72edo: Difference between revisions

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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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72edo provides the [[optimal patent val]] for [[miracle]] and [[wizard]] in the 7-limit, miracle, [[catakleismic]], [[bikleismic]], [[compton]], [[ennealimnic]], [[ennealiminal]], [[enneaportent]], [[marvolo]] and [[catalytic]] in the 11-limit, and catakleismic, bikleismic, compton, [[comptone]], [[enneaportent]], [[ennealim]], catalytic, marvolo, [[manna]], [[hendec]], [[lizard]], [[neominor]], [[hours]], and [[semimiracle]] in the 13-limit.

{| class="wikitable center-all ~~right-3~~ left-5"

{| class="wikitable center-all left-5"

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! ~~Temperaments~~

! Temperament

|-

| 1

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| [[Decades]]

|}

<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 it is distinct

== Scales ==

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=== Harmonic scale ===

Mode 8 of the harmonic series – [[overtone scale|harmonics 8 through 16]], octave repeating – is well-represented in 72edo. Note that all the different step sizes are distinguished, except for 13:12 and 14:13 (conflated to 8\72edo, 133.3 cents) and 15:14 and 16:15 (conflated to 7\72edo, 116.7 cents, the generator for miracle temperament).

Mode 8 of the harmonic series—[[overtone scale|harmonics 8 through 16]], octave repeating—is well-represented in 72edo. Note that all the different step sizes are distinguished, except for 13:12 and 14:13 (conflated to 8\72edo, 133.3 cents) and 15:14 and 16:15 (conflated to 7\72edo, 116.7 cents, the generator for miracle temperament).

{| class="wikitable"

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; [[Claudi Meneghin]]

* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']{{dead link}}

* [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]

* [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']

@@ Line 1,011: / Line 1,011: @@
 == 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 1,283: / Line 1,284: @@
 edo provides the [[optimal patent val]] for [[miracle]] and [[wizard]] in the 7-limit, miracle, [[catakleismic]], [[bikleismic]], [[compton]], [[ennealimnic]], [[ennealiminal]], [[enneaportent]], [[marvolo]] and [[catalytic]] in the 11-limit, and catakleismic, bikleismic, compton, [[comptone]], [[enneaportent]], [[ennealim]], catalytic, marvolo, [[manna]], [[hendec]], [[lizard]], [[neominor]], [[hours]], and [[semimiracle]] in the 13-limit.
-{| class="wikitable center-all right-3 left-5"
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
 |-
 ! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br />Ratio*
+! Associated<br />ratio*
-! Temperaments
+! Temperament
 |-
 | 1
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 | [[Decades]]
 |}
-<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 it is distinct
 == Scales ==
@@ Line 1,454: / Line 1,456: @@
 === Harmonic scale ===
-Mode 8 of the harmonic series – [[overtone scale|harmonics 8 through 16]], octave repeating – is well-represented in 72edo. Note that all the different step sizes are distinguished, except for 13:12 and 14:13 (conflated to 8\72edo, 133.3 cents) and 15:14 and 16:15 (conflated to 7\72edo, 116.7 cents, the generator for miracle temperament).
+Mode 8 of the harmonic series&mdash;[[overtone scale|harmonics 8 through 16]], octave repeating&mdash;is well-represented in 72edo. Note that all the different step sizes are distinguished, except for 13:12 and 14:13 (conflated to 8\72edo, 133.3 cents) and 15:14 and 16:15 (conflated to 7\72edo, 116.7 cents, the generator for miracle temperament).
 {| class="wikitable"
@@ Line 1,650: / Line 1,652: @@
 ; [[Claudi Meneghin]]
-* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']{{dead link}}
+* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon &ndash; 72 edo'']{{dead link}}
 * [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]
 * [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']