A sensi-based notation

As long as we are on the topic of 46-et notation, let me stick my oar
in. Suppose we take 11 nominals, say ABCDEFGHIJK. Let # represent 25/24,
11 sensi generators up (3 steps of 46-et.) Then a diminished seventh
chord could be written A-C-E-G, a major tetrad A-C-Eb-G, and a minor
tetrad A-C#-E-G, which seems like an excellent starting point.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> As long as we are on the topic of 46-et notation, let me stick my oar
> in. Suppose we take 11 nominals, say ABCDEFGHIJK. Let # represent 25/24,
> 11 sensi generators up (3 steps of 46-et.) Then a diminished seventh
> chord could be written A-C-E-G, a major tetrad A-C-Eb-G, and a minor
> tetrad A-C#-E-G, which seems like an excellent starting point.

I suppose though that people would be happier with the nominals the
other way around, where AC, BD etc are minor thirds. Then the major
tetrad is A-Cb-E-G, and the minor tetrad A-C-E#-G.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> As long as we are on the topic of 46-et notation, let me stick my oar
> in. Suppose we take 11 nominals, say ABCDEFGHIJK. Let # represent
25/24,
> 11 sensi generators up (3 steps of 46-et.) Then a diminished seventh
> chord could be written A-C-E-G, a major tetrad A-C-Eb-G, and a minor
> tetrad A-C#-E-G, which seems like an excellent starting point.

I don't get it. How do you come up with these spellings? A major tetrad
has the same bottom interval as a diminished seventh tetrad but a minor
tetrad doesn't??

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> >
> > As long as we are on the topic of 46-et notation, let me stick my
oar
> > in. Suppose we take 11 nominals, say ABCDEFGHIJK. Let # represent
25/24,
> > 11 sensi generators up (3 steps of 46-et.) Then a diminished seventh
> > chord could be written A-C-E-G, a major tetrad A-C-Eb-G, and a minor
> > tetrad A-C#-E-G, which seems like an excellent starting point.
>
> I suppose though that people would be happier with the nominals the
> other way around, where AC, BD etc are minor thirds. Then the major
> tetrad is A-Cb-E-G, and the minor tetrad A-C-E#-G.

Still doesn't make sense to me. Are you inverting the chords in some
way?

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus" <perlich@a...>
wrote:

> I don't get it. How do you come up with these spellings? A major tetrad
> has the same bottom interval as a diminished seventh tetrad but a minor
> tetrad doesn't??

I start from a diminished seventh chord, and chromatically adjust,
making no assumption the root is at the bottom.

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus" <perlich@a...>
wrote:

> Still doesn't make sense to me. Are you inverting the chords in some
> way?

Yes; I start with a chain of 6/5 intervals as my chord, and modify it
chromatically to get major and minor tetrads.