the harmonic series segment test

>I can't find anything else promising by this method. 6:7:8 works with
>the classic pentatonic. 7:11 is only an even number of steps in
>3-equal, below 43-equal. 5:7 gives a 9 from 11 scale, but it's nearly
>50 cents from 5:6:7 with the optimal tuning. The ideal defining chord
>is large and simple enough to be comprehensible, and has internal
>intervals close enough to be the same diatonic class, but also
>different enough to have a good approximation in the chromatic.

Let's run 8:9:10:11:12:14 through my list.
http://lumma.org/gd.txt

1. yes

2. yes; 5 < 6 < 10

3. 0.36 according to Scala 1.8; diatonic scale in 12-et is 0.77
This is failing.

4. R. stability 0.87 by Scala 1.8; diatonic scale in 12 is 0.95.
This passes.

5. Fails.

6. Passes.

7. Fails.

8. Passes.

The scale has merit, but without 3 and 5 fails to be diatonic.
Since the vast majority of subsets of this scale very strongly
invoke the same root, modality can't happen. I didn't look for
this specifically, but 3 & 5 caught it, as they always will.

6:7:8:9:10:11:12, another scale with merit, should fail in a
similar way.

-Carl

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

> Let's run 8:9:10:11:12:14 through my list.
> http://lumma.org/gd.txt

[snip]

> 6:7:8:9:10:11:12, another scale with merit, should fail in a
> similar way.

isn't that the same scale, just a different mode?

btw, to hear some wonderful music in this scale, ask prent rodgers
for a copy of his cd. he actually uses the entire tonality diamond,
but at any given point in time, the scale is usually this one.

>>6:7:8:9:10:11:12, another scale with merit, should fail in a
>>similar way.
>
>isn't that the same scale, just a different mode?

Um, yes. :)

>btw, to hear some wonderful music in this scale, ask prent rodgers
>for a copy of his cd. he actually uses the entire tonality diamond,
>but at any given point in time, the scale is usually this one.

I've got Prent's cd, and have long held his music as an example of
the workability of series segment scales. Also: Jules Siegel, which
I believe you have samples of.

-Carl

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
> 3. 0.36 according to Scala 1.8; diatonic scale in 12-et is 0.77
> This is failing.
>
> 4. R. stability 0.87 by Scala 1.8; diatonic scale in 12 is 0.95.
> This passes.

How do you get Scala to compute these?

>> 3. 0.36 according to Scala 1.8; diatonic scale in 12-et is 0.77
>> This is failing.
>>
>> 4. R. stability 0.87 by Scala 1.8; diatonic scale in 12 is 0.95.
>> This passes.
>
>How do you get Scala to compute these?

show data

-Ca.