897edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3.5
| 2.3.5
| {{monzo| 33 -34 9 }}, {{monzo| 70 -9 -24 }}
| {{monzo| 33 -34 9 }}, {{monzo| 70 -9 -24 }}
| {{mapping| 897 ​1422​ 2083​ }}
| {{mapping| 897 ​1422​ 2083​ }}
| -0.1255
| &minus;0.1255
| 0.0996
| 0.0996
| 7.44
| 7.44
Line 36: Line 28:
| 250047/250000, 67108864/66976875, 28824005/28697814
| 250047/250000, 67108864/66976875, 28824005/28697814
| {{mapping| 897​ 1422 ​2083 ​2518 }} (897)
| {{mapping| 897​ 1422 ​2083 ​2518 }} (897)
| -0.0706
| &minus;0.0706
| 0.1283
| 0.1283
| 9.59
| 9.59
Line 43: Line 35:
| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814
| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814
| {{mapping| 897 ​1422​ 2083 ​2518 ​3103 }} (897)
| {{mapping| 897 ​1422​ 2083 ​2518 ​3103 }} (897)
| -0.0480
| &minus;0.0480
| 0.1234
| 0.1234
| 9.22
| 9.22
Line 50: Line 42:
| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814
| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814
| {{mapping| 897​ 1422 ​2083 ​2518​ 3103​ 3319 }} (897)
| {{mapping| 897​ 1422 ​2083 ​2518​ 3103​ 3319 }} (897)
| -0.0222
| &minus;0.0222
| 0.1265
| 0.1265
| 9.46
| 9.46
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 81: Line 67:
| 13/12
| 13/12
| [[Avicenna (temperament)|Avicenna]] (897)
| [[Avicenna (temperament)|Avicenna]] (897)
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Music ==
== Music ==
; [[User:Francium|Francium]]
; [[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) &ndash; 3-, 13-, and 23edo polymicrotonal
 
[[Category:Listen]]

Revision as of 04:08, 16 November 2024

← 896edo 897edo 898edo →
Prime factorization 3 × 13 × 23
Step size 1.33779 ¢ 
Fifth 525\897 (702.341 ¢) (→ 175\299)
Semitones (A1:m2) 87:66 (116.4 ¢ : 88.29 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

Theory

897edo shares the same approximation to harmonic 3 with 299edo. It has sharp approximations to 5 and flat ones starting with 7. In the 13-limit at least, we want to consider the patent val ⟨897 1422 2083 2518 3103 3319] as well as the 897def 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.

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.

Odd harmonics

Approximation of odd harmonics in 897edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.386 +0.308 -0.264 -0.566 -0.147 -0.394 -0.643 -0.608 -0.523 +0.122 +0.488
Relative (%) +28.9 +23.0 -19.7 -42.3 -11.0 -29.4 -48.1 -45.4 -39.1 +9.1 +36.5
Steps
(reduced) 		1422
(525) 		2083
(289) 		2518
(724) 		2843
(152) 		3103
(412) 		3319
(628) 		3504
(813) 		3666
(78) 		3810
(222) 		3940
(352) 		4058
(470)

Subsets and supersets

Since 897 factors into 3 × 13 × 23, 897edo has subset edos 3, 13, 23, 39, 69, and 299.

Regular temperament properties

Template:Comma basis begin |- | 2.3.5 | [33 -34 9⟩, [70 -9 -24⟩ | [⟨897 ​1422​ 2083​]] | −0.1255 | 0.0996 | 7.44 |- | 2.3.5.7 | 250047/250000, 67108864/66976875, 28824005/28697814 | [⟨897​ 1422 ​2083 ​2518]] (897) | −0.0706 | 0.1283 | 9.59 |- | 2.3.5.7.11 | 3025/3024, 5632/5625, 102487/102400, 28824005/28697814 | [⟨897 ​1422​ 2083 ​2518 ​3103]] (897) | −0.0480 | 0.1234 | 9.22 |- | 2.3.5.7.11.13 | 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814 | [⟨897​ 1422 ​2083 ​2518​ 3103​ 3319]] (897) | −0.0222 | 0.1265 | 9.46 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 419\897 | 560.54 | 864/625 | Whoosh |- | 1 | 440\897 | 588.63 | 128/91 | Countritonic (897df) |- | 3 | 103\897 | 137.79 | 13/12 | Avicenna (897) Template:Rank-2 end Template:Orf

Music

Francium
  • 13|3|23 (2023) – 3-, 13-, and 23edo polymicrotonal
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