617edo: Difference between revisions

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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 ==
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! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning error
|-
|-
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|-
|-
| 2.3
| 2.3
| {{monzo|978 -617}}
| {{Monzo| 978 -617 }}
| {{mapping|617 978}}
| {{Mapping| 617 978 }}
| −0.0479
| −0.0479
| 0.0479
| 0.0479
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|-
|-
| 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
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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
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|+ style="font-size: 105%;" | 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 />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if 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 ==
== Music ==
; [[Francium]]
; [[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] &ndash; majvam in 617edo tuning
* "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]]

Latest revision as of 13:38, 13 March 2026

← 616edo 617edo 618edo →
Prime factorization 617 (prime)
Step size 1.94489 ¢ 
Fifth 361\617 (702.107 ¢)
Semitones (A1:m2) 59:46 (114.7 ¢ : 89.47 ¢)
Consistency limit 5
Distinct consistency limit 5

617 equal divisions of the octave (abbreviated 617edo or 617ed2), also called 617-tone equal temperament (617tet) or 617 equal temperament (617et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 617 equal parts of about 1.94 ¢ each. Each step represents a frequency ratio of 21/617, or the 617th root of 2.

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, tempering out 1701/1700, 1216/1215, 1729/1728, 676/675, 1127/1125, 260253/260000, 3969/3968 and 137241/137200. It supports majvam.

Using the 617c 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 (⟨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

Approximation of prime harmonics in 617edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.152 +0.720 -0.268 -0.913 -0.333 +0.069 +0.056 -0.073 -0.728 +0.507
Relative (%) +0.0 +7.8 +37.0 -13.8 -46.9 -17.1 +3.5 +2.9 -3.8 -37.4 +26.1
Steps
(reduced) 		617
(0) 		978
(361) 		1433
(199) 		1732
(498) 		2134
(283) 		2283
(432) 		2522
(54) 		2621
(153) 		2791
(323) 		2997
(529) 		3057
(589)

Subsets and supersets

617edo is the 113th prime edo.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [978 -617⟩ [⟨617 978]] −0.0479 0.0479 2.46
2.3.5 [39 -29 3⟩, [40 7 -22⟩ [⟨617 978 1433]] −0.1354 0.1297 6.67
2.3.5.7 420175/419904, 1959552/1953125, 67108864/66976875 [⟨617 978 1433 1732]] −0.0776 0.1504 7.73

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 236\617 458.995 125/96 Majvam
1 291\617 565.964 81920/59049 Alphatricot

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Music

Francium
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