Heline Scale

Corrine Heline proposed that the twelve signs of the Zodiac are mapped
to Db, Eb, Gb, Ab, Bb, C, D, E, F, G, A, B (Black keys, then white keys) in her New Age thinking.

I propose calling this the Heline Scale. Now, starting on F you get
two chains of six: F G A B Db Eb, and Gb Ab Bb C D E. And doing the
typical things in astology: Positive/Negative, Triangulation,
Quadrangles, etc. you get F A Db Gb Bb D for Positive signs, which
is Dm and GbM together. Negative signs are CM and Abm together.

Both are the hexachord (0 4 8 1 5 9) (Set A in my system, also has
triangular symmetry, it maps to itself under a transposition of 4
semitones).

Now one can take 12-tET Pajara modelled on a Moebius Strip with
a period of 6 and generator of 7:

First edge of Moebius Strip-> 0 7 2 9 4 11
Opposite edge of Moebius Strip-> 6 1 8 3 10 5

With some poetic license, reorder these chains

0 2 4 7 9 11 and 1 3 5 6 8 10 (put in order)

which is essentially the same as the Heline Scale, transposed
a period (a tritone).

The only thing that may not be justified here is reordering
each side of the Moebius Band.

Question: What tunings best model the Heline Scale?

PGH

--- In tuning-math@yahoogroups.com, "paulhjelmstad" <phjelmstad@...> wrote:
>
> Corrine Heline proposed that the twelve signs of the Zodiac are mapped
> to Db, Eb, Gb, Ab, Bb, C, D, E, F, G, A, B (Black keys, then white keys) in her New Age thinking.
>
> I propose calling this the Heline Scale. Now, starting on F you get
> two chains of six: F G A B Db Eb, and Gb Ab Bb C D E. And doing the
> typical things in astology: Positive/Negative, Triangulation,
> Quadrangles, etc. you get F A Db Gb Bb D for Positive signs, which
> is Dm and GbM together. Negative signs are CM and Abm together.
>
> Both are the hexachord (0 4 8 1 5 9) (Set A in my system, also has
> triangular symmetry, it maps to itself under a transposition of 4
> semitones).
>
> Now one can take 12-tET Pajara modelled on a Moebius Strip with
> a period of 6 and generator of 7:
>
> First edge of Moebius Strip-> 0 7 2 9 4 11
> Opposite edge of Moebius Strip-> 6 1 8 3 10 5
>
> With some poetic license, reorder these chains
>
> 0 2 4 7 9 11 and 1 3 5 6 8 10 (put in order)
>
> which is essentially the same as the Heline Scale, transposed
> a period (a tritone).
>
> The only thing that may not be justified here is reordering
> each side of the Moebius Band.
>
> Question: What tunings best model the Heline Scale?
>
> PGH
>

Also, I thought, it's a pentatonic scale, and then a diatonic scale. I think it's a great
way to unravel 12-tET in order to think about various things. Well, of course, it's just the basic keyboard idea. Various 5-limit meantones could be used, and then you merely
get two planks of whole tones which expand between sqrt(5)/2 -> 9/8 depending.

Well, of course phi is (sqrt(5) + 1)/2, the arithmetic mean, whereas 1/4 comma meatone
is the geometric mean...this might have some uses.

pgh.