719edo: Difference between revisions

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== Theory ==

719edo is only [[consistent]] to the [[3-odd-limit]] and the error of its [[harmonic]] [[3/1|3]] is quite large. Its harmonics [[5/1|5]] and [[7/1|7]] are also about halfway its steps. It can be used in the 2.9.15.21.11.17.19.23.29 [[subgroup]], [[temper out|tempering out]] [[1701/1700]], [[3025/3024]], [[2376/2375]], 8625/8624, 21888/21875, 72171/72128, 2001/2000 and 116127/116000~~. It [[support]]s [[marfifths]]~~.

719edo is only [[consistent]] to the [[3-odd-limit]] and the error of its [[harmonic]] [[3/1|3]] is quite large. Its harmonics [[5/1|5]] and [[7/1|7]] are also about halfway between its steps. Its distinction, however, is that it is the largest EDO to temper out the [[15625/15552|kleisma (15625/15552)]] and therefore [[support]] [[hanson]] in its patent val; it also supports the extension [[marfifths]] that tempers out the hemimage comma, [[10976/10935]] in addition, and in fact is the [[optimal patent val]] for marfifths. For other purposes than tempering out the kleisma, it can be used in the 2.9.15.21.11.17.19.23.29 [[subgroup]], [[temper out|tempering out]] [[1701/1700]], [[3025/3024]], [[2376/2375]], 8625/8624, 21888/21875, 72171/72128, 2001/2000 and 116127/116000.

=== Odd harmonics ===

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== Regular temperament properties ==

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

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

|-

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

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

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

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

! rowspan="2" |Optimal<br>8ve ~~Stretch~~ (¢)

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

! colspan="2" |Tuning ~~Error~~

! rowspan="2" | Optimal<br />8ve stretch (¢)

|-

! colspan="2" | Tuning error

![[TE error|Absolute]] (¢)

|-

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

! [[TE error|Absolute]] (¢)

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

|-

| 2.9

| {{monzo|-2279 719}}

| {{mapping|719 2279}}

| 0.0464

| +0.0464

| 0.0464

| 2.78

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|719}}
+{{ED intro}}
 == Theory ==
-edo is only [[consistent]] to the [[3-odd-limit]] and the error of its [[harmonic]] [[3/1|3]] is quite large. Its harmonics [[5/1|5]] and [[7/1|7]] are also about halfway its steps. It can be used in the 2.9.15.21.11.17.19.23.29 [[subgroup]], [[temper out|tempering out]] [[1701/1700]], [[3025/3024]], [[2376/2375]], 8625/8624, 21888/21875, 72171/72128, 2001/2000 and 116127/116000. It [[support]]s [[marfifths]].
+edo is only [[consistent]] to the [[3-odd-limit]] and the error of its [[harmonic]] [[3/1|3]] is quite large. Its harmonics [[5/1|5]] and [[7/1|7]] are also about halfway between its steps. Its distinction, however, is that it is the largest EDO to temper out the [[15625/15552|kleisma (15625/15552)]] and therefore [[support]] [[hanson]] in its patent val; it also supports the extension [[marfifths]] that tempers out the hemimage comma, [[10976/10935]] in addition, and in fact is the [[optimal patent val]] for marfifths. For other purposes than tempering out the kleisma, it can be used in the 2.9.15.21.11.17.19.23.29 [[subgroup]], [[temper out|tempering out]] [[1701/1700]], [[3025/3024]], [[2376/2375]], 8625/8624, 21888/21875, 72171/72128, 2001/2000 and 116127/116000.
 === Odd harmonics ===
@@ Line 13: / Line 13: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" |[[Subgroup]]
+|-
-! rowspan="2" |[[Comma list|Comma List]]
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" |[[Mapping]]
+! rowspan="2" | [[Comma list]]
-! rowspan="2" |Optimal<br>8ve Stretch (¢)
+! rowspan="2" | [[Mapping]]
-! colspan="2" |Tuning Error
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-|-
+! colspan="2" | Tuning error
-![[TE error|Absolute]] (¢)
+|-
-![[TE simple badness|Relative]] (%)
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
 |-
 | 2.9
 | {{monzo|-2279 719}}
 | {{mapping|719 2279}}
-| 0.0464
+| +0.0464
 | 0.0464
 | 2.78