The 7-limit tetrads of Blackjack

15/14, an approximate secor, translates to [0 0 2] in terms of the cubic
lattice representation. In the place of a chain of secors, we can regard
the chords of Blackjack as a chain of [0 0 1] generators, two of which
make up a 15/14 modulation up. The 7-limit commas of the 72-et are

225/224 [1 1 4]
1029/1024 [3 4 1]
4375/4374 [5 -6 -3]

and redundently but importantly,

2401/2400 [2 3 -3]

Our chain of [0 0 1] generators gives us this:

[0 1 -2] ~ [-2 -2 1] (2401/2400)
[-2 -2 0]
[-2 -2 -1] ~ [-1 -1 3] (225/224)
[-1 -1 2]
[-1 -1 1]
[-1 -1 0]
[-1 -1 -1]
[-1 -1 -2] ~ [0 0 2] (225/224)
[0 0 1]
[0 0 0]
[0 0 -1]
[0 0 -2]
[0 0 -3]
[1 1 0] ~ [0 0 -4] (225/224)
[1 1 -1]
[-1 -2 1] ~ [1 1 -2] (2401/2400)

--- In tuning-math@y..., Gene W Smith <genewardsmith@j...> wrote:
> 15/14, an approximate secor, translates to [0 0 2] in terms of the
cubic
> lattice representation. In the place of a chain of secors, we can
regard
> the chords of Blackjack as a chain of [0 0 1] generators, two of
which
> make up a 15/14 modulation up. The 7-limit commas of the 72-et are
>
> 225/224 [1 1 4]
> 1029/1024 [3 4 1]
> 4375/4374 [5 -6 -3]
>
> and redundently but importantly,
>
> 2401/2400 [2 3 -3]
>
> Our chain of [0 0 1] generators gives us this:
>
> [0 1 -2] ~ [-2 -2 1] (2401/2400)
> [-2 -2 0]
> [-2 -2 -1] ~ [-1 -1 3] (225/224)
> [-1 -1 2]
> [-1 -1 1]
> [-1 -1 0]
> [-1 -1 -1]
> [-1 -1 -2] ~ [0 0 2] (225/224)
> [0 0 1]
> [0 0 0]
> [0 0 -1]
> [0 0 -2]
> [0 0 -3]
> [1 1 0] ~ [0 0 -4] (225/224)
> [1 1 -1]
> [-1 -2 1] ~ [1 1 -2] (2401/2400)

Hi Gene,

this is probably fascinating stuff, but I can make neither head nor
tail of it. As I think I've said before, more headings on tables, more
diagrams and more textual explanations are always a good idea. I
assume your intention is to actually be understood, as opposed to say
merely posting to list as a way of recording your ideas.

Regards,
-- Dave Keenan

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> this is probably fascinating stuff, but I can make neither head nor
> tail of it.

Did you read the articles previous to this, where I explain (I hope) this representation of 7-limit chords in terms of a cubic lattice; that is, vectors [a b c] where a, b and c are integers?

Anyone else following this, or am I talking to myself? What needs explaining? I don't have the software to draw diagrams, I'm afraid.