A combination-product-set guitar (part 1)

For those of you who don't read MakeMicroMusic, I've posted there an
edited version of an email conversation that Pete McRae and I had a
year ago. We thought it might be of interest.

Summary:

In response to Pete's desiderata, I design a guitar with all
straight-across frets, that makes playable all the tetrads of Erv
Wilson's (3 of 6) 4.5.6.7.9.11 eikosany (octave-specific). It
achieves this by
(a) abandoning octaves (although it has some sub-octaves of 1172
cents)
(b) slightly tempering the ratios of 11 (by 3.6 cents).
Or, if you don't like to use the tempered 11's then it still plays
many 9-limit subsets of the eikosany, including dekanies and
hexanies, in strict JI.

It's fairly long so I'm posting it in a few parts. In part 1 we
discuss philosophy and settle some requirements of the design.

Part 1 is at:

/makemicromusic/topicId_13042.html#13042

-- Dave Keenan

Hello Dave
It would seem that the various CPS would be good point to investigate further expansions as you have started to investigate. I have more than once used them as a starting point of looking how to condense the most material with the most limited resources. usually with good results ( and interesting and musically valuable) but not the optimal.

One of the features of the Eikosany is the structure itself which when used allows all forms of cross relations and a consistent set of relationships. One example is how the opposite tones will function harmonically in the inverted functions
Once you change some of the dissonances to consonances, these become less important, or not exsistent relationships.
the Eikosany already has inherent in it at this factor level such problems.

Take the 1-3-5-9 hexanies .
taken solely by themselves, the cross relations are so consonant that it is impossible to hear it as a hexany unless one uses other means, that one does not usually bother.
It requires a certain dissonance between the farthest points otherwise one has problems hearing it.

It seems once you have nullified the structure, you want to just go forward with changing intervals how you want as i can no longer see why one would be obliged to concern oneself with the eikosany. Since it is not concerned in concept with to have the most consonances with the least amount of tones, possibly tinkering with the intervals might come up with a better result in what you are actually interested in.
The inaccuracy of the basic guitar is such that one can easily entertain such small tolerances

> Message: 18 > Date: Mon, 17 Apr 2006 05:02:41 -0000
> From: "Dave Keenan" <d.keenan@bigpond.net.au>
> Subject: A combination-product-set guitar (part 1)
>
> For those of you who don't read MakeMicroMusic, I've posted there an > edited version of an email conversation that Pete McRae and I had a > year ago. We thought it might be of interest. >
> Summary:
>
> In response to Pete's desiderata, I design a guitar with all > straight-across frets, that makes playable all the tetrads of Erv > Wilson's (3 of 6) 4.5.6.7.9.11 eikosany (octave-specific). It > achieves this by > (a) abandoning octaves (although it has some sub-octaves of 1172 > cents)
> (b) slightly tempering the ratios of 11 (by 3.6 cents). > Or, if you don't like to use the tempered 11's then it still plays > many 9-limit subsets of the eikosany, including dekanies and > hexanies, in strict JI.
>
> It's fairly long so I'm posting it in a few parts. In part 1 we > discuss philosophy and settle some requirements of the design.
>
> Part 1 is at:
>
> /makemicromusic/topicId_13042.html#13042
>
> -- Dave Keenan
>
>
>
>
>
>
> >
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Thanks Kraig,

Yes, I know what you mean about those unwanted consonances, introduced
when you have composite factors such as 9 or 15 in a CPS.

Rest assured that the small amount of tempering I use is purely to
straighten some frets, not to change any eikosany dissonances to
consonances.

Part 2 is up now, at
/makemicromusic/topicId_13048.html#13048

Please correct me if I've misinterpreted what you were saying at the
time.

-- Dave Keenan