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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|-

| 2.3

| {{~~monzo~~| -905 571 }}

| {{Monzo| -905 571 }}

| {{~~mapping~~| 571 905 }}

| {{Mapping| 571 905 }}

| +0.0090

| 0.0090

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|-

| 2.3.5

| {{~~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

| −0.0480

| 0.0810

| 3.85

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| 2.3.5.7

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

| {{~~mapping~~| 571 905 1326 1603 }}

| {{Mapping| 571 905 1326 1603 }}

| -0.0361

| −0.0361

| 0.0731

| 3.48

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| 2.3.5.7.11

| 2401/2400, 3025/3024, 5632/5625, 14348907/14336000

| {{~~mapping~~| 571 905 1326 1603 1975 }}

| {{Mapping| 571 905 1326 1603 1975 }}

| +0.0119

| 0.1161

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| 2.3.5.7.11.13

| 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653

| {{~~mapping~~| 571 905 1326 1603 1975 2113 }}

| {{Mapping| 571 905 1326 1603 1975 2113 }}

| +0.0053

| 0.1070

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| 2.3.5.7.11.13.17

| 1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095

| {{~~mapping~~| 571 905 1326 1603 1975 2113 2334 }}

| {{Mapping| 571 905 1326 1603 1975 2113 2334 }}

| +0.0002

| 0.0999

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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

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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| 123\571

| 258.49

| {{~~monzo~~| -32 13 5 }}

| {{Monzo| -32 13 5 }}

| [[Lafa]]

|-

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| 6/5

| [[Parakleismic]] (5-limit)

|-

| 1

| 187\571

| 392.99

| 2744/2187

| [[Emmthird]] (7-limit)

|-

| 1

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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 forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms|minimal form]] in parentheses if distinct

== Music ==

; [[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]

* "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 23: / Line 24: @@
 |-
 | 2.3
-| {{monzo| -905 571 }}
+| {{Monzo| -905 571 }}
-| {{mapping| 571 905 }}
+| {{Mapping| 571 905 }}
 | +0.0090
 | 0.0090
@@ Line 30: / Line 31: @@
 |-
 | 2.3.5
-| {{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
+| −0.0480
 | 0.0810
 | 3.85
@@ Line 38: / Line 39: @@
 | 2.3.5.7
 | 2401/2400, 14348907/14336000, 29360128/29296875
-| {{mapping| 571 905 1326 1603 }}
+| {{Mapping| 571 905 1326 1603 }}
-| -0.0361
+| −0.0361
 | 0.0731
 | 3.48
@@ Line 45: / Line 46: @@
 | 2.3.5.7.11
 | 2401/2400, 3025/3024, 5632/5625, 14348907/14336000
-| {{mapping| 571 905 1326 1603 1975 }}
+| {{Mapping| 571 905 1326 1603 1975 }}
 | +0.0119
 | 0.1161
@@ Line 52: / Line 53: @@
 | 2.3.5.7.11.13
 | 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653
-| {{mapping| 571 905 1326 1603 1975 2113 }}
+| {{Mapping| 571 905 1326 1603 1975 2113 }}
 | +0.0053
 | 0.1070
@@ Line 59: / Line 60: @@
 | 2.3.5.7.11.13.17
 | 1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095
-| {{mapping| 571 905 1326 1603 1975 2113 2334 }}
+| {{Mapping| 571 905 1326 1603 1975 2113 2334 }}
 | +0.0002
 | 0.0999
@@ 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
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br>ratio*
 ! Temperaments
 |-
@@ Line 77: / Line 79: @@
 | 123\571
 | 258.49
-| {{monzo| -32 13 5 }}
+| {{Monzo| -32 13 5 }}
 | [[Lafa]]
 |-
@@ Line 91: / Line 93: @@
 | 6/5
 | [[Parakleismic]] (5-limit)
+|-
+| 1
+| 187\571
+| 392.99
+| 2744/2187
+| [[Emmthird]] (7-limit)
 |-
 | 1
@@ Line 104: / Line 112: @@
 | [[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 forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms|minimal form]] in parentheses if distinct
 == Music ==
 ; [[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]
+* "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]]