Porcupine extensions: Difference between revisions

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The other pair of extensions are of higher complexity, but are well rewarded with better intonation. Porcupinefish's mapping of 13 is available at -17 generator steps. 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. Porcup's mapping of 13 is available at +20 generator steps. They unite in [[37edo]], which can be recommended as a tuning for both.

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~~]].

Prime 17 can be found at +8 generator steps, in which case -14 generator steps represent 18/17. This conflates 16/15 with 17/16, tempering out [[256/255]], and 15/14 with 18/17, tempering out [[85/84]]. It can also be found at -14 generator steps, in which case +8 generator steps represent 18/17. This conflates 17/16 with 15/14, tempering out [[120/119]], and 18/17 with 16/15, tempering out [[136/135]]. Both steps tend to be tuned between around 90 and 130 cents.

== Interval chain ==

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 The other pair of extensions are of higher complexity, but are well rewarded with better intonation. Porcupinefish's mapping of 13 is available at -17 generator steps. 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. Porcup's mapping of 13 is available at +20 generator steps. They unite in [[37edo]], which can be recommended as a tuning for both.
-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]].
+Prime 17 can be found at +8 generator steps, in which case -14 generator steps represent 18/17. This conflates 16/15 with 17/16, tempering out [[256/255]], and 15/14 with 18/17, tempering out [[85/84]]. It can also be found at -14 generator steps, in which case +8 generator steps represent 18/17. This conflates 17/16 with 15/14, tempering out [[120/119]], and 18/17 with 16/15, tempering out [[136/135]]. Both steps tend to be tuned between around 90 and 130 cents.
 == Interval chain ==