Porcupine extensions: Difference between revisions
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Tridecimal porcupine is canon, so it's addressed first. - porky since this article is about extensions of 11-limit porcupine. A dedicated article for porky may be created in future. - "161.9 cents" tuning, seems arbitrary |
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[[Porcupine]] has various [[extension]]s to the [[13-limit]]. Adding the 13th harmonic to porcupine is not very simple, because 13 tends to fall in between the simple intervals produced by porcupine's generator. The extensions are: | [[Porcupine]] has various [[extension]]s to the [[13-limit]]. Adding the 13th harmonic to porcupine is not very simple, because 13 tends to fall in between the simple intervals produced by porcupine's generator. The extensions are: | ||
* '''Tridecimal porcupine''' (15 & 22f) – tempering out 40/39, 55/54, 64/63, and 66/65; | |||
* '''Porcupinefish''' (15 & 22) – tempering out 55/54, 64/63, 91/90, and 100/99; | * '''Porcupinefish''' (15 & 22) – tempering out 55/54, 64/63, 91/90, and 100/99; | ||
* '''Porkpie''' (15f & 22) – tempering out 55/54, 64/63, 65/63, 100/99; | * '''Porkpie''' (15f & 22) – tempering out 55/54, 64/63, 65/63, 100/99; | ||
* '''Porcup''' (15f & 22f) – tempering out 55/54, 64/63, 100/99, and 196/195. | * '''Porcup''' (15f & 22f) – tempering out 55/54, 64/63, 100/99, and 196/195. | ||
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Prime 23 can be found at 4 generator steps (tempering out 256/253) or -11 generator steps (tempering out 161/160). Both of these approximations are rather crude, but may be improved by varying the tuning of the generator. For a more precise (yet more complex) mapping, +26 steps is an option. | Prime 23 can be found at 4 generator steps (tempering out 256/253) or -11 generator steps (tempering out 161/160). Both of these approximations are rather crude, but may be improved by varying the tuning of the generator. For a more precise (yet more complex) mapping, +26 steps is an option. | ||
== Interval chain == | == Interval chain == | ||