Pele: Difference between revisions
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'''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]]. | '''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]], and a 17-limit extension is available by recognizing 17/16 at the minor second (C–Db), tempering out [[256/255]]. | |||
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#). | 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#). | ||
Revision as of 14:51, 19 April 2025
Pele is a rank-3 temperament generated by a perfect fifth of ~3/2 and a step for the syntonic~septimal comma to reach the interval classes of 5, 7, and higher 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, and a 17-limit extension is available by recognizing 17/16 at the minor second (C–Db), tempering out 256/255.
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.
Interval lattice
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13-limit pele -
17-limit pele
This lattice shows pele as an extension of parapyth, generated by ~2, ~3/2, and ~7/4.
Chords
Pele enables essentially tempered chords of werckismic and pentacircle in the 11-odd-limit, in addition to mynucumic, major minthmic, minor minthmic and cuthbert in the 13-odd-limit.
Scales
- SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-24
- SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-36
- Dekany pele – a transversal scale
- The compdye scale pattern