combined ET's

Everyone is fully aware that some equal temperaments approximate various JI
intervals really well and then sacrifice the accuracy of other intervals.

But has any one thought of combining different ET's that have common
factors between them ?

If this were possible [ there is probably some mathematical reason why it
is not possible] then the good features of different ET's could be combined
!

I was inspired by the Lucy tuning which uses various sizes of intervals
that combined add up to an octave.

Justin White

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Justin White wrote,

<< If this were possible [there is probably some mathematical reason
why it is not possible] then the good features of different ET's could
be combined! >>

Well the LCM of any coupling or grouping of ETs would be the easiest
way to have the entire ETs available as subsets. However, this will
often lead to extremely large composite ETs. But yes, this sort of
thing has been done quite a bit (I had my baritone ukulele temporarily
fretted to 5 and 7 equal not to long ago in fact).

Some writers like Darreg (after Navarro I believe) would use common or
shared fractions of an octave as an example of one possible inroad to
combining ETs.

I've written in the past about what I believe are good ideological or
aesthetic (as opposed to mathematical or theory based) models for
combining tunings.

One of my favorites would the criminally under recorded Henry Brant.
In the 'Brant model' each tuning would emphasize its most natural
tendencies, and the composite would exploit the many possibilities of
the "new stresses, layered insanities, and multi-directional assaults
of contemporary life on the spirit" (as Brant himself wrote in 1950).

While this might sound like a recipe for disaster to some, there's
whole worlds of possibilities here for those with suitably empathetic
x-ray ears...

The majority of my own music combines tunings, and I was following the
example of Charles Ives -- via the polychromatic implications of the
Orchestral and Chamber Sets, and especially the Fourth Symphony -- to
also attempt to combine and integrate a wide variety of intonation
systems (i.e., tunings).

Aesthetically and ideologically (and hey, even musically!) this is an
approach that just happens to really resonates with me. I think it's
also relevant to note that composites of the type that I'm generally
interested in don't really behave much like ETs or JI, and they
usually tend to stand most related theory on its head. All of this is
no doubt a good part of why I tend to be drawn or partial to more
generalized, or non-rigid paradigms when it comes to tuning theory.

--Dan Stearns

< Well the LCM of any coupling or grouping of ETs would be the easiest
way to have the entire ETs available as subsets. However, this will
often lead to extremely large composite ETs. But yes, this sort of
thing has been done quite a bit (I had my baritone ukulele temporarily
fretted to 5 and 7 equal not to long ago in fact).

Some writers like Darreg (after Navarro I believe) would use common or
shared fractions of an octave as an example of one possible inroad to
combining ETs. >

What Darreg has done sounds like what I was intending to do. When I think
about it the possibilities are quite staggering.

I could have a 12 tet subset to represent a pythagorean scale [just fifths
and fourths, and the 17th and 19th Harmonics] and I could use something
else to hamonise this subset for instance something that represented 5:4
and 7:4 well and managed to fit into the remaining space in the octave.

Maybe I could have my barbershop guitar afterall !

Justin White

DAVID JONES LIMITED ACN 000 074 573

This email and any attachments are confidential and are intended solely for
the recipient. If you are not the intended recipient, you must not disclose
or use the information contained in it. If you have received this email in
error, please tell us immediately by return email and delete the document.

The contents and any attachments are the opinion of the sender and not
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--- In tuning@egroups.com, "Justin White" <justin.white@d...> wrote:

> I could have a 12 tet subset to represent a pythagorean scale [just fifths
> and fourths, and the 17th and 19th Harmonics] and I could use something
> else to hamonise this subset for instance something that represented 5:4
> and 7:4 well and managed to fit into the remaining space in the octave.

Of course that other ET would not line up with 12 tET in the right way to give these intervals in all
keys, unless it itself was a multiple of 12 like 72.

> Maybe I could have my barbershop guitar afterall !

A 72-tET guitar might be borderline as a "barbershop guitar", though it would lack the adaptive
tuning skills of a singing group and be very difficult to play.