444edo: Difference between revisions

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== Theory ==

~~444et~~ is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. 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. 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.

=== Odd harmonics ===

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! [[TE error|Absolute]] (¢)

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

|-

~~| 2.3~~

~~| {{monzo| 176 -111 }}~~

~~| {{mapping| 444 704 }}~~

~~| -0.2359~~

~~| 0.2358~~

~~| 8.72~~

|-

| 2.3.5

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| 497.30<br>(102.70)

| 4/3<br>(35/33)

| [[Undim]]

| [[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

@@ Line 3: / Line 3: @@
 == Theory ==
-et is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. 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. 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.
 === Odd harmonics ===
@@ Line 21: / Line 21: @@
 ! [[TE error|Absolute]] (¢)
 ! [[TE simple badness|Relative]] (%)
-|-
-| 2.3
-| {{monzo| 176 -111 }}
-| {{mapping| 444 704 }}
-| -0.2359
-| 0.2358
-| 8.72
 |-
 | 2.3.5
@@ Line 56: / Line 49: @@
 | 497.30<br>(102.70)
 | 4/3<br>(35/33)
-| [[Undim]]
+| [[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