701edo: Difference between revisions

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== Theory ==

701edo is [[consistent]] to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 1959552/1953125 and {{monzo|-29 23 -2 -1}} in the [[7-limit]]; [[5632/5625]], 2401/2400, 137781/137500 and 43923/43904 in the 11-limit; [[1001/1000]], [[1716/1715]], [[4096/4095]], 39366/39325 and [[6656/6655]] in the 13-limit. ~~701edo~~ [[support]]s [[zisa]] and [[quinmite]].

701edo is [[consistent]] to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 1959552/1953125 and {{monzo|-29 23 -2 -1}} in the [[7-limit]]; [[5632/5625]], 2401/2400, 137781/137500 and 43923/43904 in the 11-limit; [[1001/1000]], [[1716/1715]], [[4096/4095]], 39366/39325 and [[6656/6655]] in the 13-limit. It also [[support]]s [[zisa]] and [[quinmite]].

=== Prime harmonics ===

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== Regular temperament properties ==

{| 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 8ve ~~Stretch~~ (¢)

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

! colspan="2" |Tuning ~~Error~~

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

|-

! colspan="2" | Tuning error

![[TE error|Absolute]] (¢)

|-

![[TE simple badness|Relative]] (%)

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

|-

| 2.3

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| {{monzo|-22 30 -11}}, {{monzo|55 -1 -23}}

| {{mapping|701 1111 1628}}

| -0.0596

| −0.0596

| 0.1316

| 7.69

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| 2401/2400, 1959552/1953125, {{monzo|-29 23 -2 -1}}

| {{mapping|701 1111 1628 1968}}

| -0.0514

| −0.0514

| 0.1149

| 6.71

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| 5632/5625, 2401/2400, 137781/137500, 43923/43904

| {{mapping|701 1111 1628 1968 2425}}

| -0.0350

| −0.0350

| 0.1078

| 6.30

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| 1001/1000, 1716/1715, 4096/4095, 39366/39325, 6656/6655

| {{mapping|701 1111 1628 1968 2425 2594}}

| -0.0286

| −0.0286

| 0.0995

| 5.81

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=== Rank-2 temperaments ===

{| 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 per 8ve

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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| [[Quinmite]]

|}

<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]]

* "Don't Fancy Cooking Jonathan?" from ''Questions'' (2024) – [https://open.spotify.com/track/4OzV8Wjab1MyEQLKE3ErVX Spotify] | [https://francium223.bandcamp.com/track/dont-fancy-cooking-jonathan Bandcamp] | [https://www.youtube.com/watch?v=-wZcQ9t_NrE YouTube] – ~~zisa~~ in 701edo tuning

* "Don't Fancy Cooking Jonathan?" from ''Questions'' (2024) – [https://open.spotify.com/track/4OzV8Wjab1MyEQLKE3ErVX Spotify] | [https://francium223.bandcamp.com/track/dont-fancy-cooking-jonathan Bandcamp] | [https://www.youtube.com/watch?v=-wZcQ9t_NrE YouTube] – in Zisa, 701edo tuning

* "Fluffy Spider Silk" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/48K7FpEbJrCL6bZz5FoAuT Spotify] | [https://francium223.bandcamp.com/track/fluffy-spider-silk Bandcamp] | [https://www.youtube.com/watch?v=eIskpXFHhB0 YouTube]

* "Sinisterly" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3D1Y6m4OqFdA1QPjOrds6j Spotify] | [https://francium223.bandcamp.com/track/sinisterly Bandcamp] | [https://www.youtube.com/watch?v=ouCz-TxpUWM YouTube]

* "You Disnt See the Obivous" from ''Void'' (2025) – [https://open.spotify.com/track/4vToBN4eH1gSB3sxGiH0CT Spotify] | [https://francium223.bandcamp.com/track/you-disnt-see-the-obivous Bandcamp] | [https://www.youtube.com/watch?v=ouiHrGNTzsA YouTube]

* "Coco Cat" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/5FSKaut8FQ7NJN9CxGqnBA Spotify] | [https://francium223.bandcamp.com/track/coco-cat Bandcamp] | [https://www.youtube.com/watch?v=wK67ipiLKW0 YouTube]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
 == Theory ==
-edo is [[consistent]] to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 1959552/1953125 and {{monzo|-29 23 -2 -1}} in the [[7-limit]]; [[5632/5625]], 2401/2400, 137781/137500 and 43923/43904 in the 11-limit; [[1001/1000]], [[1716/1715]], [[4096/4095]], 39366/39325 and [[6656/6655]] in the 13-limit. 701edo [[support]]s [[zisa]] and [[quinmite]].
+edo is [[consistent]] to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 1959552/1953125 and {{monzo|-29 23 -2 -1}} in the [[7-limit]]; [[5632/5625]], 2401/2400, 137781/137500 and 43923/43904 in the 11-limit; [[1001/1000]], [[1716/1715]], [[4096/4095]], 39366/39325 and [[6656/6655]] in the 13-limit. It also [[support]]s [[zisa]] and [[quinmite]].
 === Prime harmonics ===
@@ Line 13: / Line 13: @@
 == Regular temperament properties ==
 {| 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
@@ Line 32: / Line 33: @@
 | {{monzo|-22 30 -11}}, {{monzo|55 -1 -23}}
 | {{mapping|701 1111 1628}}
-| -0.0596
+| −0.0596
 | 0.1316
 | 7.69
@@ Line 39: / Line 40: @@
 | 2401/2400, 1959552/1953125, {{monzo|-29 23 -2 -1}}
 | {{mapping|701 1111 1628 1968}}
-| -0.0514
+| −0.0514
 | 0.1149
 | 6.71
@@ Line 46: / Line 47: @@
 | 5632/5625, 2401/2400, 137781/137500, 43923/43904
 | {{mapping|701 1111 1628 1968 2425}}
-| -0.0350
+| −0.0350
 | 0.1078
 | 6.30
@@ Line 53: / Line 54: @@
 | 1001/1000, 1716/1715, 4096/4095, 39366/39325, 6656/6655
 | {{mapping|701 1111 1628 1968 2425 2594}}
-| -0.0286
+| −0.0286
 | 0.0995
 | 5.81
@@ Line 60: / Line 61: @@
 === Rank-2 temperaments ===
 {| 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*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 73: / Line 75: @@
 | [[Quinmite]]
 |}
-<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]]
-* "Don't Fancy Cooking Jonathan?" from ''Questions'' (2024) – [https://open.spotify.com/track/4OzV8Wjab1MyEQLKE3ErVX Spotify] | [https://francium223.bandcamp.com/track/dont-fancy-cooking-jonathan Bandcamp] | [https://www.youtube.com/watch?v=-wZcQ9t_NrE YouTube] – zisa in 701edo tuning
+* "Don't Fancy Cooking Jonathan?" from ''Questions'' (2024) – [https://open.spotify.com/track/4OzV8Wjab1MyEQLKE3ErVX Spotify] | [https://francium223.bandcamp.com/track/dont-fancy-cooking-jonathan Bandcamp] | [https://www.youtube.com/watch?v=-wZcQ9t_NrE YouTube] – in Zisa, 701edo tuning
+* "Fluffy Spider Silk" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/48K7FpEbJrCL6bZz5FoAuT Spotify] | [https://francium223.bandcamp.com/track/fluffy-spider-silk Bandcamp] | [https://www.youtube.com/watch?v=eIskpXFHhB0 YouTube]
+* "Sinisterly" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3D1Y6m4OqFdA1QPjOrds6j Spotify] | [https://francium223.bandcamp.com/track/sinisterly Bandcamp] | [https://www.youtube.com/watch?v=ouCz-TxpUWM YouTube]
+* "You Disnt See the Obivous" from ''Void'' (2025) – [https://open.spotify.com/track/4vToBN4eH1gSB3sxGiH0CT Spotify] | [https://francium223.bandcamp.com/track/you-disnt-see-the-obivous Bandcamp] | [https://www.youtube.com/watch?v=ouiHrGNTzsA YouTube]
+* "Coco Cat" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/5FSKaut8FQ7NJN9CxGqnBA Spotify] | [https://francium223.bandcamp.com/track/coco-cat Bandcamp] | [https://www.youtube.com/watch?v=wK67ipiLKW0 YouTube]
+[[Category:Listen]]