897edo: Difference between revisions

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== Theory ==

897edo shares the same approximation to [[3/1|harmonic 3]] as [[299edo]]. It has sharp approximations to [[5/1|5]] and flat ones starting with [[7/1|7]]. In the 13-limit at least, we want to consider the [[patent val]] {{val| 897 1422 2083 '''2518''' '''3103''' '''3319''' }} as well as the 897def [[val]] {{val| 897 1422 2083 '''2519''' '''3104''' '''3320''' }}.

897edo shares the same approximation to [[3/1|harmonic 3]] with [[299edo]]. It has sharp approximations to [[5/1|5]] and flat ones starting with [[7/1|7]]. In the 13-limit at least, we want to consider the [[patent val]] {{val| 897 1422 2083 '''2518''' '''3103''' '''3319''' }} as well as the 897def [[val]] {{val| 897 1422 2083 '''2519''' '''3104''' '''3320''' }}.

The patent val tempers out [[250047/250000]] in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, and 172032/171875 in the 11-limit; [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.

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=== Subsets and supersets ===

Since 897 factors into ~~3 × 13 × 23~~, 897edo has subset edos {{EDOs| 3, 13, 23, 39, 69, and 299 }}.

Since 897 factors into {{factorization|897}}, 897edo has subset edos {{EDOs| 3, 13, 23, 39, 69, and 299 }}.

== Regular temperament properties ==

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

|-

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

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

! rowspan="2" | [[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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| {{monzo| 33 -34 9 }}, {{monzo| 70 -9 -24 }}

| {{mapping| 897 1422 2083 }}

| -0.1255

| −0.1255

| 0.0996

| 7.44

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| 250047/250000, 67108864/66976875, 28824005/28697814

| {{mapping| 897 1422 2083 2518 }} (897)

| -0.0706

| −0.0706

| 0.1283

| 9.59

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| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814

| {{mapping| 897 1422 2083 2518 3103 }} (897)

| -0.0480

| −0.0480

| 0.1234

| 9.22

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| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814

| {{mapping| 897 1422 2083 2518 3103 3319 }} (897)

| -0.0222

| −0.0222

| 0.1265

| 9.46

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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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| [[Avicenna (temperament)|Avicenna]] (897)

|}

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

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

== Music ==

; [[User:Francium|Francium]]

* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13|3|23''] (2023) – 3-, 13- and 23edo polymicrotonal

* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13|3|23''] (2023) – 3-, 13-, and 23edo polymicrotonal

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|897}}
+{{ED intro}}
 == Theory ==
-edo shares the same approximation to [[3/1|harmonic 3]] as [[299edo]]. It has sharp approximations to [[5/1|5]] and flat ones starting with [[7/1|7]]. In the 13-limit at least, we want to consider the [[patent val]] {{val| 897 1422 2083 '''2518''' '''3103''' '''3319''' }} as well as the 897def [[val]] {{val| 897 1422 2083 '''2519''' '''3104''' '''3320''' }}.
+edo shares the same approximation to [[3/1|harmonic 3]] with [[299edo]]. It has sharp approximations to [[5/1|5]] and flat ones starting with [[7/1|7]]. In the 13-limit at least, we want to consider the [[patent val]] {{val| 897 1422 2083 '''2518''' '''3103''' '''3319''' }} as well as the 897def [[val]] {{val| 897 1422 2083 '''2519''' '''3104''' '''3320''' }}.
 The patent val tempers out [[250047/250000]] in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, and 172032/171875 in the 11-limit; [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.
@@ Line 13: / Line 13: @@
 === Subsets and supersets ===
-Since 897 factors into 3 × 13 × 23, 897edo has subset edos {{EDOs| 3, 13, 23, 39, 69, and 299 }}.
+Since 897 factors into {{factorization|897}}, 897edo has subset edos {{EDOs| 3, 13, 23, 39, 69, and 299 }}.
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[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 29: / Line 30: @@
 | {{monzo| 33 -34 9 }}, {{monzo| 70 -9 -24 }}
 | {{mapping| 897 1422 2083 }}
-| -0.1255
+| −0.1255
 | 0.0996
 | 7.44
@@ Line 36: / Line 37: @@
 | 250047/250000, 67108864/66976875, 28824005/28697814
 | {{mapping| 897 1422 2083 2518 }} (897)
-| -0.0706
+| −0.0706
 | 0.1283
 | 9.59
@@ Line 43: / Line 44: @@
 | 3025/3024, 5632/5625, 102487/102400, 28824005/28697814
 | {{mapping| 897 1422 2083 2518 3103 }} (897)
-| -0.0480
+| −0.0480
 | 0.1234
 | 9.22
@@ Line 50: / Line 51: @@
 | 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814
 | {{mapping| 897 1422 2083 2518 3103 3319 }} (897)
-| -0.0222
+| −0.0222
 | 0.1265
 | 9.46
@@ Line 57: / Line 58: @@
 === 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 82: / Line 84: @@
 | [[Avicenna (temperament)|Avicenna]] (897)
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 == Music ==
 ; [[User:Francium|Francium]]
-* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13|3|23''] (2023) – 3-, 13- and 23edo polymicrotonal
+* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13|3|23''] (2023) – 3-, 13-, and 23edo polymicrotonal
+[[Category:Listen]]