701edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 32: | Line 24: | ||
| {{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 31: | ||
| 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 38: | ||
| 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 45: | ||
| 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 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 72: | Line 58: | ||
| [[25/21]] | | [[25/21]] | ||
| [[Quinmite]] | | [[Quinmite]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Don't Fancy Cooking Jonathan?" from ''Questions'' (2024) | * "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 | ||
[[Category:Listen]] | |||
Revision as of 02:32, 16 November 2024
| ← 700edo | 701edo | 702edo → |
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. 701edo supports zisa and quinmite.
Prime harmonics
| 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
Template:Comma basis begin |- | 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 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 177\701 | 302.996 | 25/21 | Quinmite Template:Rank-2 end Template:Orf