335edo: Difference between revisions

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== Theory ==

335edo only is [[consistent]] to the [[5-odd-limit]]. ~~The equal temperament~~ [[~~tempering out|~~tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]), and is a quite efficient [[5-limit]] system.

335edo only is [[consistent]] to the [[5-odd-limit]]. It [[tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]), and is a quite efficient [[5-limit]] system.

The 335d [[val]] ({{val| 335 531 778 '''941''' 1159 1240 }}), which scores the best, tempers out [[6144/6125]], [[16875/16807]] and [[14348907/14336000]] in the 7-limit; [[540/539]], 1375/1372, [[3025/3024]], [[5632/5625]] in the 11-limit; and [[729/728]], [[2080/2079]], [[2200/2197]], and [[6656/6655]] in the 13-limit. It [[support]]s [[grendel]].

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=== Subsets and supersets ===

Since 335 factors into ~~5 × 67~~, 335edo has [[5edo]] and [[67edo]] as its subsets. [[670edo]], which doubles it, gives a good correction to the harmonic 7.

Since 335 factors into {{factorisation|335}}, 335edo has [[5edo]] and [[67edo]] as its subsets. [[670edo]], which doubles it, gives a good correction to the harmonic 7.

== Regular temperament properties ==

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| {{monzo| 531 -335 }}

| {{mapping| 335 531 }}

| ~~−0~~.0424

| −0.0424

| 0.0424

| 1.18

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| {{monzo| 8 14 -13 }}, {{monzo| 47 -15 -10 }}

| {{mapping| 335 531 778 }}

| ~~−0~~.1075

| −0.1075

| 0.0984

| 2.75

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| [[Quintosec]]

|}

<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 3: / Line 3: @@
 == Theory ==
-edo only is [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out|tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]), and is a quite efficient [[5-limit]] system.
+edo only is [[consistent]] to the [[5-odd-limit]]. It [[tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]), and is a quite efficient [[5-limit]] system.
 The 335d [[val]] ({{val| 335 531 778 '''941''' 1159 1240 }}), which scores the best, tempers out [[6144/6125]], [[16875/16807]] and [[14348907/14336000]] in the 7-limit; [[540/539]], 1375/1372, [[3025/3024]], [[5632/5625]] in the 11-limit; and [[729/728]], [[2080/2079]], [[2200/2197]], and [[6656/6655]] in the 13-limit. It [[support]]s [[grendel]].
@@ Line 13: / Line 13: @@
 === Subsets and supersets ===
-Since 335 factors into 5 × 67, 335edo has [[5edo]] and [[67edo]] as its subsets. [[670edo]], which doubles it, gives a good correction to the harmonic 7.
+Since 335 factors into {{factorisation|335}}, 335edo has [[5edo]] and [[67edo]] as its subsets. [[670edo]], which doubles it, gives a good correction to the harmonic 7.
 == Regular temperament properties ==
@@ Line 30: / Line 30: @@
 | {{monzo| 531 -335 }}
 | {{mapping| 335 531 }}
-| &minus;0.0424
+| −0.0424
 | 0.0424
 | 1.18
@@ Line 37: / Line 37: @@
 | {{monzo| 8 14 -13 }}, {{monzo| 47 -15 -10 }}
 | {{mapping| 335 531 778 }}
-| &minus;0.1075
+| −0.1075
 | 0.0984
 | 2.75
@@ Line 76: / Line 76: @@
 | [[Quintosec]]
 |}
-<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