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}}
{{EDO intro}}
{{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 [[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 ===
=== Prime harmonics ===
Line 33: Line 33:
| {{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
| −0.0596
| 0.1316
| 0.1316
| 7.69
| 7.69
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| 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
| −0.0514
| 0.1149
| 0.1149
| 6.71
| 6.71
Line 47: 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
| −0.0350
| 0.1078
| 0.1078
| 6.30
| 6.30
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| 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
| −0.0286
| 0.0995
| 0.0995
| 5.81
| 5.81
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| [[Quinmite]]
| [[Quinmite]]
|}
|}
<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 ==
== Music ==
; [[Francium]]
; [[Francium]]
* "Don't Fancy Cooking Jonathan?" from ''Questions'' (2024) &ndash; [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] &ndash; 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) &ndash; [https://open.spotify.com/track/48K7FpEbJrCL6bZz5FoAuT Spotify] | [https://francium223.bandcamp.com/track/fluffy-spider-silk Bandcamp] | [https://www.youtube.com/watch?v=eIskpXFHhB0 YouTube]
* "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]]
[[Category:Listen]]

Latest revision as of 13:32, 13 March 2026

← 700edo 701edo 702edo →
Prime factorization 701 (prime)
Step size 1.71184 ¢ 
Fifth 410\701 (701.854 ¢)
Semitones (A1:m2) 66:53 (113 ¢ : 90.73 ¢)
Consistency limit 15
Distinct consistency limit 15

701 equal divisions of the octave (abbreviated 701edo or 701ed2), also called 701-tone equal temperament (701tet) or 701 equal temperament (701et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 701 equal parts of about 1.71 ¢ each. Each step represents a frequency ratio of 21/701, or the 701st root of 2.

Theory

701edo is consistent to the 15-odd-limit. The equal temperament tempers out 2401/2400, 1959552/1953125 and [-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 supports zisa and quinmite.

Prime harmonics

Approximation of prime harmonics in 701edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.101 +0.562 +0.076 -0.105 -0.014 -0.533 +0.347 -0.029 -0.761 +0.186
Relative (%) +0.0 -5.9 +32.8 +4.4 -6.2 -0.8 -31.1 +20.3 -1.7 -44.5 +10.8
Steps
(reduced) 		701
(0) 		1111
(410) 		1628
(226) 		1968
(566) 		2425
(322) 		2594
(491) 		2865
(61) 		2978
(174) 		3171
(367) 		3405
(601) 		3473
(669)

Subsets and supersets

701edo is the 126th prime EDO.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [-1111 701⟩ [⟨701 1111]] +0.0317 0.0317 1.85
2.3.5 [-22 30 -11⟩, [55 -1 -23⟩ [⟨701 1111 1628]] −0.0596 0.1316 7.69
2.3.5.7 2401/2400, 1959552/1953125, [-29 23 -2 -1⟩ [⟨701 1111 1628 1968]] −0.0514 0.1149 6.71
2.3.5.7.11 5632/5625, 2401/2400, 137781/137500, 43923/43904 [⟨701 1111 1628 1968 2425]] −0.0350 0.1078 6.30
2.3.5.7.11.13 1001/1000, 1716/1715, 4096/4095, 39366/39325, 6656/6655 [⟨701 1111 1628 1968 2425 2594]] −0.0286 0.0995 5.81

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 177\701 302.996 25/21 Quinmite

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

Music

Francium
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