469edo: Difference between revisions

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== Theory ==

469et is only consistent to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is quite large. It can be considered for the 2.9.5.7.13.17 [[subgroup]], tempering out [[2601/2600]], 7616/7605, [[5832/5831]], 60112/60025 and 265625/264992. It [[support]]s [[gravity]] and [[french decimal]].

469et is only [[consistent]] to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is quite large. It can be considered for the 2.9.5.7.13.17 [[subgroup]], tempering out [[2601/2600]], 7616/7605, [[5832/5831]], 60112/60025 and 265625/264992. It [[support]]s [[gravity]] and [[french decimal]].

=== Odd harmonics ===

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=== Subsets and supersets ===

469 factors into 7 × 67, ~~with~~ [[7edo]] and [[67edo]] as its subset edos. [[938edo]], which doubles it, gives a good correction to the harmonics 3 and 5.

Since 469 factors into 7 × 67, 469edo has [[7edo]] and [[67edo]] as its subset edos. [[938edo]], which doubles it, gives a good correction to the harmonics 3 and 5.

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" |[[Subgroup]]

! rowspan="2" | [[Subgroup]]

! rowspan="2" |[[Comma list|Comma List]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" |[[Mapping]]

! 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 error|Absolute]] (¢)

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

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

|-

|2.9

| 2.9

|{{monzo|1487 -469}}

| {{monzo| 1487 -469 }}

|{{mapping|469 1487}}

| {{mapping| 469 1487 }}

| -0.1232

| 0.1232

| 4.82

|-

|2.9.5

| 2.9.5

|{{monzo|38 -1 -15}}, {{monzo|13 -29 34}}

| {{monzo| 38 -1 -15 }}, {{monzo| 13 -29 34 }}

|{{mapping|469 1487 1089}}

| {{mapping| 469 1487 1089 }}

| -0.0879

| 0.1122

| 4.39

|}

@@ Line 3: / Line 3: @@
 == Theory ==
-et is only consistent to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is quite large. It can be considered for the 2.9.5.7.13.17 [[subgroup]], tempering out [[2601/2600]], 7616/7605, [[5832/5831]], 60112/60025 and 265625/264992. It [[support]]s [[gravity]] and [[french decimal]].
+et is only [[consistent]] to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is quite large. It can be considered for the 2.9.5.7.13.17 [[subgroup]], tempering out [[2601/2600]], 7616/7605, [[5832/5831]], 60112/60025 and 265625/264992. It [[support]]s [[gravity]] and [[french decimal]].
 === Odd harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-factors into 7 × 67, with [[7edo]] and [[67edo]] as its subset edos. [[938edo]], which doubles it, gives a good correction to the harmonics 3 and 5.
+Since 469 factors into 7 × 67, 469edo has [[7edo]] and [[67edo]] as its subset edos. [[938edo]], which doubles it, gives a good correction to the harmonics 3 and 5.
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" |[[Subgroup]]
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" |[[Comma list|Comma List]]
+! rowspan="2" | [[Comma list|Comma List]]
-! rowspan="2" |[[Mapping]]
+! 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 error|Absolute]] (¢)
-![[TE simple badness|Relative]] (%)
+! [[TE simple badness|Relative]] (%)
 |-
-|2.9
+| 2.9
-|{{monzo|1487 -469}}
+| {{monzo| 1487 -469 }}
-|{{mapping|469 1487}}
+| {{mapping| 469 1487 }}
 | -0.1232
 | 0.1232
 | 4.82
 |-
-|2.9.5
+| 2.9.5
-|{{monzo|38 -1 -15}}, {{monzo|13 -29 34}}
+| {{monzo| 38 -1 -15 }}, {{monzo| 13 -29 34 }}
-|{{mapping|469 1487 1089}}
+| {{mapping| 469 1487 1089 }}
 | -0.0879
 | 0.1122
 | 4.39
 |}