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.