This is really just a proof of concept, but I like the idea enough to share.

Peace Through Sharing.
Love through Music.

-s

midi-chromatic-spiral-calculator.zip

Am pretty (>95%) sure this is correct. If not, do please let me know. As I will correct it asap.

Peace Through Sharing.
Love Through Music.

Happy Holidays. Stay safe.

Sincerely
Scott

And when applied becomes for instance a mode-key fingerings generator.

midi-chromatic-spiral-calculator-to-guitar-fingerings.zip

Maybe it's the holiday season, but I'm in the mood for giving(sharing),

Peace.
-s

The colored diagram for guitar fingering is really neat! But aren't trigonometric calculations overkill? Moving one "degree" clockwise in the spiral is going up one semitone (adding 1). Computing the full set of one key is just adding 12 until you reach > 127. Transposing a scale x semitiones is just adding x (whole numbers) to it. Maybe I am missing something?

@bocanegra
For now I'll give a short answer...until I get more time or clarity.

Conceptually, I like the cart2pol better as it gets at the dual nature(linear and cyclic) of pitches moving up in number. With results being radius (octave) and index(spoke on the constellation).

The alternative (division and subtraction) is sort of clunky to me and doesn't get at the elagance of the matter. And I think it belies and masks over the dual nature of the pitch-to-key relationship.

Glad you like the graphic. Intend to add an updated version here in a little bit with more bells and whistles.

Peace. Thanks for the input and feedback.

-S

p.s. will try to be more concise and thorough in a later message.

In the very simplest (I think maybe even most simple) terms,...

All of the pitches ([0..127]) within a mode-key combination are defined as:

All of those pitches traversed (on a Chromatic Midi Spiral) by the spokes of that mode-key's constellation with a 12-unit radius.

p.s. change the mode or rotate the key and the above is still true.

Correct?

For example, for Ionian C-Major:

@bocanegra

I must move on. Duty calls me elsewhere.
But will say this much, re: your comment about overkill...

What is loses in performance, the concept more than enough makes up for with elegance.

Peace.
-S