445edo: Difference between revisions

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== Theory ==

445edo is [[consistent]] to the [[7-odd-limit]] with [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]] all tuned flat, and it allows an extension to the [[11-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, 35937/35840, [[41503/41472]], 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably [[support]]s [[neptune]].

445edo is [[enfactoring|enfactored]] in the [[3-limit]] with the same tuning as [[89edo]], but the approximation to some of the higher harmonics are improved. It is [[consistent]] to the [[7-odd-limit]] with [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]] all tuned flat, and it allows an extension to the [[11-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, 35937/35840, [[41503/41472]], 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably [[support]]s [[neptune]].

=== Odd harmonics ===

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=== Subsets and supersets ===

445 factors into 5 × 89, ~~with~~ [[5edo]] and [[89edo]] as its ~~subset edos~~.

Since 445 factors into 5 × 89, 445edo has [[5edo]] and 89edo as its subsets.

== Regular temperament properties ==

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! [[TE error|Absolute]] (¢)

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

|-

~~| 2.3~~

~~| {{monzo| -141 89 }}~~

~~| {{mapping| 445 705 }}~~

~~| 0.2623~~

~~| 9.73~~

|-

| 2.3.5

| {{monzo| -28 25 -5 }}, {{monzo| -29 -11 20 }}

| {{mapping| 445 705 1033 }}

| 0.2748

| +0.2748

| 0.2149

| 7.97

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| 2401/2400, 7381125/7340032, 43046721/42875000

| {{mapping| 445 705 1033 1249 }}

| 0.2716

| +0.2716

| 0.1862

| 6.90

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| 2401/2400, 3025/3024, 8019/8000, 234375/234256

| {{mapping| 445 705 1033 1249 1539 }}

| 0.2870

| +0.2870

| 0.1694

| 6.28

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is [[consistent]] to the [[7-odd-limit]] with [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]] all tuned flat, and it allows an extension to the [[11-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, 35937/35840, [[41503/41472]], 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably [[support]]s [[neptune]].
+edo is [[enfactoring|enfactored]] in the [[3-limit]] with the same tuning as [[89edo]], but the approximation to some of the higher harmonics are improved. It is [[consistent]] to the [[7-odd-limit]] with [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]] all tuned flat, and it allows an extension to the [[11-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, 35937/35840, [[41503/41472]], 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably [[support]]s [[neptune]].
 === Odd harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-factors into 5 × 89, with [[5edo]] and [[89edo]] as its subset edos.
+Since 445 factors into 5 × 89, 445edo has [[5edo]] and 89edo as its subsets.
 == Regular temperament properties ==
@@ Line 21: / Line 21: @@
 ! [[TE error|Absolute]] (¢)
 ! [[TE simple badness|Relative]] (%)
-|-
-| 2.3
-| {{monzo| -141 89 }}
-| {{mapping| 445 705 }}
-| 0.2623
-| 0.2623
-| 9.73
 |-
 | 2.3.5
 | {{monzo| -28 25 -5 }}, {{monzo| -29 -11 20 }}
 | {{mapping| 445 705 1033 }}
-| 0.2748
+| +0.2748
 | 0.2149
 | 7.97
@@ Line 39: / Line 32: @@
 | 2401/2400, 7381125/7340032, 43046721/42875000
 | {{mapping| 445 705 1033 1249 }}
-| 0.2716
+| +0.2716
 | 0.1862
 | 6.90
@@ Line 46: / Line 39: @@
 | 2401/2400, 3025/3024, 8019/8000, 234375/234256
 | {{mapping| 445 705 1033 1249 1539 }}
-| 0.2870
+| +0.2870
 | 0.1694
 | 6.28