Mailing list post
From: Gene Ward Smith (2003-07-04)
Subject: Ratwolf
This is not exactly another of my circulating temperaments; instead,
it is a version of meantone which tries its hardest to circulate. It
does that by having good thirds and by attempting to tame the wolf by
making it exactly 20/13, which is a 13-limit consonance. The name
comes from "rational wolf".
Here is the triad breakdown. We have eight 5/4s, 2.96 cents flat, and
four 9/7s, 1.76 cents flat. We likewise have eight 6/5s, 3.15 cents
flat, and four 7/6s, 4.33 cents flat. The thirds in this vicinity of
meantone rock. We also of course have eleven meantone fifths, 6.12
cents flat, and a pure 20/13.
1 [433.2989450, 262.5386859, 695.8376309]
2 [383.3505284, 312.4871041, 695.8376325]
3 [383.3505268, 312.4871042, 695.8376310]
4 [383.3505264, 312.4871053, 695.8376317]
5 [383.3505267, 312.4871045, 695.8376312]
6 [433.2989446, 262.5386878, 695.8376324]
7 [383.3505282, 312.4871030, 695.8376312]
8 [433.2989453, 312.4871050, 745.7860503]
9 [383.3505283, 312.4871045, 695.8376328]
10 [383.3505270, 312.4871058, 695.8376328]
11 [433.2989450, 262.5386864, 695.8376314]
12 [383.3505283, 312.4871035, 695.8376318]
! ratwolf.scl
!
Eleven fifths of (418/5)^(1/11) and one 20/13 wolf
12
!
70.863424
191.675263
312.487105
383.350528
504.162369
575.025791
695.837632
766.701055
887.512896
1008.324736
1079.188160
1200.000000
Listen to them--the children of the night. What music they make!
Full thread (3 messages)
From: Gene Ward Smith (2003-07-04)
Subject: Ratwolf
This is not exactly another of my circulating temperaments; instead,
it is a version of meantone which tries its hardest to circulate. It
does that by having good thirds and by attempting to tame the wolf by
making it exactly 20/13, which is a 13-limit consonance. The name
comes from "rational wolf".
Here is the triad breakdown. We have eight 5/4s, 2.96 cents flat, and
four 9/7s, 1.76 cents flat. We likewise have eight 6/5s, 3.15 cents
flat, and four 7/6s, 4.33 cents flat. The thirds in this vicinity of
meantone rock. We also of course have eleven meantone fifths, 6.12
cents flat, and a pure 20/13.
1 [433.2989450, 262.5386859, 695.8376309]
2 [383.3505284, 312.4871041, 695.8376325]
3 [383.3505268, 312.4871042, 695.8376310]
4 [383.3505264, 312.4871053, 695.8376317]
5 [383.3505267, 312.4871045, 695.8376312]
6 [433.2989446, 262.5386878, 695.8376324]
7 [383.3505282, 312.4871030, 695.8376312]
8 [433.2989453, 312.4871050, 745.7860503]
9 [383.3505283, 312.4871045, 695.8376328]
10 [383.3505270, 312.4871058, 695.8376328]
11 [433.2989450, 262.5386864, 695.8376314]
12 [383.3505283, 312.4871035, 695.8376318]
! ratwolf.scl
!
Eleven fifths of (418/5)^(1/11) and one 20/13 wolf
12
!
70.863424
191.675263
312.487105
383.350528
504.162369
575.025791
695.837632
766.701055
887.512896
1008.324736
1079.188160
1200.000000
Listen to them--the children of the night. What music they make!
From: Carl Lumma (2003-07-04)
Subject: Re: [tuning] Ratwolf
>tame the wolf by making it exactly 20/13, which is a 13-limit
>consonance.
You say that based on your experience listening to it?
-Carl
From: Gene Ward Smith (2003-07-04)
Subject: Re: Ratwolf
--- In [email protected], Carl Lumma <ekin@l...> wrote:
> >tame the wolf by making it exactly 20/13, which is a 13-limit
> >consonance.
>
> You say that based on your experience listening to it?
No. I did a bit of Neilsen's 4th, and in honor of the 4th of July I
am at this very moment in the process of rendering Stars and Stripes
Forever; however it's too soon for me to draw conclusions. I make the
claim purely definitionally; by the definition I use of "p-limit
consonance", 20/13 is a 13-limit consonance.