617edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
617edo is [[consistent]] to the [[5-odd-limit]]. The equal temperament can be used in the 2.3.5.7.13.17.19.23.31 [[subgroup]], [[temper out|tempering out]] [[1701/1700]], [[1216/1215]], [[1729/1728]], [[676/675]], 1127/1125, 260253/260000, [[3969/3968]] and 137241/137200. It [[support]]s [[majvam]]. | 617edo is [[consistent]] to the [[5-odd-limit]]. The equal temperament can be used in the 2.3.5.7.13.17.19.23.31 [[subgroup]], [[temper out|tempering out]] [[1701/1700]], [[1216/1215]], [[1729/1728]], [[676/675]], 1127/1125, 260253/260000, [[3969/3968]] and 137241/137200. It [[support]]s [[majvam]]. | ||
Using the 617c val ({{val|617 978 '''1432''' 1732}}), it tempers out [[15625/15552]], [[2460375/2458624]] and 3276800000/3268642167 in the [[7-limit]], supporting [[kleismic]] and [[marthirds]]. | Using the 617c val ({{val| 617 978 '''1432''' 1732 }}), it tempers out [[15625/15552]], [[2460375/2458624]] and 3276800000/3268642167 in the [[7-limit]], supporting [[kleismic]] and [[marthirds]]. | ||
Using the 617de val ({{val|617 978 1433 '''1733''' '''2135'''}}), it tempers out [[540/539]], 5632/5631, 43923/43904 and 40960000/40920957 in the [[11-limit]], supporting [[jupiter]]. | Using the 617de val ({{val| 617 978 1433 '''1733''' '''2135''' }}), it tempers out [[540/539]], 5632/5631, 43923/43904 and 40960000/40920957 in the [[11-limit]], supporting [[jupiter]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
617edo is the 113th [[prime | 617edo is the 113th [[prime edo]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 978 -617 }} | ||
| {{ | | {{Mapping| 617 978 }} | ||
| | | −0.0479 | ||
| 0.0479 | | 0.0479 | ||
| 2.46 | | 2.46 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 39 -29 3 }}, {{monzo| 40 7 -22 }} | ||
| {{ | | {{Mapping| 617 978 1433 }} | ||
| | | −0.1354 | ||
| 0.1297 | | 0.1297 | ||
| 6.67 | | 6.67 | ||
| Line 34: | Line 43: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 420175/419904, 1959552/1953125, 67108864/66976875 | | 420175/419904, 1959552/1953125, 67108864/66976875 | ||
| {{ | | {{Mapping| 617 978 1433 1732 }} | ||
| | | −0.0776 | ||
| 0.1504 | | 0.1504 | ||
| 7.73 | | 7.73 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
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| 565.964 | | 565.964 | ||
| 81920/59049 | | 81920/59049 | ||
| [[ | | [[Alphatricot]] | ||
|} | |||
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "purple?" from ''Questions'' (2024) | * "purple?" from ''Questions'' (2024) – [https://open.spotify.com/track/0rTRdkO4ttqQaVFO3B42rc Spotify] | [https://francium223.bandcamp.com/track/purple Bandcamp] | [https://www.youtube.com/watch?v=lkfvSjQ6GnU YouTube] – majvam in 617edo tuning | ||
[[Category:Listen]] | [[Category:Listen]] | ||