MIRACLE OF MIRACLES

Dave Keenan's 31-out-of-72 MIRACLE scale contains four 2)5
[1.3.5.7.9] dekanies and four 3)5 [1.3.5.7.9] dekanies.

Considering that the 72 contains the hebdomekontany with tones left over this should not be a
surprise.

paul@stretch-music.com wrote:

> Dave Keenan's 31-out-of-72 MIRACLE scale contains four 2)5
> [1.3.5.7.9] dekanies and four 3)5 [1.3.5.7.9] dekanies.
>
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-- 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..., paul@s... wrote:
> Dave Keenan's 31-out-of-72 MIRACLE scale contains four 2)5
> [1.3.5.7.9] dekanies and four 3)5 [1.3.5.7.9] dekanies.

I was wondering about that. Thanks! I assume it doesn't contain an
eikosany. Is that right?

Does it contain any dekanies where 11 substitutes for one of the
factors above?

Does the 21-tone MOS contain any dekanies?

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> I was wondering about that. Thanks! I assume it doesn't contain an
> eikosany. Is that right?

Yup!
>
>
> Does the 21-tone MOS contain any dekanies?
>
Nope!

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Considering that the 72 contains the hebdomekontany with tones left over this should not be a
> surprise.

It's a surprise that all these 1-3-5-7-9 dekanies reside in an MOS scale with only 31 notes.

Just to review, each dekany contains

one 1-3-5-7 hexany
one 1-3-5-9 hexany
one 1-3-7-9 hexany
one 1-5-7-9 hexany
one 3-5-7-9 hexany

five 9-limit tetrads (as above -- tetrads in 2)5 dekany are otonal; those in 3)5 dekany are utonal).
Are there any saturated 9-limit tetrads too (10:12:15:18 or 12:14:18:21)?

thirty 9-limit triads (twenty otonal and ten utonal in 2)5 dekany; ten O and twenty U in 3)5
dekany)

thirty 9-limit dyads

and, of course, ten notes.

This is true of dallesandro which although has 36 tones is mapped over a 31 tone keyboard. this
contains two 1-3-7-9-11-15 eikosanies. Working with this material for so long i don't find it
surprising but i guess it could be.

BTW the 1-3-5-7-9 double dekany is a 14 tone CS -my find. I have found only one useful 14 tone just CS.
kinda rare

When you think that the hebdomekontany has 28 different eikosanies each occurring twice. Likewise
there are 56 different 2)5 dekanies each occurring 3 times. The same with 3)5 dekanies. thus you have
112 different dekanies each occurring 3 times. That's 336 dekanies!
BTW Gending Boehme (From the interiors of Anaphoria CD) is based on the 1-3-7-11-15 3)5 dekany where
the melody (vibes) is on the tetrad with the complementary hexany on the marimba. Uses all five
possibilities, each 79 beats long, repeated once. It is one of my favorite structures in the eikosany

paul@stretch-music.com wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> > Considering that the 72 contains the hebdomekontany with tones left over this should not be a
> > surprise.
>
> It's a surprise that all these 1-3-5-7-9 dekanies reside in an MOS scale with only 31 notes.
>
> Just to review, each dekany contains
>
> one 1-3-5-7 hexany
> one 1-3-5-9 hexany
> one 1-3-7-9 hexany
> one 1-5-7-9 hexany
> one 3-5-7-9 hexany
>
> five 9-limit tetrads (as above -- tetrads in 2)5 dekany are otonal; those in 3)5 dekany are utonal).
> Are there any saturated 9-limit tetrads too (10:12:15:18 or 12:14:18:21)?
>
> thirty 9-limit triads (twenty otonal and ten utonal in 2)5 dekany; ten O and twenty U in 3)5
> dekany)
>
> thirty 9-limit dyads
>
> and, of course, ten notes.
>
> You do not need web access to participate. You may subscribe through
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>
>
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-- 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..., Kraig Grady <kraiggrady@a...> wrote:
> This is true of dallesandro

I mean a _true_ MOS, with only one size of generator, like the
horagram scales.

And besides the dekanies, we've seen the plethora of hexads, pentads,
and tetrads it contains!

> BTW Gending Boehme (From the interiors of Anaphoria CD) is based on
the 1-3-7-11-15 3)5 dekany where
> the melody (vibes) is on the tetrad with the complementary hexany
on the marimba.

Cool!