571edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
Line 32: Line 24:
| {{monzo| 8 14 -13 }}, {{monzo| -69 45 -1 }}
| {{monzo| 8 14 -13 }}, {{monzo| -69 45 -1 }}
| {{mapping| 571 905 1326 }}
| {{mapping| 571 905 1326 }}
| -0.0480
| &minus;0.0480
| 0.0810
| 0.0810
| 3.85
| 3.85
Line 39: Line 31:
| 2401/2400, 14348907/14336000, 29360128/29296875
| 2401/2400, 14348907/14336000, 29360128/29296875
| {{mapping| 571 905 1326 1603 }}
| {{mapping| 571 905 1326 1603 }}
| -0.0361
| &minus;0.0361
| 0.0731
| 0.0731
| 3.48
| 3.48
Line 63: Line 55:
| 0.0999
| 0.0999
| 4.75
| 4.75
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 103: Line 89:
| 875/648
| 875/648
| [[Maviloid]]
| [[Maviloid]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Music ==
== Music ==
; [[Francium]]
; [[Francium]]
* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] | [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] | [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]
* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) &ndash; [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] | [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] | [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]
* "LEARN TO CAR" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] | [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] | [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]
* "LEARN TO CAR" from ''CAPSLOCK'' (2024) &ndash; [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] | [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] | [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]


[[Category:Listen]]
[[Category:Quasiorwell]]
[[Category:Quasiorwell]]

Revision as of 04:30, 16 November 2024

← 570edo 571edo 572edo →
Prime factorization 571 (prime)
Step size 2.10158 ¢ 
Fifth 334\571 (701.926 ¢)
Semitones (A1:m2) 54:43 (113.5 ¢ : 90.37 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

Theory

The equal temperament tempers out the parakleisma, [8 14 -13⟩, and the counterschisma, [-69 45 -1⟩, in the 5-limit, as well as the lafa comma, [77 -31 -12⟩; 2401/2400, 14348907/14336000, and 29360128/29296875 in the 7-limit; 3025/3024, 5632/5625, 41503/41472, and 17537553/17500000 in the 11-limit; 1001/1000, 1716/1715, 4096/4095, 17303/17280, and 107811/107653 in the 13-limit, supporting the 13-limit quasiorwell temperament; 1089/1088, 1701/1700, 2431/2430, 2601/2600, 5832/5831 and 7744/7735 in the 17-limit. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log27, after 109 and before 2393.

Prime harmonics

Approximation of prime harmonics in 571edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.029 +0.376 +0.001 -0.705 +0.103 +0.123 +0.911 +0.097 +0.195 +0.323
Relative (%) +0.0 -1.4 +17.9 +0.0 -33.5 +4.9 +5.9 +43.3 +4.6 +9.3 +15.4
Steps
(reduced) 		571
(0) 		905
(334) 		1326
(184) 		1603
(461) 		1975
(262) 		2113
(400) 		2334
(50) 		2426
(142) 		2583
(299) 		2774
(490) 		2829
(545)

Subsets and supersets

571edo is the 105th prime edo.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [-905 571⟩ | [⟨571 905]] | +0.0090 | 0.0090 | 0.43 |- | 2.3.5 | [8 14 -13⟩, [-69 45 -1⟩ | [⟨571 905 1326]] | −0.0480 | 0.0810 | 3.85 |- | 2.3.5.7 | 2401/2400, 14348907/14336000, 29360128/29296875 | [⟨571 905 1326 1603]] | −0.0361 | 0.0731 | 3.48 |- | 2.3.5.7.11 | 2401/2400, 3025/3024, 5632/5625, 14348907/14336000 | [⟨571 905 1326 1603 1975]] | +0.0119 | 0.1161 | 5.53 |- | 2.3.5.7.11.13 | 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653 | [⟨571 905 1326 1603 1975 2113]] | +0.0053 | 0.1070 | 5.09 |- | 2.3.5.7.11.13.17 | 1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095 | [⟨571 905 1326 1603 1975 2113 2334]] | +0.0002 | 0.0999 | 4.75 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 123\571 | 258.49 | [-32 13 5⟩ | Lafa |- | 1 | 129\571 | 271.10 | 90/77 | Quasiorwell |- | 1 | 147\571 | 315.24 | 6/5 | Parakleismic (5-limit) |- | 1 | 237\571 | 498.07 | 4/3 | Counterschismic |- | 1 | 248\571 | 521.19 | 875/648 | Maviloid Template:Rank-2 end Template:Orf

Music

Francium
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