Re: [tuning] Hexanies are sooooo different!

Joseph!
I have only worked with hexanies found within the 1-3-5-7-9-11 and 1-3-7-9-11-15 Eikosanies. I
have also used them to investigate tetrachords (thus the scale in Lou Harrison Primer) and for
rhythm. The thing I like about the Hexanies is its cyclical nature as well as the various ways
one can look at a small series of tones. If seems that the degenerate forms destroy the very
reason one would use a hexany. Even hexanies like the 1-3-5-9 I found of such perceptible
ambiguousness that i don't use them except I stellate them with tones found in the two
structures already mentioned. Actually i will use them straight in extended eikosany passages
where the function of each note has a chance to seep in. Working with these Eikosanies for
years, the statement of even a single tetrads will tell me every thing in the surrounding
tonal area. Potentially such a structure becomes a strong of force as tonality.

Joseph Pehrson wrote:

> I bet a person could devote a
> WHOLE LIFETIME to just working with different hexanies. (Is that YOU,
> Kraig Grady??) This is a MUCH different experience that working with
> the various "flavors" of 19 per octave, exciting as that is... where the
> tuning differences are subtle, at best (surprise, surprise.)
>
> The point is, one cannot easily "substitute" one hexany tuning for
> another and still have the same composition! It isn't just a different
> "flavor," it's a WHOLE DIFFERENT PIECE!!
>
> I have a question concerning "degenerate" hexanies, which are my
> favorite ;-). Why are they called "degenerate?" Is it because the
> ratios don't quite work out to small numbers. I'm thinking of the
> example:
>
> 1.3.11.33 Hexany, degenerate pentatonic form
> 0: 1/1 0.000 unison, perfect prime
> 1: 4/3 498.045 perfect fourth
> 2: 11/8 551.318 undecimal semi-augmented fourth
> 3: 16/11 648.682 undecimal semi-diminished fifth
> 4: 3/2 701.955 perfect fifth
> 5: 2/1 1200.000 octave
>
> I guess that would make sense, with the "semi-diminished fifth" and so
> forth, the "traditional" pentatonic from the pythagorean having smaller
> ratios... (that is except for the 27/16!)
>
> Please explain "degeneracy" to me. This is something I need to know
> about quickly.
>

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