113edo: Difference between revisions

Line 3:

== Theory ==

113edo is ~~distinctly~~ [[consistent]] in the [[13-odd-limit]] with a flat tendency. As a temperament, it [[tempers out]] the [[amity comma]] and the [[ampersand]] 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 is [[consistency|distinctly consistent]] in the [[13-odd-limit]] with a flat tendency. As an equal temperament, it [[tempers out]] the [[amity comma]] and the [[ampersand]] 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.

=== Prime harmonics ===

Line 27:

| 2.3

| {{monzo| -179 113 }}

| [{{~~val~~| 113 179 }}]

| {{mapping| 113 179 }}

| +0.338

| 0.338

Line 34:

| 2.3.5

| 1600000/1594323, 34171875/33554432

| [{{~~val~~| 113 179 262 }}]

| {{mapping| 113 179 262 }}

| +0.801

| 0.712

Line 41:

| 2.3.5.7

| 225/224, 1029/1024, 1071875/1062882

| [{{~~val~~| 113 179 262 317 }}]

| {{mapping| 113 179 262 317 }}

| +0.820

| 0.617

Line 48:

| 2.3.5.7.11

| 225/224, 243/242, 385/384, 980000/970299

| [{{~~val~~| 113 179 262 317 391 }}]

| {{mapping| 113 179 262 317 391 }}

| +0.604

| 0.700

Line 55:

| 2.3.5.7.11.13

| 225/224, 243/242, 325/324, 385/384, 1875/1859

| [{{~~val~~| 113 179 262 317 391 418 }}]

| {{mapping| 113 179 262 317 391 418 }}

| +0.575

| 0.643

Line 65:

|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Generator~~ (Reduced)~~

! Generator*

! Cents~~ (Reduced)~~

! Cents*

! Associated Ratio

! Associated Ratio*

! Temperaments

|-

Line 148:

| [[Gaster temperament|Gaster]]

|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is distinctly [[consistent]] in the [[13-odd-limit]] with a flat tendency. As a temperament, it [[tempers out]] the [[amity comma]] and the [[ampersand]] 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 is [[consistency|distinctly consistent]] in the [[13-odd-limit]] with a flat tendency. As an equal temperament, it [[tempers out]] the [[amity comma]] and the [[ampersand]] 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.
 === Prime harmonics ===
@@ Line 27: / Line 27: @@
 | 2.3
 | {{monzo| -179 113 }}
-| [{{val| 113 179 }}]
+| {{mapping| 113 179 }}
 | +0.338
 | 0.338
@@ Line 34: / Line 34: @@
 | 2.3.5
 | 1600000/1594323, 34171875/33554432
-| [{{val| 113 179 262 }}]
+| {{mapping| 113 179 262 }}
 | +0.801
 | 0.712
@@ Line 41: / Line 41: @@
 | 2.3.5.7
 | 225/224, 1029/1024, 1071875/1062882
-| [{{val| 113 179 262 317 }}]
+| {{mapping| 113 179 262 317 }}
 | +0.820
 | 0.617
@@ Line 48: / Line 48: @@
 | 2.3.5.7.11
 | 225/224, 243/242, 385/384, 980000/970299
-| [{{val| 113 179 262 317 391 }}]
+| {{mapping| 113 179 262 317 391 }}
 | +0.604
 | 0.700
@@ Line 55: / Line 55: @@
 | 2.3.5.7.11.13
 | 225/224, 243/242, 325/324, 385/384, 1875/1859
-| [{{val| 113 179 262 317 391 418 }}]
+| {{mapping| 113 179 262 317 391 418 }}
 | +0.575
 | 0.643
@@ Line 65: / Line 65: @@
 |+Table of rank-2 temperaments by generator
 ! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-
@@ Line 148: / Line 148: @@
 | [[Gaster temperament|Gaster]]
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct