Re: more on composing in X tuning (was: Good 5-limit scale generators (was Ls scales, LMs ...))

Paul H. Erlich wrote:

>Dave Keenan wrote,
>
>>Anyone recognise it? It is Lssssss
>>where L=4 steps and s=3 steps of 22-tET.
>
>That was one of the three scales used in the "Improvisation" I did with Ara
>Sarkissian at the last Microthon. The mode we used was sssLsss, with its
>tetrachordal structure.

Makes sense. I didn't mean to imply a particular mode above.

>In rehearsal, Ara found this mode on the keyboard
>and stuck with it, citing its similarity to music of some particular locale
>in the Middle East (I forget which). Just shows you that nothing beats
>having all 22 (or X) notes at your fingertips.

I thought that if anyone had found it, you would have.

>>I guess that melodically, 4 steps
>>isn't really different enough from 3 steps.
>
>What do you mean???

Just displaying my ignorance and hoping someone like you would fill me in.
I guess you are saying that it is quite obvious.

>Have you tried it?

No.

>>It only has 2 major and 2 minor
>>triads.
>
>Yeah -- a really good amount for a 7-tone scale!

I assume you're being facetious. But in fact I'm suggesting that the _only_
7-tone scales that have _more_ complete 5-limit triads than this one (with
errors not worse than 12-tET) are diatonic. Do you know of any
counter-example?

Regards,
-- Dave Keenan
http://dkeenan.com

Dave Keenan wrote,

> >>It only has 2 major and 2 minor
> >>triads.
> >
> >Yeah -- a really good amount for a 7-tone scale!
>
> I assume you're being facetious. But in fact I'm suggesting that the
> _only_
> 7-tone scales that have _more_ complete 5-limit triads than this one
> (with
> errors not worse than 12-tET) are diatonic. Do you know of any
> counter-example?

More than 4 5-limit triads in a 7 note scale? I most certainly do!

A-----E
/ \ / \
/ \ / \
F-----C-----G
\ / \ /
\ / \ /
Ab----Eb

I worked all this stuff out a while back, and wrote it up at:

<http://x31eq.com/genera.htm>

I notice a misteak there, in that not all the scales I say have >4 triads
really do. But I don't see much point in correcting it after all this
time :)

Graham

--- In tuning@egroups.com, David C Keenan
<D.KEENAN@U...> wrote:

> >>It only has 2 major and 2 minor
> >>triads.
> >
> >Yeah -- a really good amount for a 7-tone scale!
>
> I assume you're being facetious.

No, I'm being serious! 4 triads in 7 notes --
that's a good ratio! And in the Lssssss mode,
you can make the tonic major triad into a
4:5:6:9:11!

--- In tuning@egroups.com, graham@m...
wrote:
> Dave Keenan wrote,
> > But in fact I'm suggesting that the
> > _only_
> > 7-tone scales that have _more_ complete 5-limit triads than this
one
> > (with
> > errors not worse than 12-tET) are diatonic. Do you know of any
> > counter-example?
>
> More than 4 5-limit triads in a 7 note scale? I most certainly do!
>
> A-----E
> / \ / \
> / \ / \
> F-----C-----G
> \ / \ /
> \ / \ /
> Ab----Eb
>
Dave probably meant scales with a single
generator, and specifically MOS scales.

> I worked all this stuff out a while back, and wrote it up at:
>
> <http://x31eq.com/genera.htm>
>
> I notice a misteak there,

Mmmm, steak . . .

(I just biked 30 miles so I'm hungry)

>More than 4 5-limit triads in a 7 note scale? I most certainly do!
>
> A-----E
> / \ / \
> / \ / \
> F-----C-----G
> \ / \ /
> \ / \ /
> Ab----Eb

Graham,

I think Dave was talking about single-generator/proper scales. This is a
member of a family of harmonic lattice derived scales that Fokker
discusses, all of these scales have two generators, and most if them
(especially this one and its siblings) are improper. And I think he's
propbably right about the diatonic, given either the generator or propriety
constraint.

jason

>I also forgot you can get 5 triads with 7 notes using 4 chains 1/4 octave
>apart. The smallest MOS it embeds in is 8 notes (with 8 triads).

What scale is this?

-Carl