Quintupole: Difference between revisions
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'''Quintupole''' is a temperament for the 7, 11, 13, 17, and 19 [[Harmonic limit|prime limits]]. It is a member of [[quintaleap family]], [[octagar temperaments]], and [[mistismic temperaments]]. It has a semitone inverval which represents [[18/17]], [[35/33]], [[52/49]], [[55/52]] and [[135/128]] as a generator. [[121edo|121EDO]] is an excellent tuning for quintupole, with a semitone generator of 10\121, and MOS of 13, 25, 37, 49, 61, 73, 85, 97, or 109 notes are available. | '''Quintupole''' is a temperament for the 7, 11, 13, 17, and 19 [[Harmonic limit|prime limits]]. It is a member of [[quintaleap family]], [[octagar temperaments]], and [[mistismic temperaments]]. It has a semitone inverval which represents [[18/17]], [[35/33]], [[52/49]], [[55/52]] and [[135/128]] as a generator, five of them give a fourth (~2.2 cents flat of [[4/3]]), sixteen give [[5/2]], and thirty-four give [[7/1|seventh harmonic]]. [[121edo|121EDO]] is an excellent tuning for quintupole, with a semitone generator of 10\121, and MOS of 13, 25, 37, 49, 61, 73, 85, 97, or 109 notes are available. | ||
== Temperament data == | == Temperament data == | ||
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== Interval chain == | == Interval chain == | ||
Quintupole is considered as a [[cluster temperament]] with twelve clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents 100/99～120/119～171/170～196/195～209/208～210/209～221/220～225/224～289/288～324/323～441/440～513/512 all tempered together. | |||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
! Number of <br>generator | ! Number of <br>generator | ||
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| 0 | | 0 | ||
| 0.000 | | 0.000 | ||
| 1/1 | | [[1/1]] | ||
|- | |- | ||
| 1 | | 1 | ||
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{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |- | ||
! [[Eigenmonzo| | ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]] | ||
! Generator<br>(¢) | ! Generator<br>(¢) | ||
! Comments | ! Comments | ||
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|} | |} | ||
[[Category: | == Scales == | ||
* [[Quintupole13]] | |||
* [[Quintupole25]] | |||
* [[Quintupole37]] | |||
* [[Quintupole49]] | |||
* [[Quintupole61]] | |||
* [[Quintupole73]] | |||
* [[Quintupole85]] | |||
* [[Quintupole97]] | |||
[[Category:Quintupole| ]] <!-- main article --> | |||
[[Category:Rank-2 temperaments]] | |||
[[Category:Quintaleap family]] | [[Category:Quintaleap family]] | ||
[[Category:Octagar temperaments]] | [[Category:Octagar temperaments]] | ||
[[Category:Mistismic temperaments]] | [[Category:Mistismic temperaments]] | ||