332edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Francium (talk | contribs)
4,827 edits
mNo edit summary
Review
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|332}}
{{EDO intro|332}}
== Theory ==
== Theory ==
332edo tempers out 118098/117649, 134217728/133984375, 29360128/29296875 and [[2401/2400]] in the 7-limit. It provides the optimal patent val for [[majvamoid]] and [[sedia]].
332edo is [[consistent]] to the [[7-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], [[19683/19600]], 118098/117649, and 29360128/29296875 in the 7-limit. It provides the [[optimal patent val]] for 11-, 13-, and 17-limit [[sedia]].
 
=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal}}
{{Harmonics in equal|332}}
 
=== Subsets and supersets ===
=== Subsets and supersets ===
332 factors into 2<sup>2</sup> × 83, with subset edos {{EDOs|2, 4, 83, and 166}}.
Since 332 factors into 2<sup>2</sup> × 83, 332edo has subset edos {{EDOs| 2, 4, 83, and 166 }}.
 
== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! 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]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3.5
|{{monzo|-263 166}}
| {{monzo| -13 17 -6 }}, {{monzo| -53 10 16 }}
|{{mapping|332 526}}
| {{mapping| 332 526 771 }}
| 0.2367
| 0.2367
| 6.55
|-
|2.3.5
|{{monzo|-13 17 -6}}, {{monzo|-53 10 16}}
|{{mapping|332 526 771}}
| 0.0955
| 0.0955
| 0.2778
| 0.2778
| 7.69
| 7.69
|-
|-
|2.3.5.7
| 2.3.5.7
|2401/2400, 19683/19600, 29360128/29296875
| 2401/2400, 19683/19600, 29360128/29296875
|{{mapping|332 526 771 932}}
| {{mapping| 332 526 771 932 }}
| 0.0851
| 0.0851
| 0.2412
| 0.2412
Line 49: Line 46:
! Temperaments
! Temperaments
|-
|-
|1
| 1
|33\332
| 33\332
|119.28
| 119.28
|15/14
| 15/14
|[[Septidiasemi]]
| [[Septidiasemi]]
|-
|-
|1
| 1
|75\332
| 75\332
|271.08
| 271.08
|1024/875
| 1024/875
|[[Quasiorwell]]
| [[Quasiorwell]]
|-
|-
|1
| 1
|127\332
| 127\332
|459.04
| 459.04
|125/96
| 125/96
|[[Majvam]]
| [[Majvam]]
|-
|-
|1
| 1
|143\332
| 143\332
|516.87
| 516.87
|27/20
| 27/20
|[[Gravity]]
| [[Gravity]]
|-
|-
|2
| 2
|143\332<br>(23\332)
| 143\332<br>(23\332)
|516.87<br>(83.13)
| 516.87<br>(83.13)
|27/20<br>(21/20)
| 27/20<br>(21/20)
|[[Harry]]
| [[Harry]]
|-
|-
|2
| 2
|45\332
| 45\332
|162.65
| 162.65
|1125/1024
| 1125/1024
|[[Kwazy]]
| [[Kwazy]]
|}
|}
<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>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
[[Category:Sedia]]

Revision as of 16:41, 5 December 2023

← 331edo 332edo 333edo →
Prime factorization 22 × 83
Step size 3.61446 ¢ 
Fifth 194\332 (701.205 ¢) (→ 97\166)
Semitones (A1:m2) 30:26 (108.4 ¢ : 93.98 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

Theory

332edo is consistent to the 7-odd-limit. The equal temperament tempers out 2401/2400, 19683/19600, 118098/117649, and 29360128/29296875 in the 7-limit. It provides the optimal patent val for 11-, 13-, and 17-limit sedia.

Prime harmonics

Approximation of prime harmonics in 332edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.75 +0.43 -0.15 +1.69 +1.64 -0.14 -1.13 +0.64 +0.54 +0.75
Relative (%) +0.0 -20.8 +12.0 -4.2 +46.9 +45.4 -3.8 -31.2 +17.7 +15.0 +20.7
Steps
(reduced) 		332
(0) 		526
(194) 		771
(107) 		932
(268) 		1149
(153) 		1229
(233) 		1357
(29) 		1410
(82) 		1502
(174) 		1613
(285) 		1645
(317)

Subsets and supersets

Since 332 factors into 22 × 83, 332edo has subset edos 2, 4, 83, and 166.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3.5 [-13 17 -6⟩, [-53 10 16⟩ [⟨332 526 771]] 0.0955 0.2778 7.69
2.3.5.7 2401/2400, 19683/19600, 29360128/29296875 [⟨332 526 771 932]] 0.0851 0.2412 6.67

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
Ratio* 		Temperaments
1 33\332 119.28 15/14 Septidiasemi
1 75\332 271.08 1024/875 Quasiorwell
1 127\332 459.04 125/96 Majvam
1 143\332 516.87 27/20 Gravity
2 143\332
(23\332) 		516.87
(83.13) 		27/20
(21/20) 		Harry
2 45\332 162.65 1125/1024 Kwazy

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Retrieved from "https://en.xen.wiki/index.php?title=332edo&oldid=128489"