292edo: 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
| 2.3
| {{monzo| 463 -292 }}
| {{monzo| 463 -292 }}
| {{mapping| 292 463 }}
| {{mapping| 292 463 }}
| -0.2476
| &minus;0.2476
| 0.2475
| 0.2475
| 6.02
| 6.02
Line 34: Line 26:
| {{monzo| 3 -18 11 }}, {{monzo| 38 -2 -15 }}
| {{monzo| 3 -18 11 }}, {{monzo| 38 -2 -15 }}
| {{mapping| 292 463 678 }}
| {{mapping| 292 463 678 }}
| -0.1633
| &minus;0.1633
| 0.2346
| 0.2346
| 5.71
| 5.71
Line 41: Line 33:
| 5120/5103, 390625/388962, 420175/419904
| 5120/5103, 390625/388962, 420175/419904
| {{mapping| 292 463 678 820 }}
| {{mapping| 292 463 678 820 }}
| -0.2148
| &minus;0.2148
| 0.2219
| 0.2219
| 5.40
| 5.40
Line 48: Line 40:
| 1375/1372, 5120/5103, 5632/5625, 14641/14580
| 1375/1372, 5120/5103, 5632/5625, 14641/14580
| {{mapping| 292 463 678 820 1010 }}
| {{mapping| 292 463 678 820 1010 }}
| -0.1353
| &minus;0.1353
| 0.2544
| 0.2544
| 6.19
| 6.19
Line 55: Line 47:
| 352/351, 625/624, 847/845, 1716/1715, 14641/14580
| 352/351, 625/624, 847/845, 1716/1715, 14641/14580
| {{mapping| 292 463 678 820 1010 1081 }}
| {{mapping| 292 463 678 820 1010 1081 }}
| -0.3480
| &minus;0.3480
| 0.2736
| 0.2736
| 6.66
| 6.66
Line 62: Line 54:
| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023
| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023
| {{mapping| 292 463 678 820 1010 1081 1194 }}
| {{mapping| 292 463 678 820 1010 1081 1194 }}
| -0.2376
| &minus;0.2376
| 0.2696
| 0.2696
| 6.56
| 6.56
Line 68: Line 60:


=== 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 117: Line 103:
| 4/3
| 4/3
| [[Undim]]
| [[Undim]]
|}
{{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}}


[[Category:Hemifamity]]
[[Category:Hemifamity]]

Revision as of 04:26, 16 November 2024

← 291edo 292edo 293edo →
Prime factorization 22 × 73
Step size 4.10959 ¢ 
Fifth 171\292 (702.74 ¢)
Semitones (A1:m2) 29:21 (119.2 ¢ : 86.3 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

Theory

292edo is closely related to 146edo, but the patent vals differ on the mapping for 3. The equal temperament tempers out [3 -18 11⟩ (quartonic comma) and [38 -2 -15⟩ (luna/hemithirds comma) in the 5-limit; 5120/5103 (hemifamity), 390625/388962 (dimcomp), 420175/419904 (wizma), and 4802000/4782969 (canousma) in the 7-limit; 1375/1372, 5632/5625, 6250/6237, 9801/9800 and 14641/14580 in the 11-limit; 352/351, 625/624, 847/845, 1716/1715, and 2080/2079 in the 13-limit.

It provides the optimal patent val for the undim temperament in the 7-, 11-, and 13-limit, and notably supports semiseptiquarter and semiluna.

Prime harmonics

Approximation of prime harmonics in 292edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.78 -0.01 +1.04 -0.63 +1.94 +1.89 -1.62 +0.49 +1.93 +1.54
Relative (%) +0.0 +19.1 -0.3 +25.2 -15.4 +47.2 +46.1 -39.5 +12.0 +47.0 +37.5
Steps
(reduced) 		292
(0) 		463
(171) 		678
(94) 		820
(236) 		1010
(134) 		1081
(205) 		1194
(26) 		1240
(72) 		1321
(153) 		1419
(251) 		1447
(279)

Subsets and supersets

Since 292 factors into 22 × 73, 292edo has subset edos 2, 4, 73, and 146.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [463 -292⟩ | [⟨292 463]] | −0.2476 | 0.2475 | 6.02 |- | 2.3.5 | [3 -18 11⟩, [38 -2 -15⟩ | [⟨292 463 678]] | −0.1633 | 0.2346 | 5.71 |- | 2.3.5.7 | 5120/5103, 390625/388962, 420175/419904 | [⟨292 463 678 820]] | −0.2148 | 0.2219 | 5.40 |- | 2.3.5.7.11 | 1375/1372, 5120/5103, 5632/5625, 14641/14580 | [⟨292 463 678 820 1010]] | −0.1353 | 0.2544 | 6.19 |- | 2.3.5.7.11.13 | 352/351, 625/624, 847/845, 1716/1715, 14641/14580 | [⟨292 463 678 820 1010 1081]] | −0.3480 | 0.2736 | 6.66 |- | 2.3.5.7.11.13.17 | 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023 | [⟨292 463 678 820 1010 1081 1194]] | −0.2376 | 0.2696 | 6.56 |}

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 11\292 | 45.21 | 250/243 | Quartonic (5-limit) |- | 1 | 47\292 | 193.15 | 262144/234375 | Luna |- | 1 | 59\292 | 242.47 | 147/128 | Septiquarter |- | 1 | 111\292 | 456.16 | 125/96 | Qak |- | 2 | 47\292 | 193.15 | 121/108 | Semiluna |- | 2 | 59\292 | 242.47 | 121/105 | Semiseptiquarter |- | 4 | 121\292 | 497.26 | 4/3 | Undim Template:Rank-2 end Template:Orf

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