Porcupine extensions: Difference between revisions

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[[Porcupine]] has various [[extension]]s to the [[13-limit]].
[[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.
== Exotempering options ==
13 has two viable mappings within the simple intervals of porcupine. 13 can be mapped to +5 generators (tempering out 65/64, the wilsorma), or to -2 generators (tempering out [[40/39]], the unintendo comma, leading to the canonical tridecimal extension of porcupine). The former flattens it by about 20 cents, and the latter sharpens it by about 30.
== More complex mappings ==
Another mapping of 13 is available at -17 generators (leading to porcupinefish). This equates the sharply tuned diatonic major third of porcupine with 13/10 along with 9/7, and requires a much more precise tuning of the porcupine generator to 161.5-163.5 cents to tune the 13th harmonic well.
== Higher primes ==
Prime 17 has a much more obvious mapping, as it can be found at +8 generators, which is tuned between around 80 and 120 cents. This is also the mapping of 16/15, tempering out the [[256/255|charisma]].


== Tuning spectrum ==
== Tuning spectrum ==