponents ranging from -3 to 4, and 7 exponents
only from -1 to 1, and with nine fifths this time. Aaron.scl seems to
be more what Aaron was looking for, but this also is an interesting
scale, and should be excellent for making Michael Harrison style
music.
! akj.scl
64/63 6561/6272 Fokker block 5,5,4,4
12
!
28/27
9/8
7/6
9/7
4/3
81/56
3/2
14/9
27/16
16/9
27/14
2
From: Aaron K. Johnson (2004-04-06)
Subject: Re: [tuning] Six more {2,3,7} Fokker blocks
On Tuesday 06 April 2004 03:46 am, Gene Ward Smith wrote:
> These are, up to transposition, all the Fokker blocks with 64/63 and
> 6561/6272 as commas.
>
> [1 28/27 9/8 7/6 81/64 21/16 112/81 3/2 14/9 27/16 7/4 49/27]
> [1 28/27 9/8 7/6 9/7 4/3 81/56 3/2 14/9 27/16 16/9 27/14]
> [1 28/27 9/8 7/6 81/64 21/16 112/81 3/2 14/9 27/16 7/4 243/128]
> [1 28/27 9/8 7/6 81/64 4/3 112/81 3/2 14/9 27/16 7/4 27/14]
> [1 54/49 8/7 32/27 9/7 4/3 81/56 32/21 81/49 12/7 16/9 27/14]
> [1 28/27 9/8 32/27 9/7 4/3 81/56 3/2 14/9 12/7 16/9 27/14]
>
Gene,
Your math skill is dangerous!
Please, honor yourself, and not me, by dubbing these scales 'GWS scales' and
not 'akj' scales.
Oy!!!! now I have 6 more reasons not to get any work done....this list is
dangerous to productivity ;) Hopefully, these will inspire work, however.
Best,
Aaron Krister Johnson
http://www.akjmusic.com
http://www.dividebypi.com
OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'
From: Gene Ward Smith (2004-04-07)
Subject: Re: Six more {2,3,7} Fokker blocks
--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:
> Oy!!!! now I have 6 more reasons not to get any work done....this
list is
> dangerous to productivity ;) Hopefully, these will inspire work,
however.
They do seem to fit your requirements. I would be most interested to
hear what you could do with "aaron" or "akj".
From: Aaron K. Johnson (2004-04-16)
Subject: Re: [tuning] Re: Six more {2,3,7} Fokker blocks
On Wednesday 07 April 2004 12:44 am, Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
>
> wrote:
> > Oy!!!! now I have 6 more reasons not to get any work done....this
>
> list is
>
> > dangerous to productivity ;) Hopefully, these will inspire work,
>
> however.
>
> They do seem to fit your requirements. I would be most interested to
> hear what you could do with "aaron" or "akj".
gene-
i fooled around with the 'akj' scale today--improvising. it's very promising.
i think i'll sketch out a toccata for synthesizer using this scale !!!!
thanks for thinking it up.
BTW, are we still doing a collaboration, even though i offered only one voice?
best,
Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com
From: Gene Ward Smith (2004-04-16)
Subject: Re: Six more {2,3,7} Fokker blocks
--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:
> i fooled around with the 'akj' scale today--improvising. it's very
promising.
> i think i'll sketch out a toccata for synthesizer using this
scale !!!!
> thanks for thinking it up.
Great, Aaron! I think the "aaron" scale might be even better for your
purposes, if I understand correctly what they are.
> BTW, are we still doing a collaboration, even though i offered only
one voice?
I'd like four voices. I can get one voice just by firing up Fractal
Tune Smithy, so one voice isn't much of a collaboration and misses
the point anyway.