A 1029/1024 (385/384) planar temperament scale

I suggested my data on bases for planar temperaments could help locate scales, and I tried it out on the 1029/1024 planar temperament, which extends to the closely related 11-limit planar temperament tempering out 385/384 and 441/440. If we take two chains
of four 8/7s separated by a 35/32, we get in the 72-et version
a 9595959597 pattern, or the scale [0,9,14,23,28,37,42,51,56,65]. This
has the following number of consonant intervals and triads at these odd limits:

7: 24, 16
9: 24, 16
11: 34, 46

Since I don't keep very good track of scales, I wonder if Carl or Paul can tell us if they've seen this one before?

>we get in the 72-et version a 9595959597 pattern, or the scale
>[0,9,14,23,28,37,42,51,56,65]. This has the following number of
>consonant intervals and triads at these odd limits:
>
>7: 24, 16
>9: 24, 16
>11: 34, 46
>
>Since I don't keep very good track of scales, I wonder if Carl or
>Paul can tell us if they've seen this one before?

That's a mode of this scale:

10-tone scale, e=24 c=4, in 72-tET
(0 5 14 19 28 33 42 49 58 63)

Connectivity seems so good, I'm not sure why we're not using it
more often.

Gene, can we get _tetrads_ for 7 and greater limits from now on?
Triadic music is such a bore.

-Carl

>>we get in the 72-et version a 9595959597 pattern, or the scale
>>[0,9,14,23,28,37,42,51,56,65]. This has the following number of
>>consonant intervals and triads at these odd limits:
/.../
>>Since I don't keep very good track of scales, I wonder if Carl or
>>Paul can tell us if they've seen this one before?
>
>That's a mode of this scale:
>
>10-tone scale, e=24 c=4, in 72-tET
>(0 5 14 19 28 33 42 49 58 63)

I actually asked about this only two days ago...

>What's this:
>
>10-tone scale, e=24 c=4, in 72-tET
>(0 5 14 19 28 33 42 49 58 63 72)

...how's that for coincidences?

-Carl

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> Gene, can we get _tetrads_ for 7 and greater limits from now on?
> Triadic music is such a bore.

I'd have to write some code, and the counting operation would take some time. Triads are much easier since they can be computed using the characteristic polynomial of the graph.

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> That's a mode of this scale:
>
> 10-tone scale, e=24 c=4, in 72-tET
> (0 5 14 19 28 33 42 49 58 63)
>
> Connectivity seems so good, I'm not sure why we're not using it
> more often.

It's also h10-epimorphic. This is clearly an important scale, and needs a name. Does Joe know about it?

>>Gene, can we get _tetrads_ for 7 and greater limits from now on?
>>Triadic music is such a bore.
>
>I'd have to write some code, and the counting operation would take some
>time. Triads are much easier since they can be computed using the
>characteristic polynomial of the graph.

Eh? The biggest scales I'm interested in at the moment have 10 notes.
That means at most 210 tetrads to test.

-Carl

>>10-tone scale, e=24 c=4, in 72-tET
>>(0 5 14 19 28 33 42 49 58 63)
>>
>>Connectivity seems so good, I'm not sure why we're not using it
>>more often.
>
>It's also h10-epimorphic. This is clearly an important scale, and needs
>a name.

You've discovered it twice now, so the ball is clearly in your court.
I have it as sa118.

Does this address why we haven't just been using connectivity? Do
you have code which searches for high c, or just code that measures c?

-Carl

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> Does this address why we haven't just been using connectivity? Do
> you have code which searches for high c, or just code that measures c?

Maple will measure c, but it also will find intervals and triads even more quickly using the characteristic polynomial. The latter seemed to me more relevant, so I quit showing c--do you think I should reintroduce it?

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> You've discovered it twice now, so the ball is clearly in your court.
> I have it as sa118.

How about gamelion?

>>Does this address why we haven't just been using connectivity? Do
>>you have code which searches for high c, or just code that measures c?
>
>Maple will measure c, but it also will find intervals and triads even more
>quickly using the characteristic polynomial. The latter seemed to me more
>relevant, so I quit showing c--do you think I should reintroduce it?

I don't know... why don't we keep our eye on it for a while. (that's a
yes).

-Carl

>> You've discovered it twice now, so the ball is clearly in your court.
>> I have it as sa118.
>
>How about gamelion?

Good one!

-Carl