897edo: Difference between revisions

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== Theory ==

897edo ~~has sharp approximations~~ to ~~harmonics~~ [[3/1|3]] ~~and~~ [[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]] 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''' }}.

The patent val tempers out [[250047/250000]] in the 7-limit; [[3025/3024]], [[5632/5625]], 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.

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.

The 897def val tempers out [[4375/4374]] in the 7-limit; [[4000/3993]], 46656/46585, and 172032/171875 in the 11-limit; [[1716/1715]], and [[10648/10647]] in the 13-limit.

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! [[TE error|Absolute]] (¢)

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

|-

~~| 2.3~~

~~| {{monzo| 474 -299 }}~~

~~| {{mapping| 897 1422 }}~~

~~| -0.1218~~

~~| 0.1218~~

~~| 9.10~~

|-

| 2.3.5

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| {{mapping| 897 1422 2083 }}

| -0.1255

| 0.~~010~~

| 0.0996

| 0.75

| 7.44

|-

| 2.3.5.7

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|-

| 2.3.5.7.11

| 3025/3024, 5632/5625, ~~160083~~/~~160000~~, 28824005/28697814

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

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

| -0.0480

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|-

| 2.3.5.7.11.13

| ~~2080~~/~~2079~~, 1001/1000, 3025/3024, 4096/4095, ~~2058857500~~/~~2051893701~~

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

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

| -0.0222

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! Associated<br>Ratio

! Temperaments

|-

| 3

| 103\897

| 137.79

| 13/12

| [[Avicenna]] (897)

|-

| 1

| 419\897

| 560.~~535~~

| 560.54

| 864/625

| [[Whoosh]]

|-

| 1

| 440\897

| 588.63

| 128/91

| [[Countritonic]] (897df)

|}

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

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== Music ==

; [[User:Francium|Francium]]

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

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

@@ Line 3: / Line 3: @@
 == Theory ==
-edo has sharp approximations to harmonics [[3/1|3]] and [[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]] 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''' }}.
-The patent val tempers out [[250047/250000]] in the 7-limit; [[3025/3024]], [[5632/5625]], 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.
+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.
 The 897def val tempers out [[4375/4374]] in the 7-limit; [[4000/3993]], 46656/46585, and 172032/171875 in the 11-limit; [[1716/1715]], and [[10648/10647]] in the 13-limit.
@@ Line 22: / Line 22: @@
 ! [[TE error|Absolute]] (¢)
 ! [[TE simple badness|Relative]] (%)
-|-
-| 2.3
-| {{monzo| 474 -299 }}
-| {{mapping| 897 1422 }}
-| -0.1218
-| 0.1218
-| 9.10
 |-
 | 2.3.5
@@ Line 34: / Line 27: @@
 | {{mapping| 897 1422 2083 }}
 | -0.1255
-| 0.010
+| 0.0996
-| 0.75
+| 7.44
 |-
 | 2.3.5.7
@@ Line 45: / Line 38: @@
 |-
 | 2.3.5.7.11
-| 3025/3024, 5632/5625, 160083/160000, 28824005/28697814
+| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814
 | {{mapping| 897 1422 2083 2518 3103 }} (897)
 | -0.0480
@@ Line 52: / Line 45: @@
 |-
 | 2.3.5.7.11.13
-| 2080/2079, 1001/1000, 3025/3024, 4096/4095, 2058857500/2051893701
+| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814
 | {{mapping| 897 1422 2083 2518 3103 3319 }} (897)
 | -0.0222
@@ Line 67: / Line 60: @@
 ! Associated<br>Ratio
 ! Temperaments
+|-
+| 3
+| 103\897
+| 137.79
+| 13/12
+| [[Avicenna]] (897)
 |-
 | 1
 | 419\897
-| 560.535
+| 560.54
 | 864/625
 | [[Whoosh]]
+|-
+| 1
+| 440\897
+| 588.63
+| 128/91
+| [[Countritonic]] (897df)
 |}
 <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 78: / Line 83: @@
 == Music ==
 ; [[User:Francium|Francium]]
-* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13|3|23''] – 3-, 13- and 23edo polymicrotonal
+* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13|3|23''] (2023) – 3-, 13- and 23edo polymicrotonal