571edo: Difference between revisions

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~~{{novelty}}{{stub}}~~{{Infobox ET}}

== Theory ==

~~571edo~~ [[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 ===

571edo is the 105th [[prime edo]].

~~=== Prime harmonics ===~~

~~{{Harmonics in equal|571|columns=11}}~~

== 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 }}

| [{{~~val~~| 571 905 }}]

| {{mapping| 571 905 }}

| +0.0090

| 0.0090

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| 2.3.5

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

| [{{~~val~~| 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

| [{{~~val~~| 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

| [{{~~val~~| 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

| [{{~~val~~| 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

| [{{~~val~~| 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 ~~Octave~~

|-

! Generator~~ (Reduced)~~

! Periods per 8ve

! Cents~~ (Reduced)~~

! Generator*

! Associated ~~Ratio~~

! Cents*

! Associated ratio*

! Temperaments

|-

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| [[Maviloid]]

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|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:~~Equal divisions of the octave|###]] ~~

[[Category:Listen]]

~~[[Category:Prime EDO~~]]

[[Category:Quasiorwell]]

@@ Line 1: / Line 1: @@
-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-{{EDO intro|571}}
+{{ED intro}}
 == Theory ==
-edo [[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}}
+=== Subsets and supersets ===
 edo is the 105th [[prime edo]].
-=== Prime harmonics ===
-{{Harmonics in equal|571|columns=11}}
 == 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 25: @@
 | 2.3
 | {{monzo| -905 571 }}
-| [{{val| 571 905 }}]
+| {{mapping| 571 905 }}
 | +0.0090
 | 0.0090
@@ Line 30: / Line 32: @@
 | 2.3.5
 | {{monzo| 8 14 -13 }}, {{monzo| -69 45 -1 }}
-| [{{val| 571 905 1326 }}]
+| {{mapping| 571 905 1326 }}
-| -0.0480
+| −0.0480
 | 0.0810
 | 3.85
@@ Line 37: / Line 39: @@
 | 2.3.5.7
 | 2401/2400, 14348907/14336000, 29360128/29296875
-| [{{val| 571 905 1326 1603 }}]
+| {{mapping| 571 905 1326 1603 }}
-| -0.0361
+| −0.0361
 | 0.0731
 | 3.48
@@ Line 44: / Line 46: @@
 | 2.3.5.7.11
 | 2401/2400, 3025/3024, 5632/5625, 14348907/14336000
-| [{{val| 571 905 1326 1603 1975 }}]
+| {{mapping| 571 905 1326 1603 1975 }}
 | +0.0119
 | 0.1161
@@ Line 51: / Line 53: @@
 | 2.3.5.7.11.13
 | 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653
-| [{{val| 571 905 1326 1603 1975 2113 }}]
+| {{mapping| 571 905 1326 1603 1975 2113 }}
 | +0.0053
 | 0.1070
@@ Line 58: / Line 60: @@
 | 2.3.5.7.11.13.17
 | 1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095
-| [{{val| 571 905 1326 1603 1975 2113 2334 }}]
+| {{mapping| 571 905 1326 1603 1975 2113 2334 }}
 | +0.0002
 | 0.0999
@@ Line 66: / 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 Octave
+|-
-! Generator<br>(Reduced)
+! Periods<br />per 8ve
-! Cents<br>(Reduced)
+! Generator*
-! Associated<br>Ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 103: / Line 106: @@
 | [[Maviloid]]
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|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:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Listen]]
-[[Category:Prime EDO]]
 [[Category:Quasiorwell]]