Re: 14-tet

HI there,

14-tet consists of two interleaved 7-et scales, and those have
nice concordant thirds - rich in texture,
very close to 9/7. I've done a bit of composing in
7-et. The fifths are very dissonant and when
composing you feel they need to be resolved rather
than used as a point of rest. But the 7-et
"triad" is no more dissonant than say a 12 equal
dom 7th, and you can resolve it to the 7-et
third diad, which I think is somewhat more consonant
than a 12-et major third triad and somewhat similar
in its role. It works well as a point of rest
at the end of a piece - and you can make a
very pleasant sounding cadence from descending
thirds e.g. degrees 2 4 to 0 2 in 7-et.
You can add a bit more dissonance by using
the triad e.g. 2 4 6 to 0 2.

So 14-tet sounds to me like an interesting
way of extending 7-et, by introducing
"sharps and flats". In diatonic music
you use the circle of fifths to
introduce the accidentals - but that
won't work in 7-et as the fifths only
take you around in 7-et and are dissonances
anyway.

So I wonder, how you could get from one
of the 7-et scales to the other?
Maybe you could use the three step 11/9
approximation in some way, as perhaps the
next most consonant interval in 14-et
after the 9/7.

(I'm temporarily without sound so can't
listen to anything or try it out just this
moment).

Thanks,

Robert

--- In MakeMicroMusic@yahoogroups.com, "Robert Walker"
<robertwalker@n...> wrote:
> HI there,
>
> 14-tet consists of two interleaved 7-et scales, and those have
> nice concordant thirds - rich in texture,
> very close to 9/7.
>
> So I wonder, how you could get from one
> of the 7-et scales to the other?
> Maybe you could use the three step 11/9
> approximation in some way, as perhaps the
> next most consonant interval in 14-et
> after the 9/7.

Not sure if I'm understanding you correctly, but I thought I'd point
out . . .

9/7 is indeed approximated somewhat well in 14-equal, by in interval
of 5 steps. The interval doesn't exist in 7-equal.

11/9 is approximated well by 4 steps in 14-equal, and therefore by 2
steps in 7-equal. So it won't hep you get from one of the 7-equal
scales to the other.

So perhaps you switched 9/7 and 11/9 in your post?

-Paul

Hi Paul,

> So perhaps you switched 9/7 and 11/9 in your post?

Yes! The 11/9 approx. is the interval I used for diads in my 7-et pieces
in place of triads for the cadences. So the 9/7 approx. will
be the one to get from one of the 7-et s to the other
rather than 11/9 as I said in my post.

Thanks

Robert

--- In MakeMicroMusic@yahoogroups.com, "Robert Walker"
<robertwalker@n...> wrote:
> Hi Paul,
>
> > So perhaps you switched 9/7 and 11/9 in your post?
>
> Yes! The 11/9 approx. is the interval I used for diads in my 7-et
pieces
> in place of triads for the cadences. So the 9/7 approx. will
> be the one to get from one of the 7-et s to the other
> rather than 11/9 as I said in my post.
>
> Thanks
>
> Robert

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. I
remember Dan Stearns influencing Dave Keenan to upgrade his
assessment of certain tempered systems with this triad as the
specific example. Although the 'root' or '1' of the chord isn't
available in the 14-equal tuning system, the triad has certain
properties which, with a bit of attention to timbre, register,
duration, and loudness, can lend it an unmistakeable 'consonance'
or 'concordance'.

If any of the 14-tETters out there want to try composing music with
such triads and related harmonies, I'd love to hear it. Otherwise, I
should shut up now, until I make some such musical examples of my
own . . .