451edo: Difference between revisions

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== Theory ==

451 = 11 × 41, and 451edo shares its [[3/2|fifth]] with [[41edo]]. Unlike 41, however, 451 is only [[consistent]] to the [[7-odd-limit]], though it has a reasonable approximation up to the [[13-limit]] using the [[patent val]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], [[65625/65536]], [[703125/702464]], [[2100875/2097152]], ~~and 390625000/387420489~~ in the 7-limit; [[6250/6237]], 42592/42525, 42875/42768, 43923/43904 in the 11-limit; and [[625/624]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], 4459/4455, and 17303/17280 in the 13-limit. It [[support]]s [[tertiaseptal]], [[tertiseptisix]], and [[hemermacomp]].

451 = 11 × 41, and 451edo shares its [[3/2|fifth]] with [[41edo]]. Unlike 41, however, 451 is only [[consistent]] to the [[7-odd-limit]], though it has a reasonable approximation up to the [[13-limit]] using the [[patent val]]. The equal temperament [[tempering out|tempers out]] 390625000/387420489 ([[quartonic comma]]) in the 5-limit; [[2401/2400]], [[65625/65536]], [[703125/702464]], [[2100875/2097152]], in the 7-limit; [[6250/6237]], 42592/42525, 42875/42768, 43923/43904 in the 11-limit; and [[625/624]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], 4459/4455, and 17303/17280 in the 13-limit. It [[support]]s [[tertiaseptal]], [[tertiseptisix]], and [[hemermacomp]], providing the [[optimal patent val]] for 5-limit [[quartonic]].

=== Prime harmonics ===

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|-

| 2.3.5

| ~~{{monzo| 3 -18 11 }}~~, {{monzo| -59 5 22 }}

| 390625000/387420489, {{monzo| -59 5 22 }}

| {{mapping| 451 715 1047 }}

| -0.0294

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! Associated<br>Ratio*

! Temperaments

|-

| 1

| 17\451

| 45.23

| 250/243

| [[Quartonic]] (5-limit)

|-

| 1

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|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

[[Category:Quartonic]]

@@ Line 3: / Line 3: @@
 == Theory ==
-= 11 × 41, and 451edo shares its [[3/2|fifth]] with [[41edo]]. Unlike 41, however, 451 is only [[consistent]] to the [[7-odd-limit]], though it has a reasonable approximation up to the [[13-limit]] using the [[patent val]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], [[65625/65536]], [[703125/702464]], [[2100875/2097152]], and 390625000/387420489 in the 7-limit; [[6250/6237]], 42592/42525, 42875/42768, 43923/43904 in the 11-limit; and [[625/624]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], 4459/4455, and 17303/17280 in the 13-limit. It [[support]]s [[tertiaseptal]], [[tertiseptisix]], and [[hemermacomp]].
+= 11 × 41, and 451edo shares its [[3/2|fifth]] with [[41edo]]. Unlike 41, however, 451 is only [[consistent]] to the [[7-odd-limit]], though it has a reasonable approximation up to the [[13-limit]] using the [[patent val]]. The equal temperament [[tempering out|tempers out]] 390625000/387420489 ([[quartonic comma]]) in the 5-limit; [[2401/2400]], [[65625/65536]], [[703125/702464]], [[2100875/2097152]], in the 7-limit; [[6250/6237]], 42592/42525, 42875/42768, 43923/43904 in the 11-limit; and [[625/624]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], 4459/4455, and 17303/17280 in the 13-limit. It [[support]]s [[tertiaseptal]], [[tertiseptisix]], and [[hemermacomp]], providing the [[optimal patent val]] for 5-limit [[quartonic]].
 === Prime harmonics ===
@@ Line 23: / Line 23: @@
 |-
 | 2.3.5
-| {{monzo| 3 -18 11 }}, {{monzo| -59 5 22 }}
+| 390625000/387420489, {{monzo| -59 5 22 }}
 | {{mapping| 451 715 1047 }}
 | -0.0294
@@ Line 59: / Line 59: @@
 ! Associated<br>Ratio*
 ! Temperaments
+|-
+| 1
+| 17\451
+| 45.23
+| 250/243
+| [[Quartonic]] (5-limit)
 |-
 | 1
@@ Line 67: / Line 73: @@
 |}
 <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+[[Category:Quartonic]]