Pele: Difference between revisions
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'''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 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]]. | ||
[[Category: | |||
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 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 == | |||
* [[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 | |||
== Tunings == | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 703.2829{{c}}, ~5/4 = 386.5647{{c}} | |||
| CWE: ~3/2 = 703.2804{{c}}, ~5/4 = 387.3911{{c}} | |||
| POTE: ~3/2 = 703.2791{{c}}, ~5/4 = 387.7906{{c}} | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 703.4398{{c}}, ~5/4 = 386.8933{{c}} | |||
| CWE: ~3/2 = 703.4225{{c}}, ~5/4 = 387.7761{{c}} | |||
| POTE: ~3/2 = 703.4143{{c}}, ~5/4 = 388.1971{{c}} | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 17-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 703.5544{{c}}, ~5/4 = 387.9654{{c}} | |||
| CWE: ~3/2 = 703.4518{{c}}, ~5/4 = 388.4909{{c}} | |||
| POTE: ~3/2 = 703.4265{{c}}, ~5/4 = 388.6202{{c}} | |||
|} | |||
[[Category:Pele| ]] <!-- main article --> | |||
[[Category:Rank-3 temperaments]] | |||
[[Category:Aberschismic family]] | |||
[[Category:Pentacircle clan]] | |||
[[Category:Werckismic temperaments]] | [[Category:Werckismic temperaments]] | ||