571edo: Difference between revisions

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== Theory ==

~~The equal temperament~~ [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}, and the [[counterschisma]], {{monzo| -69 45 -1 }}, in the [[5-limit]], as well as the lafa comma, {{monzo| 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 [[109edo|109]] and before [[2393edo|2393]].

571et [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}, and the [[counterschisma]], {{monzo| -69 45 -1 }}, in the [[5-limit]], as well as the lafa comma, {{monzo| 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 [[109edo|109]] and before [[2393edo|2393]].

=== Prime harmonics ===

=== Subsets and supersets ===

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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" | [[Comma list]]

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

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

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

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

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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| {{monzo| 8 14 -13 }}, {{monzo| -69 45 -1 }}

| {{mapping| 571 905 1326 }}

| -0.0480

| −0.0480

| 0.0810

| 3.85

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| 2401/2400, 14348907/14336000, 29360128/29296875

| {{mapping| 571 905 1326 1603 }}

| -0.0361

| −0.0361

| 0.0731

| 3.48

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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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| [[Maviloid]]

|}

<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 lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

== Music ==

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* "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]

* "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]

* "George Crispell" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/3mZBLdkeEvHYMDgmHNJu4H Spotify] | [https://francium223.bandcamp.com/track/george-crispell Bandcamp] | [https://www.youtube.com/watch?v=I7SdSaP1UJs YouTube] − in Gentic, 571edo tuning

[[Category:Listen]]

[[Category:Quasiorwell]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|571}}
+{{ED intro}}
 == Theory ==
-The equal temperament [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}, and the [[counterschisma]], {{monzo| -69 45 -1 }}, in the [[5-limit]], as well as the lafa comma, {{monzo| 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 log<sub>2</sub>7, after [[109edo|109]] and before [[2393edo|2393]].
+et [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}, and the [[counterschisma]], {{monzo| -69 45 -1 }}, in the [[5-limit]], as well as the lafa comma, {{monzo| 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 log<sub>2</sub>7, after [[109edo|109]] and before [[2393edo|2393]].
 === Prime harmonics ===
-{{Harmonics in equal|571|columns=11}}
+{{Harmonics in equal|571}}
 === Subsets and supersets ===
@@ 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" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 32: / Line 33: @@
 | {{monzo| 8 14 -13 }}, {{monzo| -69 45 -1 }}
 | {{mapping| 571 905 1326 }}
-| -0.0480
+| −0.0480
 | 0.0810
 | 3.85
@@ Line 39: / Line 40: @@
 | 2401/2400, 14348907/14336000, 29360128/29296875
 | {{mapping| 571 905 1326 1603 }}
-| -0.0361
+| −0.0361
 | 0.0731
 | 3.48
@@ Line 67: / Line 68: @@
 === 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 104: / Line 106: @@
 | [[Maviloid]]
 |}
-<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 lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 == Music ==
@@ Line 110: / Line 112: @@
 * "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]
 * "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]
+* "George Crispell" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/3mZBLdkeEvHYMDgmHNJu4H Spotify] | [https://francium223.bandcamp.com/track/george-crispell Bandcamp] | [https://www.youtube.com/watch?v=I7SdSaP1UJs YouTube] − in Gentic, 571edo tuning
+[[Category:Listen]]
 [[Category:Quasiorwell]]