Pele: Difference between revisions

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'''Pele''' is ~~the~~ [[~~Rank~~-3 temperament|rank-3]] [[temperament]] [[tempering out]] [[441/440]] and [[896/891]], ~~with the~~ canonical [[extension]] to the [[13-limit]] tempering out [[196/195]], [[352/351]] and [[847/845]]. ~~It shares the same [[lattice]] structure as~~ [[parapyth]], ~~but extends~~ it to ~~include~~ the [[5/~~1|harmonic 5]]~~.

'''Pele''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] generated by a perfect fifth of [[~]][[3/2]] and a step for the [[81/80|syntonic]]~[[64/63|septimal comma]] to reach the interval classes of [[5/1|5]], [[7/1|7]], and higher [[prime harmonic|primes]]. Using an arrow to represent this comma step, we have [[5/4]] at the down major third (C–vE), [[7/4]] at the down minor seventh (C–vBb), and [[11/8]] at the down diminished fifth (C–vGb), [[tempering out]] [[441/440]] and [[896/891]], which makes it a member of both [[werckismic temperaments]] and [[pentacircle clan]]. The canonical [[extension]] to the [[13-limit]] finds [[13/8]] at the double-down diminished seventh (C–vBbb), tempering out [[196/195]], [[352/351]] and [[847/845]].

Another way to view this temperament is to look at it relative to [[parapyth]], for which it is an extension that addresses the missing prime 5. If we use an arrow to represent the quartertone spacer of parapyth, we have 5/4 at the up augmented second (C–^D#).

See [[Hemifamity family #Pele]] for technical details.

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-'''Pele''' is the [[Rank-3 temperament|rank-3]] [[temperament]] [[tempering out]] [[441/440]] and [[896/891]], with the canonical [[extension]] to the [[13-limit]] tempering out [[196/195]], [[352/351]] and [[847/845]]. It shares the same [[lattice]] structure as [[parapyth]], but extends it to include the [[5/1|harmonic 5]].
+'''Pele''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] generated by a perfect fifth of [[~]][[3/2]] and a step for the [[81/80|syntonic]]~[[64/63|septimal comma]] to reach the interval classes of [[5/1|5]], [[7/1|7]], and higher [[prime harmonic|primes]]. Using an arrow to represent this comma step, we have [[5/4]] at the down major third (C–vE), [[7/4]] at the down minor seventh (C–vBb), and [[11/8]] at the down diminished fifth (C–vGb), [[tempering out]] [[441/440]] and [[896/891]], which makes it a member of both [[werckismic temperaments]] and [[pentacircle clan]]. The canonical [[extension]] to the [[13-limit]] finds [[13/8]] at the double-down diminished seventh (C–vBbb), tempering out [[196/195]], [[352/351]] and [[847/845]].
+Another way to view this temperament is to look at it relative to [[parapyth]], for which it is an extension that addresses the missing prime 5. If we use an arrow to represent the quartertone spacer of parapyth, we have 5/4 at the up augmented second (C–^D#).
 See [[Hemifamity family #Pele]] for technical details.