Pele: Difference between revisions

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~~#redirect~~ [[~~Hemifamity family #Pele~~]]

'''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]].

[[Category:~~Temperaments~~]]

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 ==

File:Lattice Pele.png|13-limit pele

File:Lattice Pele17.png|17-limit pele

</gallery>

This lattice shows pele as an extension of parapyth, generated by ~2, ~3/2, and ~7/4.

== Chords ==

Pele enables [[essentially tempered chord]]s of [[werckismic chords|werckismic]] and [[pentacircle chords|pentacircle]] in the [[11-odd-limit]], in addition to [[mynucumic chords|mynucumic]], [[major minthmic chords|major minthmic]], [[minor minthmic chords|minor minthmic]] and [[cuthbert chords|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

[[Category:Pele| ]]

[[Category:Rank-3 temperaments]]

[[Category:Hemifamity family]]

[[Category:Pentacircle clan]]

[[Category:Werckismic temperaments]]

~~[[Category:Pentacircle clan]]~~

@@ Line 1: / Line 1: @@
-#redirect [[Hemifamity family #Pele]]
+'''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]].
-[[Category:Temperaments]]
+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 ==
+<gallery>
+File:Lattice Pele.png|13-limit pele
+File:Lattice Pele17.png|17-limit pele
+</gallery>
+This lattice shows pele as an extension of parapyth, generated by ~2, ~3/2, and ~7/4.
+== Chords ==
+Pele enables [[essentially tempered chord]]s of [[werckismic chords|werckismic]] and [[pentacircle chords|pentacircle]] in the [[11-odd-limit]], in addition to [[mynucumic chords|mynucumic]], [[major minthmic chords|major minthmic]], [[minor minthmic chords|minor minthmic]] and [[cuthbert chords|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
+[[Category:Pele| ]] <!-- main article -->
+[[Category:Rank-3 temperaments]]
 [[Category:Hemifamity family]]
+[[Category:Pentacircle clan]]
 [[Category:Werckismic temperaments]]
-[[Category:Pentacircle clan]]