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]].

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 ===

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=== Subsets and supersets ===

617edo is the 113th [[prime ~~EDO~~]].

617edo is the 113th [[prime edo]].

== Regular temperament properties ==

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! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve stretch (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning error

|-

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|-

| 2.3

| {{~~monzo~~|978 -617}}

| {{Monzo| 978 -617 }}

| {{~~mapping~~|617 978}}

| {{Mapping| 617 978 }}

| −0.0479

| 0.0479

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|-

| 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

| 0.1297

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| 2.3.5.7

| 420175/419904, 1959552/1953125, 67108864/66976875

| {{~~mapping~~|617 978 1433 1732}}

| {{Mapping| 617 978 1433 1732 }}

| −0.0776

| 0.1504

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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Periods per 8ve

! Generator*

! Cents*

! Associated ratio*

! Associated ratio*

! Temperaments

|-

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| 565.964

| 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 lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|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

* "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]]

@@ Line 5: / Line 5: @@
 edo 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 ===
@@ Line 13: / Line 13: @@
 === Subsets and supersets ===
-edo is the 113th [[prime EDO]].
+edo is the 113th [[prime edo]].
 == Regular temperament properties ==
@@ Line 21: / Line 21: @@
 ! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br />8ve stretch (¢)
+! rowspan="2" | Optimal<br>8ve stretch (¢)
 ! colspan="2" | Tuning error
 |-
@@ Line 28: / Line 28: @@
 |-
 | 2.3
-| {{monzo|978 -617}}
+| {{Monzo| 978 -617 }}
-| {{mapping|617 978}}
+| {{Mapping| 617 978 }}
 | −0.0479
 | 0.0479
@@ Line 35: / Line 35: @@
 |-
 | 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
 | 0.1297
@@ Line 43: / Line 43: @@
 | 2.3.5.7
 | 420175/419904, 1959552/1953125, 67108864/66976875
-| {{mapping|617 978 1433 1732}}
+| {{Mapping| 617 978 1433 1732 }}
 | −0.0776
 | 0.1504
@@ Line 53: / Line 53: @@
 |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
 |-
-! Periods<br />per 8ve
+! Periods<br>per 8ve
 ! Generator*
 ! Cents*
-! Associated<br />ratio*
+! Associated<br>ratio*
 ! Temperaments
 |-
@@ Line 69: / Line 69: @@
 | 565.964
 | 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 lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|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] &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]]