Math-Tonalities a creator for all possible tonalities

Hi everybody,

I've just programmed an algorithm for the create-library function, building up a complete set of all the mathematically possible tonalities.

They are organized by this way:

- Ditonic scales: 11

- Tritonic scales: 55

- Tetratonic scales: 165

- Pentatonic scales: 330

- Hexatonic scales: 462

- Heptatonic scales: 462

- Octatonic scales: 330

- Nonatonic scales: 165

- Decatonic scales: 55

- Undecatonic scales: 11

Total mathematical tonalities generated: 2046

Here comes an excerpt of the code (2275 lines):

;; Ditonic tonalities (11 scales)

;; ---------------------------------------------------------------

(create-tonality math-ditonic-1 '(0 1))

(create-tonality math-ditonic-2 '(0 2))

(create-tonality math-ditonic-3 '(0 3))

(create-tonality math-ditonic-4 '(0 4))

(create-tonality math-ditonic-5 '(0 5))

(create-tonality math-ditonic-6 '(0 6))

(create-tonality math-ditonic-7 '(0 7))

(create-tonality math-ditonic-8 '(0 8))

(create-tonality math-ditonic-9 '(0 9))

(create-tonality math-ditonic-10 '(0 10))

(create-tonality math-ditonic-11 '(0 11))

;; Tritonic tonalities (55 scales)

;; ---------------------------------------------------------------

;; Group 1 (width 2)

;; ----------------------------------------------

(create-tonality math-tritonic-1-1 '(0 1 2))

;; Group 2 (width 3)

;; ----------------------------------------------

(create-tonality math-tritonic-2-1 '(0 1 3))

(create-tonality math-tritonic-2-2 '(0 2 3))

;; Group 3 (width 4)

;; ----------------------------------------------

(create-tonality math-tritonic-3-1 '(0 1 4))

(create-tonality math-tritonic-3-2 '(0 2 4))

(create-tonality math-tritonic-3-3 '(0 3 4))

....

;; Undecatonic tonalities (11 scales)

;; ---------------------------------------------------------------

;; Group 1 (width 10)

;; ----------------------------------------------

(create-tonality math-undecatonic-1-1 '(0 1 2 3 4 5 6 7 8 9 10))

;; Group 2 (width 11)

;; ----------------------------------------------

(create-tonality math-undecatonic-2-1 '(0 1 2 3 4 5 6 7 8 9 11))

(create-tonality math-undecatonic-2-2 '(0 1 2 3 4 5 6 7 8 10 11))

(create-tonality math-undecatonic-2-3 '(0 1 2 3 4 5 6 7 9 10 11))

(create-tonality math-undecatonic-2-4 '(0 1 2 3 4 5 6 8 9 10 11))

(create-tonality math-undecatonic-2-5 '(0 1 2 3 4 5 7 8 9 10 11))

(create-tonality math-undecatonic-2-6 '(0 1 2 3 4 6 7 8 9 10 11))

(create-tonality math-undecatonic-2-7 '(0 1 2 3 5 6 7 8 9 10 11))

(create-tonality math-undecatonic-2-8 '(0 1 2 4 5 6 7 8 9 10 11))

(create-tonality math-undecatonic-2-9 '(0 1 3 4 5 6 7 8 9 10 11))

(create-tonality math-undecatonic-2-10 '(0 2 3 4 5 6 7 8 9 10 11))

Feel free to use it partially or integrally. This set is another way to the sublect, based on a mathematical approach. This systematic approach is completing the musical, cultural and subjective way, scales and modes are commonly considered. The many redundancies found in the usual approach is avoided here and I hope, it completes the excellent, very extensive, tonality-library found in Opusmodus.

If you are interested in more of my stuff, follow me on GitHub:

GitHub

collect-all-math-tonalities.lisp