Eikosany Guitar

Hi there!
Sorry to enter this so late in the game as i just got back on this list for a while.
Pete Mc Rae has a electric guitar that we came up with that uses the 1-3-7-9-11-15 Eikosany fretting all 22 tones straight across.
tuning used for open strings was D# A# D# G# A# D#
D#=1 7 11 in the 22 the others a 4/3 and 3/2 above.
Now dallesandro has two 1-3-7-9-11-15 Eikosanies which this guitar can play. Do to the close fretting the idea of playing all the tetrads is not really
feasable. To do that i think one could build a Surrogate Kithara using 9 strings or 9 sets of unison strings where the middle three strings were tuned
to a 1-3-9 (two fifths, actually being 4-6-9). one set of the adjacent three strings are tuned to the 5-7-11 while the other set treats the 4-6-9 as the
subharmonic 9/6/4 and tunes it strings to a subharmonic 5 -7 -11. then the player plays only 6 strings at a time which will give him either a harmonic
or subharmonic hexad. The only disadvantages of this is appegios will not be from low to high, but then again this might be an advantage and more
interesting musically. If i were going to demand a guitar , i would be more interested in a subset of the eikosany because in my humble opinion, the
eikosany is out of your basic guitar "Language" Still one has all types of tetrachordal scales that can be taken from this mother set to musical
advantage. The Eikosany is good for instruments that can be played on a Bosanquet keyboard or keyboard lay out. The 22 1-3-7-9-11-15 eikosany
scales does do some funny rthings on your convential keyboard. the fifth looks like a Minor ninth, but your M3 looks like a fifth and your 9/8 looks
like a Major 3. something kinda Yassarian if one wanted to indulge in so "evolutional " speculation. the third becoming /in place of the fifth , the
second becoming /in place of the third etc. Margo has already pointed out some problems with this:)

--- In tuning@y..., kraiggrady@a... wrote:
> Hi there!
> Sorry to enter this so late in the game as i just got back on
this list for a while.

Good to hear from you, Kraig.

> Pete Mc Rae has a electric guitar that we came up with that uses the
1-3-7-9-11-15 Eikosany fretting all 22 tones straight across.

How can an eikosany have 22 tones? Please educate me.

> tuning used for open strings was D# A# D# G# A# D#
> D#=1 7 11 in the 22 the others a 4/3 and 3/2 above.

My design procedure forbids intervals as big as a 2:3 between adjacent
strings, but it still usually manages to do just as well re missing
notes.

> Now dallesandro has two 1-3-7-9-11-15 Eikosanies which this guitar
can play. Do to the close fretting the idea of playing all the tetrads
is not really
> feasable.

Maybe I can design one without the close fretting. Why 1-3-7-9-11-15
instead of 1-3-5-7-9-11?

...
>If i were going to demand a guitar , i would
be more interested in a subset of the eikosany because in my humble
opinion, the
> eikosany is out of your basic guitar "Language".

I'd like to understand more about this.

-- Dave Keenan

Dave Keenan wrote:

>
>
> How can an eikosany have 22 tones? Please educate me.

yes it is an Eikosany plus two tones which makes it a Constant
Structure.
http://www.anaphoria.com/dal.PDF has this 22 tone scale calling it
Pascal.
It was a tuning i used over 15 years and is the one i usually mention in
context to eikosanies.

>
>
> > tuning used for open strings was D# A# D# G# A# D#
> > D#=1 7 11 in the 22 the others a 4/3 and 3/2 above.
>
> My design procedure forbids intervals as big as a 2:3 between adjacent
>
> strings, but it still usually manages to do just as well re missing
> notes.

Sorry i missed that. but why?

> > Now dallesandro has two 1-3-7-9-11-15 Eikosanies which this guitar
> can play. Do to the close fretting the idea of playing all the tetrads
>
> is not really
> > feasable.
>
> Maybe I can design one without the close fretting. Why 1-3-7-9-11-15
> instead of 1-3-5-7-9-11?

The first to have a Constant structure requires 22 tones while the later
requires 31. Although it was the later that i used the longest having
made instruments in the full 1-3-5-7-9-11- CPS

> >If i were going to demand a guitar , i would
> be more interested in a subset of the eikosany because in my humble
> opinion, the
> > eikosany is out of your basic guitar "Language".

> I'd like to understand more about this.

As each tetrad occurs only once in the Eikosany, and each tetrad is made
of a different set of 6 elements. it is really hard to come up with a
string and fretting pattern that makes it easy to play all of them. Now
if one wants to use hexanies this makes it even harder, although it
seems even harder. With the guitar it is a part of its language to
transpose a given chord position up and down your fret board, which you
can do, but then you will be using more the melodic properties of the
constant structure and I would guess would wanted material to be
repeated higher or lower which might lead you back to tetrachoral
scales.
The very nature of the structural possibilities of the Eikosany is
how each material , tetrad and hexanies has very defined places that
they occur. After using this structure, one becomes quite familiar where
one is in the structure by where each of these structures occur. It sets
up a strong as structure as tonality, at least this was my final
perception of it. You have other things such as those tetrachordal
scales found as a fringe benefit will be mirrored on those tones
farthest away from your original set of pitches. The inversion of
something becomes tied in with the most dissonant.
Having a guitar, this was the only way we were able to us it without
the complexity making it just to hard to play. Not trying to ruin your
party , just don't want you to not put alot an effort into a guitar that
might not pan out for you. Having had almost a 50% failure of
instruments to do what i wanted them to do (which i am sure Partch's
record was about the same). It can cause one to turn away from making
another attempt, which often means abandoning the entire path that lead
to a particular design. Notice that Partch abandoned fretting the
diamond after a certain point.
Anyway sometimes the answer to a problem might be useful for other
reasons so proceed. Often in working in the Eikosany, the best solution
are those that are self mirroring. I would look at tuning to a hexany
maybe or the hexagon formed by the pattern ABC BCD CDE DEF EFA FAB where
each letter could stand for each factor of 1-3-5-7-9-11.

>
> -- Dave Keenan
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., kraiggrady@a... wrote:
> > Hi there!
> > Sorry to enter this so late in the game as i just got back on
> this list for a while.
>
> Good to hear from you, Kraig.
>
> > Pete Mc Rae has a electric guitar that we came up with that uses
the
> 1-3-7-9-11-15 Eikosany fretting all 22 tones straight across.
>
> How can an eikosany have 22 tones? Please educate me.

Kraig is referring to the 22-tone CS (aka periodicity block) which
includes the 1-3-7-9-11-15 (notice 5 and 13 are skipped) plus two
extra tones. You'll find this at the bottom of
<http://www.anaphoria.com/musinst.html>.
>
> Maybe I can design one without the close fretting. Why 1-3-7-9-11-
15
> instead of 1-3-5-7-9-11?

I think this is mainly because 1-3-5-7-9-11 can't be embedded in a CS
with a relatively small number of notes, such as 22. I of course
defer to Kraig should I be incorrect.