Xenharmonic Wiki

292edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Fredg999 category edits (talk | contribs)
autopatrolled, Bots, emailconfirmed
4,474 edits
m Removing from Category:Theory using Cat-a-lot
Expansion (+infobox; +prime error table; +RTT table and rank-2 temperaments)
Line 1: Line 1:
The '''292 equal divisions of the octave''' ('''292edo''') is the [[EDO|equal division of the octave]] into 292 parts of 4.1095 [[cent]]s each.
{{Infobox ET
| Prime factorization = 2<sup>2</sup> × 73
| Step size = 4.10959¢
| Fifth = 171\292 (702.74¢)
| Semitones = 29:21 (119.18¢ : 86.30¢)
| Consistency = 9
}}
{{EDO intro|292}}


== Theory ==
292edo is closely related to [[146edo]], but the patent vals differ on the mapping for 3. It tempers out {{monzo| 3 -18 11 }} (quartonic comma) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma) in the [[5-limit]]; 5120/5103 ([[5120/5103|hemifamity]]), 390625/388962 ([[dimcomp comma|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]].  
292edo is closely related to [[146edo]], but the patent vals differ on the mapping for 3. It tempers out {{monzo| 3 -18 11 }} (quartonic comma) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma) in the [[5-limit]]; 5120/5103 ([[5120/5103|hemifamity]]), 390625/388962 ([[dimcomp comma|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 [[support]]s [[Hemifamity temperaments #Semiseptiquarter|semiseptiquarter]] and [[Luna family #Semiluna|semiluna]].  
It provides the [[optimal patent val]] for the [[undim]] temperament in the 7-, 11-, and 13-limit, and notably [[support]]s [[Hemifamity temperaments #Semiseptiquarter|semiseptiquarter]] and [[semiluna]].
 
{{Harmonics in equal|292}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 463 -292 }}
| [{{val| 292 463 }}]
| -0.2476
| 0.2475
| 6.02
|-
| 2.3.5
| {{monzo| 3 -18 11 }}, {{monzo| 38 -2 -15 }}
| [{{val| 292 463 678 }}]
| -0.1633
| 0.2346
| 5.71
|-
| 2.3.5.7
| 5120/5103, 390625/388962, 420175/419904
| [{{val| 292 463 678 820 }}]
| -0.2148
| 0.2219
| 5.40
|-
| 2.3.5.7.11
| 1375/1372, 5120/5103, 5632/5625, 14641/14580
| [{{val| 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
| [{{val| 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
| [{{val| 292 463 678 820 1010 1081 1194 }}]
| -0.2376
| 0.2696
| 6.56
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
| 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]]
|}


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
Retrieved from "https://en.xen.wiki/w/292edo"