Pele: Difference between revisions

(7 intermediate revisions by 3 users not shown)

Line 1:

'''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]], 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.

Line 6:

Line 10:

File:Lattice Pele.png|13-limit pele

File:Lattice Pele17.png|17-limit pele

</gallery>

Line 11:

Line 16:

== 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]], [[minthmic chords|minthmic]], [[~~gentle~~ chords|~~gentle~~]] and [[cuthbert chords|cuthbert]] in the [[13-odd-limit]].

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 ==

Line 17:

Line 22:

* [[SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-36]]

* [[Dekany pele]] – a transversal scale

* The [[compdye]] scale pattern

~~[[Category:Temperaments]]~~

[[Category:Pele| ]]

[[Category:Rank-3 temperaments]]

[[Category:Hemifamity family]]

[[Category:Pentacircle clan]]

[[Category:Werckismic temperaments]]

@@ Line 1: / Line 1: @@
-'''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]], 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.
@@ Line 6: / Line 10: @@
 <gallery>
 File:Lattice Pele.png|13-limit pele
+File:Lattice Pele17.png|17-limit pele
 </gallery>
@@ Line 11: / Line 16: @@
 == 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]], [[minthmic chords|minthmic]], [[gentle chords|gentle]] and [[cuthbert chords|cuthbert]] in the [[13-odd-limit]].
+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 ==
@@ Line 17: / Line 22: @@
 * [[SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-36]]
 * [[Dekany pele]] – a transversal scale
+* The [[compdye]] scale pattern
-[[Category:Temperaments]]
 [[Category:Pele| ]] <!-- main article -->
+[[Category:Rank-3 temperaments]]
 [[Category:Hemifamity family]]
 [[Category:Pentacircle clan]]
 [[Category:Werckismic temperaments]]