113edo: Difference between revisions

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113edo is [[consistency|distinctly consistent]] in the [[13-odd-limit]] with a flat tendency. As an equal temperament, it [[tempering out|tempers out]] the [[amity comma]] and the [[ampersand comma]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and 1071875/1062882 in the [[7-limit]]; [[243/242]], [[385/384]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[325/324]], [[364/363]], [[729/728]], and 1625/1617 in the [[13-limit]]. It notably [[support]]s the 5-limit [[amity]] temperament, 7-limit [[amicable]] temperament, 7- and 11-limit [[miracle]] temperament, and 13-limit [[manna]] temperament.

113edo ~~might be~~ notable as a no-fives system, where it is consistent in the [[29-odd-limit]] (nearly the [[33-odd-limit]], as only [[31/21]] and its complement are inconsistent, being 50.8% off) and serves as a nearly optimal tuning for [[slendric]], in particular a 2.3.7.13.17.29 extension of slendric harmonies known as [[euslendric]].

113edo is also notable as a no-fives [[31-limit]] system, where it is consistent in the [[29-odd-limit]], and nearly the [[33-odd-limit]], as only [[31/21]] and its complement are inconsistent, being 50.8% off - and serves as a nearly optimal tuning for [[slendric]], in particular a 2.3.7.13.17(.19.23).29 extension of slendric harmonies known as [[euslendric]].

=== Prime harmonics ===

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| 27/25

| [[Quartemka]]

|-

| 1

| 20\113

| 212.39

| 26/23

| [[Shoal]]

|-

| 1

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| 233.63

| 8/7

| [[Slendric]]

| [[Slendric]] / [[euslendric]]

|-

| 1

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Line 136:

| 1

| 34\113

| ~~360~~.06

| 361.06

| 16/13

| [[Phicordial]]

@@ Line 5: / Line 5: @@
 edo is [[consistency|distinctly consistent]] in the [[13-odd-limit]] with a flat tendency. As an equal temperament, it [[tempering out|tempers out]] the [[amity comma]] and the [[ampersand comma]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and 1071875/1062882 in the [[7-limit]]; [[243/242]], [[385/384]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[325/324]], [[364/363]], [[729/728]], and 1625/1617 in the [[13-limit]]. It notably [[support]]s the 5-limit [[amity]] temperament, 7-limit [[amicable]] temperament, 7- and 11-limit [[miracle]] temperament, and 13-limit [[manna]] temperament.
-edo might be notable as a no-fives system, where it is consistent in the [[29-odd-limit]] (nearly the [[33-odd-limit]], as only [[31/21]] and its complement are inconsistent, being 50.8% off) and serves as a nearly optimal tuning for [[slendric]], in particular a 2.3.7.13.17.29 extension of slendric harmonies known as [[euslendric]].
+edo is also notable as a no-fives [[31-limit]] system, where it is consistent in the [[29-odd-limit]], and nearly the [[33-odd-limit]], as only [[31/21]] and its complement are inconsistent, being 50.8% off - and serves as a nearly optimal tuning for [[slendric]], in particular a 2.3.7.13.17(.19.23).29 extension of slendric harmonies known as [[euslendric]].
 === Prime harmonics ===
@@ Line 103: / Line 103: @@
 | 27/25
 | [[Quartemka]]
+|-
+| 1
+| 20\113
+| 212.39
+| 26/23
+| [[Shoal]]
 |-
 | 1
@@ Line 108: / Line 114: @@
 | 233.63
 | 8/7
-| [[Slendric]]
+| [[Slendric]] / [[euslendric]]
 |-
 | 1
@@ Line 130: / Line 136: @@
 | 1
 | 34\113
-| 360.06
+| 361.06
 | 16/13
 | [[Phicordial]]