It's the "thirds", stupid!

I'm currently looking for 3DE scales such that one interval class has three different simple consonances, mimicking the 6/5's and 5/4's of meantone, but now in three different flavors rather than two.

Here are two finds featuring {7/6, 6/5, 5/4} as the "thirds" (archytas7 is also in this category):

! zeus7.scl
!
A distributionally even scale in zeus temperament, aabacab
7
!
157.111
388.032
545.143
702.254
933.175
1090.286
1200.172

! portent11.scl
!
A distributionally even scale in portent temperament, abababababc
11
!
151.534
233.784
385.318
467.568
619.102
701.352
852.886
935.136
966.707
1118.241
1200.491

Keenan

More scales with all-consonance interval classes:

Does the 686/675 planar temperament
http://x31eq.com/cgi-bin/rt.cgi?ets=27_19_10&limit=7
have a name? I've been calling "sengic" but Mike said he hated that name for some reason. It has a good 13-limit extension too:
http://x31eq.com/cgi-bin/rt.cgi?ets=8d_9_19p&limit=2.3.5.7.13
(no 11)

Anyway it has quite a few good scales, for example this one in which "thirds" are {7/6,16/13,9/7} and "fourths" are {5/4,4/3,7/5}:

! sengic7.scl
!
A distributionally even scale in sengic temperament
7
!
237.096
366.622
496.148
811.775
941.301
1070.827
1200.353

This one, in which "thirds" are {7/6,6/5,16/13} and "fourths" are {5/4,9/7,4/3}:

! sengic8.scl
!
A distributionally even scale in sengic temperament
8
!
237.096
366.622
496.148
625.674
811.775
941.301
1070.827
1200.353

And this one, in which "thirds" are {8/7,7/6,6/5}, "fourths" are {16/13,5/4,9/7}, and "fifths" are mostly 4/3 and 7/5 (with one wolfy 518-cent interval thrown in):

! sengic9.scl
!
A distributionally even scale in sengic temperament
9
!
129.526
259.052
388.578
518.104
704.205
833.731
963.257
1092.783
1200.353

Consonances everywhere in sight!

We also have some scales in zeus:

! zeus7a.scl
!
A distributionally even scale in zeus temperament
7
!
157.111
314.222
471.333
702.254
859.365
1016.476
1200.172

! zeus7b.scl
!
A distributionally even scale in zeus temperament
7
!
157.111
314.222
471.333
812.14
969.251
1126.362
1200.172

which can be merged into an 8-note scale:

! zeus8.scl
!
A distributionally even scale in zeus temperament
8
!
157.111
314.222
471.333
655.029
812.14
969.251
1126.362
1200.172

Keenan

--- In tuning-math@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> More scales with all-consonance interval classes:
>
> Does the 686/675 planar temperament
> http://x31eq.com/cgi-bin/rt.cgi?ets=27_19_10&limit=7
> have a name? I've been calling "sengic" but Mike said he hated that name for some reason.

Is there some reason other than Mike's dislike to change this page?

http://xenharmonic.wikispaces.com/Sengic+family

On Sat, Aug 6, 2011 at 12:13 AM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
> >
> > More scales with all-consonance interval classes:
> >
> > Does the 686/675 planar temperament
> > http://x31eq.com/cgi-bin/rt.cgi?ets=27_19_10&limit=7
> > have a name? I've been calling "sengic" but Mike said he hated that name for some reason.
>
> Is there some reason other than Mike's dislike to change this page?
>
> http://xenharmonic.wikispaces.com/Sengic+family

It's a fine name. Keenan asked how to pronounce it, and I didn't see
any immediate answer pop out, so I said that sengic was a bad
temperament and 686/675 was a bad comma too, and that we should never
speak of it again. Just a little bit of humor that got tempered out by
the unfortunate medium of email.

-Mike