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617edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|617}} == 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, [..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|617}}
{{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 EDO]].
617edo is the 113th [[prime edo]].


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
|-
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Comma list]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | [[Mapping]]
! colspan="2" |Tuning Error
! rowspan="2" | Optimal<br>8ve stretch (¢)
|-
! colspan="2" | Tuning error
![[TE error|Absolute]] (¢)
|-
![[TE simple badness|Relative]] (%)
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo|978 -617}}
| {{Monzo| 978 -617 }}
| {{mapping|617 978}}
| {{Mapping| 617 978 }}
| -0.0479
| −0.0479
| 0.0479
| 0.0479
| 2.46
| 2.46
|-
|-
| 2.3.5
| 2.3.5
| {{monzo|39 -29 3}}, {{monzo|40 7 -22}}
| {{Monzo| 39 -29 3 }}, {{monzo| 40 7 -22 }}
| {{mapping|617 978 1433}}
| {{Mapping| 617 978 1433 }}
| -0.1354
| −0.1354
| 0.1297
| 0.1297
| 6.67
| 6.67
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| 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}}
| {{Mapping| 617 978 1433 1732 }}
| -0.0776
| −0.0776
| 0.1504
| 0.1504
| 7.73
| 7.73
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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
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| 565.964
| 565.964
| 81920/59049
| 81920/59049
| [[Tricot]]
| [[Alphatricot]]
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<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 ==
; [[Francium]]
* "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]]
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