Pentatonic Functional Just System: Difference between revisions

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In [[13-limit]] [[superpyth]], [[11/8]] is a sub-sub-sub-5fourth, and [[13/8]] is a sub-sub-5fifth.

Primes beyond 13 are classified somewhat like the FJS, with generator ranges from -6 to +5, with priority 0, 1, -1, 2, -2, etc. Unlike FJS, however, the RoT is not the same in both directions: The RoT of a pythagorean interval of <math>i</math> cents is <math>i-68</math> through <math>i+46</math> cents. This range was chosen so that it works for the 13-limit, and it spans just over an [[2187/2048|apotome]], the large step in the pythagorean chromatic scale. ~~It also considers~~ a few large primes: Prime 41 is just barely not a 5P341, but rather a 5s341~~. Prime 37~~ is just barely not a 5m237, but rather a 5M237.

Primes beyond 13 are classified somewhat like the FJS, with generator ranges from -6 to +5, with priority 0, 1, -1, 2, -2, etc. Unlike FJS, however, the RoT is not the same in both directions. The RoT of a pythagorean interval of <math>i</math> cents is <math>i-68</math> through <math>i+46</math> cents. This range was chosen so that it works for the 13-limit, and it spans just over an [[2187/2048|apotome]], the large step in the pythagorean chromatic scale. The exact range was set considering a few large primes: Prime [[37/1|37]] is just barely not a 5m237, but rather a 5M237; similarly, prime [[41/1|41]] is just barely not a 5P341, but rather a 5s341.

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 In [[13-limit]] [[superpyth]], [[11/8]] is a sub-sub-sub-<sub>5</sub>fourth, and [[13/8]] is a sub-sub-<sub>5</sub>fifth.
-Primes beyond 13 are classified somewhat like the FJS, with generator ranges from -6 to +5, with priority 0, 1, -1, 2, -2, etc. Unlike FJS, however, the RoT is not the same in both directions: The RoT of a pythagorean interval of <math>i</math> cents is <math>i-68</math> through <math>i+46</math> cents. This range was chosen so that it works for the 13-limit, and it spans just over an [[2187/2048|apotome]], the large step in the pythagorean chromatic scale. It also considers a few large primes: Prime 41 is just barely not a <sub>5</sub>P3<sup>41</sup>, but rather a <sub>5</sub>s3<sup>41</sup>. Prime 37 is just barely not a <sub>5</sub>m2<sup>37</sup>, but rather a <sub>5</sub>M2<sup>37</sup>.
+Primes beyond 13 are classified somewhat like the FJS, with generator ranges from -6 to +5, with priority 0, 1, -1, 2, -2, etc. Unlike FJS, however, the RoT is not the same in both directions. The RoT of a pythagorean interval of <math>i</math> cents is <math>i-68</math> through <math>i+46</math> cents. This range was chosen so that it works for the 13-limit, and it spans just over an [[2187/2048|apotome]], the large step in the pythagorean chromatic scale. The exact range was set considering a few large primes: Prime [[37/1|37]] is just barely not a <sub>5</sub>m2<sup>37</sup>, but rather a <sub>5</sub>M2<sup>37</sup>; similarly, prime [[41/1|41]] is just barely not a <sub>5</sub>P3<sup>41</sup>, but rather a <sub>5</sub>s3<sup>41</sup>.
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