612edo: Difference between revisions

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=== Prime harmonics ===

== Regular temperament properties ==

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

! rowspan="2" | Subgroup

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

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

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

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

! rowspan="2" | Optimal 8ve ~~stretch~~ (¢)

! rowspan="2" | Optimal 8ve Stretch (¢)

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

! colspan="2" | Tuning Error

|-

! [[TE error|Absolute]] (¢)

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| 4.68

|}

612et has a lower relative error than any previous equal temperaments in the 5-limit. Not until [[1171edo|1171]] do we find a better equal temperament in terms of either absolute error or relative error. Besides, it has a lower absolute error in the 7- and 11-limit than any previous equal temperaments, and is only bettered by [[935edo|935]] and [[836edo|836]], respectively.

* 612et has a lower relative error than any previous equal temperaments in the 5-limit. Not until [[1171edo|1171]] do we find a better equal temperament in terms of either absolute error or relative error.

* Besides, it has a lower absolute error in the 7- and 11-limit than any previous equal temperaments, and is only bettered by [[935edo|935]] and [[836edo|836]], respectively.

=== Rank-2 temperaments ===

{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

! Periods per ~~octave~~

! Periods per 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperaments

|-

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| 1125/1024

| [[Kwazy]]

|-

| 4

| 194\612 (41\612)

| 380.39 (80.39)

| 81/65 (22/21)

| [[Quasithird]]

|-

| 9

@@ Line 8: / Line 8: @@
 === Prime harmonics ===
-{{Harmonics in equal|612}}
+{{Harmonics in equal|612|columns=11}}
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Comma list|Comma List]]
 ! 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]] (¢)
@@ Line 56: / Line 56: @@
 | 4.68
 |}
-et has a lower relative error than any previous equal temperaments in the 5-limit. Not until [[1171edo|1171]] do we find a better equal temperament in terms of either absolute error or relative error. Besides, it has a lower absolute error in the 7- and 11-limit than any previous equal temperaments, and is only bettered by [[935edo|935]] and [[836edo|836]], respectively.
+* 612et has a lower relative error than any previous equal temperaments in the 5-limit. Not until [[1171edo|1171]] do we find a better equal temperament in terms of either absolute error or relative error.
+* Besides, it has a lower absolute error in the 7- and 11-limit than any previous equal temperaments, and is only bettered by [[935edo|935]] and [[836edo|836]], respectively.
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per octave
+! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-
@@ Line 84: / Line 85: @@
 | 1125/1024
 | [[Kwazy]]
+|-
+| 4
+| 194\612<br>(41\612)
+| 380.39<br>(80.39)
+| 81/65<br>(22/21)
+| [[Quasithird]]
 |-
 | 9