Porcupine extensions: Difference between revisions
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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: | ||
* '''Porcupinefowl''' ({{nowrap|15 & 22f}}) – tempering out 40/39, 55/54, 64/63, and 66/65; | * '''Porcupinefowl''' ({{nowrap| 15 & 22f }}) – tempering out 40/39, 55/54, 64/63, and 66/65; | ||
* '''Porcupinefish''' ({{nowrap|15 & 22}}) – tempering out 55/54, 64/63, 91/90, and 100/99; | * '''Porcupinefish''' ({{nowrap| 15 & 22 }}) – tempering out 55/54, 64/63, 91/90, and 100/99; | ||
* '''Porkpie''' ({{nowrap|15f & 22}}) – tempering out 55/54, 64/63, 65/63, 100/99; | * '''Porkpie''' ({{nowrap| 15f & 22 }}) – tempering out 55/54, 64/63, 65/63, 100/99; | ||
* '''Pourcup''' ({{nowrap|15f & 22f}}) – tempering out 55/54, 64/63, 100/99, and 196/195. | * '''Pourcup''' ({{nowrap| 15f & 22f }}) – tempering out 55/54, 64/63, 100/99, and 196/195. | ||
Additionally, there are alternative extensions to prime 7: | |||
* '''[[Opossum]]''' ({{nowrap| 8d & 15 }}) – tempering out 28/27, 40/39, 55/54, and 66/65. | |||
* '''Porky''' ({{nowrap| 22 & 29 }}) – tempering out 55/54, 65/64, 91/90, and 100/99; | |||
* '''Coendou''' ({{nowrap| 29 & 36ce }}) – tempering out 55/54, 65/64, 100/99, and 105/104. | |||
Porcupinefowl maps [[13/8]] to −2 generator steps and conflates it with [[5/3]] and [[18/11]], tempering out [[40/39]]. This is where the generator, representing [[10/9]], [[11/10]], and [[12/11]], goes one step further to stand in for ~[[13/12]]. Porkpie maps 13/8 to +5 generator steps and conflates it with [[8/5]], tempering out [[65/64]]. The generator now represents ~[[14/13]]. Without optimization for the 13-limit, porcupinefowl sharpens the interval class of 13 by about 30{{cent}}, and porkpie flattens it by about 20{{cent}}. | Porcupinefowl maps [[13/8]] to −2 generator steps and conflates it with [[5/3]] and [[18/11]], tempering out [[40/39]]. This is where the generator, representing [[10/9]], [[11/10]], and [[12/11]], goes one step further to stand in for ~[[13/12]]. Porkpie maps 13/8 to +5 generator steps and conflates it with [[8/5]], tempering out [[65/64]]. The generator now represents ~[[14/13]]. Without optimization for the 13-limit, porcupinefowl sharpens the interval class of 13 by about 30{{cent}}, and porkpie flattens it by about 20{{cent}}. | ||
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|- | |- | ||
! Edo<br>generator | ! Edo<br>generator | ||
! | ! Unchanged interval<br>(eigenmonzo) | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||