The Four Mistyschism Scales

A hoary eccelesiastical joke has it that mysticism should really be
spelled "misty schism", so this is how I am spelling the four Fokker
blocks which come from misty and the schisma. The two most notable
things about these scales is that Scala classifies all four of them
as well-temperments, and that this concludes the classification,
though I'll check the latter claim. Mistyschism2 is the same scale as
Scala's duoden12.scl, about which we read "Almost equal 12-tone
subset of Duodenarium".

! mistyschism1.scl
Mistyschism scale 2048/2025 67108864/66430125
12
!
524288/492075
9/8
1215/1024
512/405
4/3
64/45
3/2
262144/164025
2048/1215
3645/2048
256/135
2

! mistyschism2.scl
Mistyschism scale 2048/2025 67108864/66430125 = duoden12.scl
12
!
135/128
9/8
1215/1024
512/405
4/3
64/45
3/2
405/256
2048/1215
3645/2048
256/135
2

! mistyschism3.scl
Mistyschism scale 2048/2025 67108864/66430125
12
!
135/128
9/8
1215/1024
512/405
4/3
1476225/1048576
3/2
405/256
2048/1215
3645/2048
256/135
2

! mistyschism4.scl
Mistyschism scale 2048/2025 67108864/66430125
12
!
524288/492075
9/8
1215/1024
512/405
4/3
64/45
3/2
405/256
2048/1215
3645/2048
256/135
2

Is Kirberger's approximation to 12-equal in Scala? It would be
interesting if you actually had to go all the way out to atomic to
maximize the number of Scala matches in this big 12-tone exercise of
yours.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> A hoary eccelesiastical joke has it that mysticism should really be
> spelled "misty schism", so this is how I am spelling the four
Fokker
> blocks which come from misty and the schisma. The two most notable
> things about these scales is that Scala classifies all four of them
> as well-temperments, and that this concludes the classification,
> though I'll check the latter claim. Mistyschism2 is the same scale
as
> Scala's duoden12.scl, about which we read "Almost equal 12-tone
> subset of Duodenarium".
>
> ! mistyschism1.scl
> Mistyschism scale 2048/2025 67108864/66430125
> 12
> !
> 524288/492075
> 9/8
> 1215/1024
> 512/405
> 4/3
> 64/45
> 3/2
> 262144/164025
> 2048/1215
> 3645/2048
> 256/135
> 2
>
> ! mistyschism2.scl
> Mistyschism scale 2048/2025 67108864/66430125 = duoden12.scl
> 12
> !
> 135/128
> 9/8
> 1215/1024
> 512/405
> 4/3
> 64/45
> 3/2
> 405/256
> 2048/1215
> 3645/2048
> 256/135
> 2
>
> ! mistyschism3.scl
> Mistyschism scale 2048/2025 67108864/66430125
> 12
> !
> 135/128
> 9/8
> 1215/1024
> 512/405
> 4/3
> 1476225/1048576
> 3/2
> 405/256
> 2048/1215
> 3645/2048
> 256/135
> 2
>
> ! mistyschism4.scl
> Mistyschism scale 2048/2025 67108864/66430125
> 12
> !
> 524288/492075
> 9/8
> 1215/1024
> 512/405
> 4/3
> 64/45
> 3/2
> 405/256
> 2048/1215
> 3645/2048
> 256/135
> 2

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:

> Is Kirberger's approximation to 12-equal in Scala? It would be
> interesting if you actually had to go all the way out to atomic to
> maximize the number of Scala matches in this big 12-tone exercise
of
> yours.

Is atomic a comma of 12-et?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
>
> > Is Kirberger's approximation to 12-equal in Scala? It would be
> > interesting if you actually had to go all the way out to atomic
to
> > maximize the number of Scala matches in this big 12-tone exercise
> of
> > yours.
>
> Is atomic a comma of 12-et?

Yes. <12 19 28|161 -84 -12> = 0
(Did I notate this incorrectly?)

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:

> Yes. <12 19 28|161 -84 -12> = 0
> (Did I notate this incorrectly?)

Wow. Is the tuning list ready for this kind of stuff? I could go up
to the epimericity of the atom.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
>
> > Yes. <12 19 28|161 -84 -12> = 0
> > (Did I notate this incorrectly?)
>
> Wow. Is the tuning list ready for this kind of stuff?

Well, this is probably the only way you're going to get Kirnberger's
tuning (the one that's a JI approximation of 12-equal: a chain of
schisma-flattened fifths), and that's the sort of tuning you might
find in Scala.