Some chords in 31tet.

There appear to be seventeen 3-note chords in 31tet which might have
theoretical legitimacy. They are grouped into five families. Family one
triads are: 0-271-619, 0-310-619 and 0-348-619. Family two triads are:
0-271-658, 0-310-658, 0-348-658 and 0-387-658. Family three triads are:
0-271-697, 0-310-697, 0-348-697, 0-387-697 and 0-426-697. Family four
triads are: 0-310-735, 0-348-735, 0-387-735 and 0-426-735. Family five
triad is 0-387-774.

off hand it seems like there should be at least 38.
if you take the combinations of 3 out of 6 of
1-3-5-7-9-11 you get 20.
then you have the subharmonics of these
but 1-3-9 and the 1-5-9 are the same in both directions = 38
I know i am missing probably some other matches
but then there is the question of the 15 as in 9-11-15 etc.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

robert thomas martin wrote:
>
> There appear to be seventeen 3-note chords in 31tet which might have
> theoretical legitimacy. They are grouped into five families. Family one
> triads are: 0-271-619, 0-310-619 and 0-348-619. Family two triads are:
> 0-271-658, 0-310-658, 0-348-658 and 0-387-658. Family three triads are:
> 0-271-697, 0-310-697, 0-348-697, 0-387-697 and 0-426-697. Family four
> triads are: 0-310-735, 0-348-735, 0-387-735 and 0-426-735. Family five
> triad is 0-387-774.
>
>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> off hand it seems like there should be at least 38.
> if you take the combinations of 3 out of 6 of
> 1-3-5-7-9-11 you get 20.
> then you have the subharmonics of these
> but 1-3-9 and the 1-5-9 are the same in both directions = 38
> I know i am missing probably some other matches
> but then there is the question of the 15 as in 9-11-15 etc.
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria
<http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> robert thomas martin wrote:
> >
> > There appear to be seventeen 3-note chords in 31tet which might
have
> > theoretical legitimacy. They are grouped into five families.
Family one
> > triads are: 0-271-619, 0-310-619 and 0-348-619. Family two triads
are:
> > 0-271-658, 0-310-658, 0-348-658 and 0-387-658. Family three
triads are:
> > 0-271-697, 0-310-697, 0-348-697, 0-387-697 and 0-426-697. Family
four
> > triads are: 0-310-735, 0-348-735, 0-387-735 and 0-426-735. Family
five
> > triad is 0-387-774.
> >
> > I only listed the triads which can be substituted into I-IV-V
situations to produce heptatonic scales. I didn't include 232 and
465cents because they seem to function as a 2nd and a 4th
respectively. Some of the other mathematical possibilities overlap
when applied to a I-IV-V situation.
>