701edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == 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 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 === | === Prime harmonics === | ||
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== 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 | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! 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 | ||
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| {{monzo|-22 30 -11}}, {{monzo|55 -1 -23}} | | {{monzo|-22 30 -11}}, {{monzo|55 -1 -23}} | ||
| {{mapping|701 1111 1628}} | | {{mapping|701 1111 1628}} | ||
| | | −0.0596 | ||
| 0.1316 | | 0.1316 | ||
| 7.69 | | 7.69 | ||
| Line 39: | Line 40: | ||
| 2401/2400, 1959552/1953125, {{monzo|-29 23 -2 -1}} | | 2401/2400, 1959552/1953125, {{monzo|-29 23 -2 -1}} | ||
| {{mapping|701 1111 1628 1968}} | | {{mapping|701 1111 1628 1968}} | ||
| | | −0.0514 | ||
| 0.1149 | | 0.1149 | ||
| 6.71 | | 6.71 | ||
| Line 46: | Line 47: | ||
| 5632/5625, 2401/2400, 137781/137500, 43923/43904 | | 5632/5625, 2401/2400, 137781/137500, 43923/43904 | ||
| {{mapping|701 1111 1628 1968 2425}} | | {{mapping|701 1111 1628 1968 2425}} | ||
| | | −0.0350 | ||
| 0.1078 | | 0.1078 | ||
| 6.30 | | 6.30 | ||
| Line 53: | Line 54: | ||
| 1001/1000, 1716/1715, 4096/4095, 39366/39325, 6656/6655 | | 1001/1000, 1716/1715, 4096/4095, 39366/39325, 6656/6655 | ||
| {{mapping|701 1111 1628 1968 2425 2594}} | | {{mapping|701 1111 1628 1968 2425 2594}} | ||
| | | −0.0286 | ||
| 0.0995 | | 0.0995 | ||
| 5.81 | | 5.81 | ||
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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> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| [[Quinmite]] | | [[Quinmite]] | ||
|} | |} | ||
<nowiki>* | <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]] | ||
* "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] – | * "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]] | |||