diadiaschis1

From: Gene Ward Smith (2004-01-11)
Subject: The Two Diadiaschisma Scales

These are based on the diaschisma and the diaschisma-schisma (check 
Manuel's list if you don't believe me) of 67108864/66430125. Scala 
tells me the scale closest to diadiaschis1 in my scale archives is
bp12_17 "12-tET approximation with minimal order 17 beats". For 
closest to diadiaschis2 I find that it is, according to Scala, 
exactly equidistant from duoden12 "Almost equal 12-tone subset of 
Duodenarium". These scales seem to be warping into some sort of 
circulating temperament.

! diadiaschis1.scl
Diadiaschisma scale 2048/2025 67108864/66430125
12
!
135/128
18225/16384
1215/1024
512/405
4/3
45/32
3/2
405/256
54675/32768
16/9
256/135
2

! diadiaschis2.scl
Diadiaschisma scale 2048/2025 67108864/66430125
12
!
135/128
9/8
1215/1024
512/405
4/3
64/45
3/2
405/256
54675/32768
32768/18225
256/135
2

From: Gene Ward Smith (2004-01-11)
Subject: The Two Diadiaschisma Scales

These are based on the diaschisma and the diaschisma-schisma (check 
Manuel's list if you don't believe me) of 67108864/66430125. Scala 
tells me the scale closest to diadiaschis1 in my scale archives is
bp12_17 "12-tET approximation with minimal order 17 beats". For 
closest to diadiaschis2 I find that it is, according to Scala, 
exactly equidistant from duoden12 "Almost equal 12-tone subset of 
Duodenarium". These scales seem to be warping into some sort of 
circulating temperament.

! diadiaschis1.scl
Diadiaschisma scale 2048/2025 67108864/66430125
12
!
135/128
18225/16384
1215/1024
512/405
4/3
45/32
3/2
405/256
54675/32768
16/9
256/135
2

! diadiaschis2.scl
Diadiaschisma scale 2048/2025 67108864/66430125
12
!
135/128
9/8
1215/1024
512/405
4/3
64/45
3/2
405/256
54675/32768
32768/18225
256/135
2

From: Paul Erlich (2004-01-11)
Subject: Re: The Two Diadiaschisma Scales

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> 
wrote:
> These are based on the diaschisma and the diaschisma-schisma (check 
> Manuel's list if you don't believe me) of 67108864/66430125.

That's diaschisma *minus* schisma.

I've been seeing to on all the latest charts. Note its appearance as 
the "misty" comma here, connecting 12, (51,) 63, 75, and the 
excellent 87 and 99:

http://tonalsoft.com/enc/eqtemp.htm


> Scala 
> tells me the scale closest to diadiaschis1 in my scale archives is
> bp12_17 "12-tET approximation with minimal order 17 beats". For 
> closest to diadiaschis2 I find that it is, according to Scala, 
> exactly equidistant from duoden12 "Almost equal 12-tone subset of 
> Duodenarium".

The duodenarium is a huge Euler genus in the 5-limit lattice, with 
over 100 notes, I believe.

From: Gene Ward Smith (2004-01-12)
Subject: Re: The Two Diadiaschisma Scales

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

> I've been seeing to on all the latest charts. Note its appearance 
as 
> the "misty" comma here, connecting 12, (51,) 63, 75, and the 
> excellent 87 and 99:

"Misty" is certainly less clumbersome than diaschisma-schisma. I 
think I'll call these the Diamisty scales.