5-limit note groups

Inspired by Harold Fortiun's group generated by the thirds {7/6, 6/5,
11/9, 5/4, 9/7} I thought it would be interesting to look at note
groups generated by sets of p-limit consonances in the range 1 <
interval <= 2.
Obviously the place to start is with the 5-limit, and since groups
generated by one consonance are obvious to classify, with two or more
generators. Here they are in the 5-limit:

Two generator groups

Octave containing subgroups:
[2, 3] (Pythagorean), [2, 5] (no threes), [2, 5/3]

Nonoctave subgroups: [5/4, 3/2], [3/2, 5/2], [3/2, 8/5], [6/5, 4/3],
[4/3, 5/3], [5/3, 8/3]

Three generator groups: [2, 3, 5] (the 5-limit), [4, 6, 10]

In terms of nonoctave groups, has anyone ever considered [4, 6, 10]?
If we can make a big deal out of tritave equivalence, why not
two-octave equivalence?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@c...> wrote:
>
> Inspired by Harold Fortiun's group generated by the thirds {7/6,
6/5,
> 11/9, 5/4, 9/7} I thought it would be interesting to look at note
> groups generated by sets of p-limit consonances in the range 1 <
> interval <= 2.
> Obviously the place to start is with the 5-limit, and since groups
> generated by one consonance are obvious to classify, with two or
more
> generators. Here they are in the 5-limit:
>
> Two generator groups
>
> Octave containing subgroups:
> [2, 3] (Pythagorean), [2, 5] (no threes), [2, 5/3]
>
> Nonoctave subgroups: [5/4, 3/2], [3/2, 5/2], [3/2, 8/5], [6/5, 4/3],
> [4/3, 5/3], [5/3, 8/3]
>
> Three generator groups: [2, 3, 5] (the 5-limit), [4, 6, 10]
>
> In terms of nonoctave groups, has anyone ever considered [4, 6, 10]?
> If we can make a big deal out of tritave equivalence, why not
> two-octave equivalence?

I've met Dr. Harold Fortuin. He invented the "Clavette", a microtonal
keyboard (it uses hexagons over buttons and can be programmed for
different ETs). I think he might be really interested in this and the
tuning newsgroup. Does anyone know his email?