Re: [tuning] 12-tone tunings for 7-limit harmony (for Joseph Pehrson et al)

Joseph!
if you are interested in something in more than just chords and would like some
melodically based 7-limit scales may i suggest http://www.anaphoria.com/centaur.html.

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

Paul!
OUCH! YOU GOT TO BE KIDDING!
How about 1/1 21/20 9/8 7/6 5/4 21/16 7/5 45/32 7/5 3/2 7/4 15/8 28/15
This one also has 4 tetrads . in fact 2 Pentads and 2 tetrads harmonic and subharmonic. And at
least SOME repeating tetrachords. Frankly I would reject even my scale here as being rather
elementary and in the nature of nothing more than number/paper games!

Paul Erlich wrote:

>
>
> Finally, if one is a stickler for exact JI, one can only have 4 7-
> limit tetrads in a roughly even 12-tone scale. There are many ways to
> do this (including several ways of "de-tempering" the Fokker-Lumma-
> Keenan scale). Here is the lattice diagram of one from Paul Hahn,
> Mills Tuning Digest 1598 (12/1/98):
>
> 42:25------21:20-------21:16
> \'-. .-'/ \'-. .-'/ \'-.
> \ 6:5--/---\--3:2--/---\-15:8
> \ /|\ / \ /|\ / \ /|
> \ | / \ | / \ |
> / \|/ \ / \|/ \ / \|
> / 7:5---------7:4--------35:32
> /.-' '-.\ /.-' '-.\ /.-'
> 8:5---------1:1---------5:4
>
> which you will note has two hexanies in addition to the four tetrads.
> An equally good scale is obtained by substituting 25:15 for 8:5 and
> 105:64 for 42:25:
>
> 21:20-------21:16------105:64
> .-'/ \'-. .-'/ \'-. .-'/
> 6:5--/---\--3:2--/---\-15:8 /
> |\ / \ /|\ / \ /|\ /
> | / \ | / \ | /
> |/ \ / \|/ \ / \|/ \
> 7:5---------7:4--------35:32 \
> '-.\ /.-' '-.\ /.-' '-.\
> 1:1---------5:4--------25:16
>
>

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