332edo: 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
Line 36: Line 27:
| 0.2412
| 0.2412
| 6.67
| 6.67
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 83: Line 67:
| 1125/1024
| 1125/1024
| [[Kwazy]]
| [[Kwazy]]
|}
{{rank-2 end}}
{{orf}}
{{orf}}


[[Category:Sedia]]
[[Category:Sedia]]

Revision as of 01:50, 16 November 2024

← 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

Template:Comma basis begin |- | 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 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 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 Template:Rank-2 end Template:Orf

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