12 of 23-tet

My attraction theoretically to 23-tet would be its relative lack of good
approximations to the 7-limit harmonics. (it does have a good 6/5
though)...So it would be good for noise-based music with inharmonic partials,
I think.

2 questions:

1) What would be a good approach to this (12 of 23)? I'm thinking in terms of
a quasi-symmetrical 'mode' of 23, using 12 notes so a standard keyboard could
play it.

One idea would be this mode:

step sizes: 1 2 3 1 2 3 1 2 3 1 3 1
result: 0 1 3 6 7 9 12 13 15 18 19 22 23

Can anyone see any other logical approach to a quasi-symmetrical layout for 12
of 23-tet?

2) Has anyone used, or does anyone know of example works in 23-tet? Darreg
refers to it as 'strange', but points out that it is rarely used.

Best,
--
Aaron Krister Johnson
http://www.akjmusic.com
http://www.dividebypi.com

Aaron K. Johnson wrote:
> My attraction theoretically to 23-tet would be its relative lack of good > approximations to the 7-limit harmonics. (it does have a good 6/5 > though)...So it would be good for noise-based music with inharmonic partials, > I think.
> > 2 questions:
> > 1) What would be a good approach to this (12 of 23)? I'm thinking in terms of > a quasi-symmetrical 'mode' of 23, using 12 notes so a standard keyboard could > play it.
> > One idea would be this mode:
> > step sizes: 1 2 3 1 2 3 1 2 3 1 3 1
> result: 0 1 3 6 7 9 12 13 15 18 19 22 23
> > Can anyone see any other logical approach to a quasi-symmetrical layout for 12 > of 23-tet?

You could use every other note of 23, resulting in 1 small step and 11 large steps (122222222222). Or along the same lines as your 123123123131 scale, you could use subsets with different numbers of 1-step, 2-step, and 3 step intervals (122232221222, 122321223212). The last of these scales is a subset of superpelog (see below).

> 2) Has anyone used, or does anyone know of example works in 23-tet? Darreg > refers to it as 'strange', but points out that it is rarely used.
> > Best,

Not specifically 23-tet, but I've used a 14-note scale that I call "superpelog", which can be tuned as a subset of 23-ET. The scale is produced by repeating a generator of approximately 261 cents, which is close to 5 steps of 23-ET.

generators 0 5 10 1 6 11 2 7 12 3 8 13 4 9 0
degree of 23-ET 0 2 4 5 7 9 10 12 14 15 17 19 20 22 23

I call it "superpelog" because it has a number of pelog-sounding modes, two of which are similar to scales from the Scala archive that are attributed to (Erich) von Hornbostel: pelog_pa.scl and pelog_pb.scl. Easley Blackwood's 23-tet etude (from his _Twelve Microtonal Etudes for Electronic Music Media_, Op. 28) also takes advantage of the pelog modes of 23-et.

I have two MIDI samples of music in superpelog tuning: one is a retuning of a piece that I originally wrote in 14-ET: "This Way to the Egress".

http://www.io.com/~hmiller/midi/egress-superpelog.mid

I also have an unfinished excerpt that I wrote specifically for this tuning. Each instrument is playing notes from a different overlapping subset of the tuning, so no single instrument plays all 14 notes. You might want to consider using 12-note modes of 23-tet in a similar way.

http://www.io.com/~hmiller/music/ex/mahali.mid

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...> wrote:
> 1) What would be a good approach to this (12 of 23)? I'm thinking in terms of
> a quasi-symmetrical 'mode' of 23, using 12 notes so a standard keyboard could
> play it.

Check out Herman Miller's <www.io.com/~hmiller/music/superpelog.html>. A chain of
260-cent super-seconds or sub-thirds or... The whole thing requires 14 notes, but since
it's a linearly generated sequence of notes you can just take the first 12:

2 3 2 1 2 2 1 2 2 1 2 1 3

or some such mode. With this you can get these nice 5-note modes that sound remotely
Indonesian. Herman mentions a couple.

> 2) Has anyone used, or does anyone know of example works in 23-tet? Darreg
> refers to it as 'strange', but points out that it is rarely used.

Wouldn't you know it but just yesterday I got to hear Easley Blackwood's Microtonal
Compositions. And he says the 23-tone movement uses modes similar to slendro and
pelog scales, modulated through a few keys. The first one I hear is not mentioned by
Herman, though: 7 3 3 7 3.