444edo: Difference between revisions

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== Theory ==

444edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. 444 = 4 × 111, ~~and~~ its harmonic [[3/1|3]] derives from [[111edo]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[250047/250000]], 29360128/29296875, 67108864/66976875 and in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, 172032/171875, 322102/321489, 391314/390625 and [[1771561/1769472]] in the 11-limit. It [[support]]s the [[magnesium]] temperament.

444edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. Since {{nowrap|444 {{=}} 4 × 111}}, its harmonic [[3/1|3]] derives from [[111edo]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[250047/250000]], 29360128/29296875, 67108864/66976875 and in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, 172032/171875, 322102/321489, 391314/390625 and [[1771561/1769472]] in the 11-limit. It [[support]]s the [[magnesium]] temperament.

=== Odd harmonics ===

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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]] (¢)

! [[TE simple badness|Relative]] (%)

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| {{monzo| 41 -20 -4 }}, {{monzo| -29 -11 20 }}

| {{mapping| 444 704 1031 }}

| -0.1821

| −0.1821

| 0.2071

| 7.66

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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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| [[Undim]] (444d)

|}

<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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|444}}
+{{ED intro}}
 == Theory ==
-edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. 444 = 4 × 111, and its harmonic [[3/1|3]] derives from [[111edo]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[250047/250000]], 29360128/29296875, 67108864/66976875 and in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, 172032/171875, 322102/321489, 391314/390625 and [[1771561/1769472]] in the 11-limit. It [[support]]s the [[magnesium]] temperament.
+edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. Since {{nowrap|444 {{=}} 4 × 111}}, its harmonic [[3/1|3]] derives from [[111edo]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[250047/250000]], 29360128/29296875, 67108864/66976875 and in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, 172032/171875, 322102/321489, 391314/390625 and [[1771561/1769472]] in the 11-limit. It [[support]]s the [[magnesium]] temperament.
 === Odd harmonics ===
@@ 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]] (¢)
 ! [[TE simple badness|Relative]] (%)
@@ Line 25: / Line 26: @@
 | {{monzo| 41 -20 -4 }}, {{monzo| -29 -11 20 }}
 | {{mapping| 444 704 1031 }}
-| -0.1821
+| −0.1821
 | 0.2071
 | 7.66
@@ Line 32: / Line 33: @@
 === 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 51: / Line 53: @@
 | [[Undim]] (444d)
 |}
-<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