14 EDO

>Another implication of all this is that a potentially useful harmonic
>structure in 14-equal is the approximate 7:9:11 triad (0 5 9 in 14-
>equal), a triad which features heavily in Prent Rodgers' music.

Viz. the following scale

0 2 3 5 6 8 9 11 13 (0

which contains three such triads, ish:

0 5 9
2 6 11
3 8 13
(5 9 0)

Transposing the scale up 11 steps, we get
11 13 0 2 3 5 6 8 10 (11

So you can get modulations etc. There are also some other interesting
chords in there.

Mark

--- In MakeMicroMusic@yahoogroups.com, "M Gould" <mark.gould@a...>
wrote:
> >Another implication of all this is that a potentially useful
harmonic
> >structure in 14-equal is the approximate 7:9:11 triad (0 5 9 in 14-
> >equal), a triad which features heavily in Prent Rodgers' music.
>
> Viz. the following scale
>
> 0 2 3 5 6 8 9 11 13 (0
>
> which contains three such triads, ish:
>
> 0 5 9
> 2 6 11
> 3 8 13
> (5 9 0)
>
> Transposing the scale up 11 steps, we get
> 11 13 0 2 3 5 6 8 10 (11
>
> So you can get modulations etc. There are also some other
interesting
> chords in there.
>
>
> Mark

Thanks Mark. This is right up my alley.

May I invite you to repost this to tuning-math? I think it could spur
some interesting discussion there, which could lead to more practical
ideas, which we could then report back here.

The tuning list would work fine for all this too.

-Paul

Margo asked me to forward her comments to this list:

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The one comment I might about 22-tET or a similar regular temperament
if I were writing this is that for the question of primes 2-3-7, this
solution is just as straightforward, and fits traditional European
notation and compositional techniques, as meantone is for 2-3-5.

Often I find this a bit humorous -- that I should be playing or
composing in kind of historical European style where something like
22 doesn't present the kind of problems so often, and quite rightly,
emphasized for 16th-19th century European music.

By the way, might I ask a friendly favor: to ask if you might let the
people at makemicromusic know that I'm using 14-tET and really
enjoying it? One thing that occurred to me is that it has two chains
of fifths at 600 cents apart -- and, of course, a 600-cent tritone --
although we'd probably agree that it's rather distinct from a
paultone (which I might guess is a category starting somewhere around
707 cents, say 56-tET, as opposed to 686 cents, and also one that
involves a regular diatonic
tuning) <grin>.

The main trick, not so surprisingly, is to choose or design a timbre
where the fifths and fourths can sound like reasonably smooth or
blending perfect consonances -- for my approach, of course, where
these intervals are the goals of directed progressions.

Why don't I note that one of the first progressions I tried -- and
please quote me on this if you would, because this is one aspect of
my musicmaking where you've been especially influential -- involves
the 14-tET equivalent of 4:6:7:9. To write it using step numbers
(maybe the notation of least astonishment), I mean this:

16 17 21 22
11 9 16 14
8 9 13 14
0 -5 or 5 0

Curiously, I pleasantly find it a lot like a tuning such as 22. Given
the way you've made 4:6:7:9 one of my favorite sonorities -- I wrote
about it specifically and had an example in an article I did in 1/1
on my 17-tone just thirdtone system, JOT-17 -- I find it appropriate
to make this my first technical observation about 14-tET.

Please let me invite you, if it seems appropriate, to post these
comments on 14-tET to makemicromusic and/or the Tuning List. It looks
like I might have some technical problems at Yahoo with access, but I
would like to let people know that I'm much enjoying this tuning.
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