A 72-et decatonic

There were 66 scales of this type, but one was something of a standout, so I'll give just it:

[0, 5, 14, 19, 28, 33, 42, 49, 58, 63]
[5, 9, 5, 9, 5, 9, 7, 9, 5, 9]
edges 11 24 34 connectivity 0 4 6

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> There were 66 scales of this type, but one was something of a
standout, so I'll give just it:
>
> [0, 5, 14, 19, 28, 33, 42, 49, 58, 63]
> [5, 9, 5, 9, 5, 9, 7, 9, 5, 9]
> edges 11 24 34 connectivity 0 4 6

Are you now taking into account _all_ the consonances of 72-tET?

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > There were 66 scales of this type, but one was something of a
> standout, so I'll give just it:
> >
> > [0, 5, 14, 19, 28, 33, 42, 49, 58, 63]
> > [5, 9, 5, 9, 5, 9, 7, 9, 5, 9]
> > edges 11 24 34 connectivity 0 4 6
>
> Are you now taking into account _all_ the consonances of 72-tET?

I'm doing the same thing as before--looking at the 5, 7, and 11-limits. I don't know what you mean by "all the consonances", but if you define this by means of a particular list of intervals which you think amount to that, this could be done.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...>
wrote:
> > > There were 66 scales of this type, but one was something of a
> > standout, so I'll give just it:
> > >
> > > [0, 5, 14, 19, 28, 33, 42, 49, 58, 63]
> > > [5, 9, 5, 9, 5, 9, 7, 9, 5, 9]
> > > edges 11 24 34 connectivity 0 4 6
> >
> > Are you now taking into account _all_ the consonances of 72-tET?
>
> I'm doing the same thing as before--looking at the 5, 7, and 11-
>limits. I don't know what you mean by "all the consonances", but if
>you define this by means of a particular list of intervals which you
>think amount to that, this could be done.

If you were already doing that all along, what did it mean when you
said you were only taking one particular comma into account? I though
it meant you were treating some of the consonant 72-tET intervals as
dissonances, since they would be broken if not _all_ the members of a
complete defining basis of commas of 72-tET were being tempered out.

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:

> If you were already doing that all along, what did it mean when you
> said you were only taking one particular comma into account?

In the 7-limit, four vals which make a unimodular matrix, and all of which are positive, can be considered to define the step sizes and multiplicities of an RI scale. If I take three vals instead, all of which have a certain comma in the kernel, and such that the 72-et val or whatever et I am looking at is an integer combination with positive coefficients of these vals, I get intervals which I can use to construct 72-et scales. I could also use one or two 11-limit vals, two 7-limit vals (a linear temperament), and so forth.

In general, I might simply take any partition of 72 and its dual, and look at all permutations. In practice this is far too much to deal, and I am trying to look at things which would tend to take advantage of the 72-et commas.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
>
> > If you were already doing that all along, what did it mean when
you
> > said you were only taking one particular comma into account?
>
> In the 7-limit, four vals which make a unimodular matrix, and all
of which are positive, can be considered to define the step sizes and
multiplicities of an RI scale. If I take three vals instead, all of
which have a certain comma in the kernel, and such that the 72-et val
or whatever et I am looking at is an integer combination with
positive coefficients of these vals, I get intervals which I can use
to construct 72-et scales. I could also use one or two 11-limit vals,
two 7-limit vals (a linear temperament), and so forth.
>
> In general, I might simply take any partition of 72 and its dual,
and look at all permutations. In practice this is far too much to
deal, and I am trying to look at things which would tend to take
advantage of the 72-et commas.

So were you taking all 72-tET consonances into account all along, and
simply using certain generators?

I'm unclear . . . why don't we go over this process in 12-tone,
starting from the beginning . . . or better yet, focus on our linear
temperament paper first. I'd really like to work the "heuristic" into
it.