Fwd: Re: [tuning-math] Combinatorics and Tuning Systems?

I certainly wouldn't try to convince you that
pentachords are not included in hexachords which
are in turn included in heptachords ("septachords").

I don't think we are in any disagreement on that point.

I just think that heptachord inclusion is probably the
least interesting thing about relations between
pentachords and heptachords.

Good luck with 24tet.

I've also yet to see much pc set theory for
19tet, which I suspect would interest a few people
other than me.

If you have the technology, I would encourage
you to look into it a bit.

---- Original message ----
>Date: Fri, 20 Sep 2002 11:11:48 -0500
>From: paul.hjelmstad@us.ing.com
>Subject: Re: [tuning-math] Combinatorics and Tuning
Systems?
>To: tuning-math@yahoogroups.com
>
>
>Interesting. But I disagree with part of this: Actually,
most pentachords
>in 12tET fit into septachords, through regular hexachords.
There are 2 that
>fit in by means of Z-related hexachords, and one
(0,1,3,5,6) does not fit
>in to its septachord complement by means of ANY hexachord.
This is Allen
>Forte's "weakly related 7-5 set complexes (complices?)"
Unless you were
>talking about something else when you stated "7-12 does not
include any
>forms of 5-12"
>
>It is true that the study of hexachords in 12tET is pretty
exhausted, but I
>am also interested in C{24,6} for example.Created a program
(my brother
>wrote it actually) to count sets based on their interval
vectors. Counting
>interval vectors in 12tET for diads through hexachords
gives 6, 12, 28, 35,
>35. (Before reducing for Forte's Z-relation you get
6,12,29,38,50 Tn/TnI
>types). So I feel something is going on here, which I have
extended to
>16tET, 19tET, and (am working on) 24tET. If anything, there
are some
>amazing patterns in the behaviour of the Z-relations (in
16tET and 19tET
>for example.) Once I run sets in 24tET for diads through
dodecads(?) I
>will post the results. Hope to find a beautiful pattern!
>
>

--- In tuning-math@y..., <Josh@o...> wrote:

> I've also yet to see much pc set theory for
> 19tet, which I suspect would interest a few people
> other than me.

There was a discussion of difference sets in relation to the 19-et
here recently.

Thanks. I'll check the archives.

---- Original message ----
>Date: Sat, 21 Sep 2002 11:30:50 -0000
>From: "Gene Ward Smith" <genewardsmith@juno.com>

>There was a discussion of difference sets in relation to
the 19-et
>here recently.