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]].

'''Pele''' is a [[rank-3 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]].

The canonical [[extension]] to the [[13-limit]] finds [[13/8]] at the 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 up 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#).

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

== Chords ==

== Chords and harmony ==

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 ==

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|-

! Tenney

| CTE: ~3/2 = 703.2829, ~5/4 = 386.5647{{c}}

| CTE: ~3/2 = 703.2829{{c}}, ~5/4 = 386.5647{{c}}

| CWE: ~3/2 = 703.2804, ~5/4 = 387.3911{{c}}

| CWE: ~3/2 = 703.2804{{c}}, ~5/4 = 387.3911{{c}}

| POTE: ~3/2 = 703.2791, ~5/4 = 387.7906{{c}}

| POTE: ~3/2 = 703.2791{{c}}, ~5/4 = 387.7906{{c}}

|}

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|-

! Tenney

| CTE: ~3/2 = 703.4398, ~5/4 = 386.8933{{c}}

| CTE: ~3/2 = 703.4398{{c}}, ~5/4 = 386.8933{{c}}

| CWE: ~3/2 = 703.4225, ~5/4 = 387.7761{{c}}

| CWE: ~3/2 = 703.4225{{c}}, ~5/4 = 387.7761{{c}}

| POTE: ~3/2 = 703.4143, ~5/4 = 388.1971{{c}}

| POTE: ~3/2 = 703.4143{{c}}, ~5/4 = 388.1971{{c}}

|}

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|-

! Tenney

| CTE: ~3/2 = 703.5544, ~5/4 = 387.9654{{c}}

| CTE: ~3/2 = 703.5544{{c}}, ~5/4 = 387.9654{{c}}

| CWE: ~3/2 = 703.4518, ~5/4 = 388.4909{{c}}

| CWE: ~3/2 = 703.4518{{c}}, ~5/4 = 388.4909{{c}}

| POTE: ~3/2 = 703.4265, ~5/4 = 388.6202{{c}}

| POTE: ~3/2 = 703.4265{{c}}, ~5/4 = 388.6202{{c}}

|}

[[Category:Pele| ]]

[[Category:Rank-3 temperaments]]

[[Category:~~Hemifamity~~ family]]

[[Category:Aberschismic family]]

[[Category:Pentacircle clan]]

[[Category:Werckismic temperaments]]

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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]].
+'''Pele''' is a [[rank-3 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]].
+The canonical [[extension]] to the [[13-limit]] finds [[13/8]] at the 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 up 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#).
@@ Line 15: / Line 15: @@
 This lattice shows pele as an extension of parapyth, generated by ~2, ~3/2, and ~7/4.
-== Chords ==
+== Chords and harmony ==
 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 36: / Line 36: @@
 |-
 ! Tenney
-| CTE: ~3/2 = 703.2829, ~5/4 = 386.5647{{c}}
+| CTE: ~3/2 = 703.2829{{c}}, ~5/4 = 386.5647{{c}}
-| CWE: ~3/2 = 703.2804, ~5/4 = 387.3911{{c}}
+| CWE: ~3/2 = 703.2804{{c}}, ~5/4 = 387.3911{{c}}
-| POTE: ~3/2 = 703.2791, ~5/4 = 387.7906{{c}}
+| POTE: ~3/2 = 703.2791{{c}}, ~5/4 = 387.7906{{c}}
 |}
@@ Line 52: / Line 52: @@
 |-
 ! Tenney
-| CTE: ~3/2 = 703.4398, ~5/4 = 386.8933{{c}}
+| CTE: ~3/2 = 703.4398{{c}}, ~5/4 = 386.8933{{c}}
-| CWE: ~3/2 = 703.4225, ~5/4 = 387.7761{{c}}
+| CWE: ~3/2 = 703.4225{{c}}, ~5/4 = 387.7761{{c}}
-| POTE: ~3/2 = 703.4143, ~5/4 = 388.1971{{c}}
+| POTE: ~3/2 = 703.4143{{c}}, ~5/4 = 388.1971{{c}}
 |}
@@ Line 68: / Line 68: @@
 |-
 ! Tenney
-| CTE: ~3/2 = 703.5544, ~5/4 = 387.9654{{c}}
+| CTE: ~3/2 = 703.5544{{c}}, ~5/4 = 387.9654{{c}}
-| CWE: ~3/2 = 703.4518, ~5/4 = 388.4909{{c}}
+| CWE: ~3/2 = 703.4518{{c}}, ~5/4 = 388.4909{{c}}
-| POTE: ~3/2 = 703.4265, ~5/4 = 388.6202{{c}}
+| POTE: ~3/2 = 703.4265{{c}}, ~5/4 = 388.6202{{c}}
 |}
 [[Category:Pele| ]] <!-- main article -->
 [[Category:Rank-3 temperaments]]
-[[Category:Hemifamity family]]
+[[Category:Aberschismic family]]
 [[Category:Pentacircle clan]]
 [[Category:Werckismic temperaments]]