1289edo: Difference between revisions

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== Theory ==

1289edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], it [[tempering out|tempers out]] [[3025/3024]], 180224/180075, [[2460375/2458624]] and 50014503/50000000 in the [[11-limit]]; ~~3025/3024,~~ [[1716/1715]], [[4096/4095]], 91125/91091 and 5282739/5281250 in the [[13-limit]]. It [[~~support]]s [[honeybrookic~~]], [[~~totziensismic]] and [[minortone~~]].

1289edo is [[consistent]] to the [[9-odd-limit]]. As an equal temperament, it tempers out {{monzo| -16 35 -17 }} ([[minortone comma]]) in the 5-limit. Using the [[patent val]], it [[tempering out|tempers out]] [[3025/3024]], 180224/180075, [[2460375/2458624]] and 50014503/50000000 in the [[11-limit]]; [[1716/1715]], [[4096/4095]], 91125/91091 and 5282739/5281250 in the [[13-limit]]. In the 2.3.13.23.29.31 subgroup it tempers out [[19344/19343]], in the 2.3.5.7.11.23.31 subgroup [[19251/19250]].

=== Prime harmonics ===

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=== Subsets and supersets ===

1289edo is the 209th [[prime ~~EDO~~]].

1289edo is the 209th [[prime edo]].

== 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 8ve ~~Stretch~~ (¢)

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

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

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

|-

! colspan="2" | Tuning error

![[TE error|Absolute]] (¢)

|-

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

! [[TE error|Absolute]] (¢)

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

|-

| 2.3

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| {{monzo|-16 35 -17}}, {{monzo|91 -12 -31}}

| {{mapping|1289 2043 2993}}

| -0.0014

| −0.0014

| 0.0097

| 1.04

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| 2460375/2458624, 78125000/78121827, 12884901888/12867859375

| {{mapping|1289 2043 2993 3619}}

| -0.0275

| −0.0275

| 0.0461

| 4.95

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| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000

| {{mapping|1289 2043 2993 3619 4459}}

| -0.0109

| −0.0109

| 0.0530

| 5.69

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| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250

| {{mapping|1289 2043 2993 3619 4459 4770}}

| -0.0146

| −0.0146

| 0.0491

| 5.27

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| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000

| {{mapping|1289 2043 2993 3619 4459 4770 5269}}

| -0.0210

| −0.0210

| 0.0481

| 5.17

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| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712

| {{mapping|1289 2043 2993 3619 4459 4770 5269 5476}}

| -0.0299

| −0.0299

| 0.0508

| 5.46

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=== Rank-2 temperaments ===

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

|+Table of rank-2 temperaments by generator

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Periods per 8ve

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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| [[Fortune]]

|}

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

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

== Music ==

; [[Francium]]

* "Baking With Honey" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/4MS4KuEo2jocbD1F968mBE Spotify] | [https://francium223.bandcamp.com/track/baking-with-honey Bandcamp] | [https://www.youtube.com/watch?v=mh0-dZt9NI8 YouTube] – in Honeybrookic, 1289edo tuning

* "Those Peas, With That Hat?" from ''Questions, Vol. 2'' (2025) – [https://open.spotify.com/track/3huEuNHvcAeKM6smXRSALR Spotify] | [https://francium223.bandcamp.com/track/those-peas-with-that-hat Bandcamp] | [https://www.youtube.com/watch?v=6us1wSQjn7w YouTube]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1289}}
+{{ED intro}}
 == Theory ==
-edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], it [[tempering out|tempers out]] [[3025/3024]], 180224/180075, [[2460375/2458624]] and 50014503/50000000 in the [[11-limit]]; 3025/3024, [[1716/1715]], [[4096/4095]], 91125/91091 and 5282739/5281250 in the [[13-limit]]. It [[support]]s [[honeybrookic]], [[totziensismic]] and [[minortone]].
+edo is [[consistent]] to the [[9-odd-limit]]. As an equal temperament, it tempers out {{monzo| -16 35 -17 }} ([[minortone comma]]) in the 5-limit. Using the [[patent val]], it [[tempering out|tempers out]] [[3025/3024]], 180224/180075, [[2460375/2458624]] and 50014503/50000000 in the [[11-limit]]; [[1716/1715]], [[4096/4095]], 91125/91091 and 5282739/5281250 in the [[13-limit]]. In the 2.3.13.23.29.31 subgroup it tempers out [[19344/19343]], in the 2.3.5.7.11.23.31 subgroup [[19251/19250]].
 === Prime harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-edo is the 209th [[prime EDO]].
+edo is the 209th [[prime edo]].
 == 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]] (%)
 |-
 | 2.3
@@ Line 32: / Line 33: @@
 | {{monzo|-16 35 -17}}, {{monzo|91 -12 -31}}
 | {{mapping|1289 2043 2993}}
-| -0.0014
+| −0.0014
 | 0.0097
 | 1.04
@@ Line 39: / Line 40: @@
 | 2460375/2458624, 78125000/78121827, 12884901888/12867859375
 | {{mapping|1289 2043 2993 3619}}
-| -0.0275
+| −0.0275
 | 0.0461
 | 4.95
@@ Line 46: / Line 47: @@
 | 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000
 | {{mapping|1289 2043 2993 3619 4459}}
-| -0.0109
+| −0.0109
 | 0.0530
 | 5.69
@@ Line 53: / Line 54: @@
 | 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250
 | {{mapping|1289 2043 2993 3619 4459 4770}}
-| -0.0146
+| −0.0146
 | 0.0491
 | 5.27
@@ Line 60: / Line 61: @@
 | 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000
 | {{mapping|1289 2043 2993 3619 4459 4770 5269}}
-| -0.0210
+| −0.0210
 | 0.0481
 | 5.17
@@ Line 67: / Line 68: @@
 | 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712
 | {{mapping|1289 2043 2993 3619 4459 4770 5269 5476}}
-| -0.0299
+| −0.0299
 | 0.0508
 | 5.46
@@ Line 74: / Line 75: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 99: / Line 101: @@
 | [[Fortune]]
 |}
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+== Music ==
+; [[Francium]]
+* "Baking With Honey" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/4MS4KuEo2jocbD1F968mBE Spotify] | [https://francium223.bandcamp.com/track/baking-with-honey Bandcamp] | [https://www.youtube.com/watch?v=mh0-dZt9NI8 YouTube] – in Honeybrookic, 1289edo tuning
+* "Those Peas, With That Hat?" from ''Questions, Vol. 2'' (2025) – [https://open.spotify.com/track/3huEuNHvcAeKM6smXRSALR Spotify] | [https://francium223.bandcamp.com/track/those-peas-with-that-hat Bandcamp] | [https://www.youtube.com/watch?v=6us1wSQjn7w YouTube]