16ed5/2: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each. | '''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each. 16 equal divisions of the just major tenth is not a "real" xenharmonic tuning; it is a slightly compressed version of the normal [[12edo|12-tone scale]]. | ||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 102: | Line 101: | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 16 | |||
| num = 5 | |||
| denom = 2 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 16 | |||
| num = 5 | |||
| denom = 2 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
== Regular temperaments == | == Regular temperaments == | ||
{{Main| Quintaleap family }} | {{Main| Quintaleap family }} | ||
16ed5/2 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[subgroup temperament]] which tempers out 256/255, 361/360, and 4624/4617, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintaleap'' temperament). This temperament is supported by {{ | 16ed5/2 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[subgroup temperament]] which tempers out 256/255, 361/360, and 4624/4617, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintaleap'' temperament). This temperament is supported by {{Optimal ET sequence| 12-, 109-, 121-, 133-, 145- }}, and [[157edo]]. | ||
Tempering out 400/399 (equating 20/19 and 21/20) leads to ''[[quintupole]]'' (12&121), and tempering out 476/475 (equating 19/17 with 28/25) leads to ''[[quinticosiennic]]'' (12&145). | Tempering out 400/399 (equating 20/19 and 21/20) leads to ''[[quintupole]]'' (12&121), and tempering out 476/475 (equating 19/17 with 28/25) leads to ''[[quinticosiennic]]'' (12&145). | ||
Another temperament related to 16ed5/2 is ''[[quintapole]]'' (12&85). It is practically identical to the [[18/17s equal temperament #Related temperament|Galilei tuning]], which is generated by the ratios 2/1 and 18/17. | Another temperament related to 16ed5/2 is ''[[quintapole]]'' (12&85). It is practically identical to the [[18/17s equal temperament #Related temperament|Galilei tuning]], which is generated by the ratios 2/1 and 18/17. | ||
== Scale tree == | |||
Ed5/2 scales can be approximated in [[EDO]]s by subdividing their approximations of 5/2. | |||
{| class="wikitable" | |||
|+ | |||
! colspan="4" |Major tenth | |||
! Period | |||
!Notes | |||
|- | |||
|9\7 | |||
| | |||
| | |||
| | |||
|96.429 | |||
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins | |||
|- | |||
| | |||
|31\24 | |||
| | |||
| | |||
|96.875 | |||
| | |||
|- | |||
|22\17 | |||
| | |||
| | |||
| | |||
|97.059 | |||
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins | |||
|- | |||
| | |||
|35\27 | |||
| | |||
| | |||
|97.{{Overline|2}} | |||
| | |||
|- | |||
| 13\10 | |||
| | |||
| | |||
| | |||
|97.5 | |||
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins | |||
|- | |||
|17\13 | |||
| | |||
| | |||
| | |||
|98.077 | |||
| | |||
|- | |||
|21\16 | |||
| | |||
| | |||
| | |||
|98.4375 | |||
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins | |||
|- | |||
| | |||
|25\19 | |||
| | |||
| | |||
|98.684 | |||
| | |||
|- | |||
| | |||
| | |||
|29\22 | |||
| | |||
|98.8{{Overline|63}} | |||
| | |||
|- | |||
| | |||
| | |||
| | |||
|33\25 | |||
|99 | |||
| | |||
|- | |||
|4\3 | |||
| | |||
| | |||
| | |||
|100 | |||
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins | |||
|- | |||
| | |||
| 19\14 | |||
| | |||
| | |||
|101.786 | |||
| | |||
|- | |||
|15\11 | |||
| | |||
| | |||
| | |||
|102.{{Overline|27}} | |||
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins | |||
|- | |||
| | |||
|26\19 | |||
| | |||
| | |||
|102.632 | |||
| | |||
|- | |||
|11\8 | |||
| | |||
| | |||
| | |||
|103.125 | |||
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins | |||
|- | |||
| | |||
|18\13 | |||
| | |||
| | |||
|103.846 | |||
| | |||
|- | |||
| | |||
| | |||
|25\18 | |||
| | |||
|104.1{{Overline|6}} | |||
| | |||
|} | |||
== See also == | == See also == | ||
* [[12edo|12EDO]] - relative EDO | * [[12edo|12EDO]] - relative EDO | ||
* [[28ed5|28ED5]] - relative ED5 | * [[28ed5|28ED5]] - relative ED5 | ||
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* [[18/17 equal-step tuning|AS18/17]] - relative [[AS|ambitonal sequence]] | * [[18/17 equal-step tuning|AS18/17]] - relative [[AS|ambitonal sequence]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||