352edo: 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 35: Line 27:
| 0.2500
| 0.2500
| 7.33
| 7.33
|}
{{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 71: Line 57:
|-
|-
| 4
| 4
| 93\352<br>(5\352)
| 93\352<br />(5\352)
| 317.05<br>(17.05)
| 317.05<br />(17.05)
| 6/5<br>(126/125)
| 6/5<br />(126/125)
| [[Quadritikleismic]]
| [[Quadritikleismic]]
|-
|-
| 4
| 4
| 117\352<br>(29\352)
| 117\352<br />(29\352)
| 398.86<br>(98.86)
| 398.86<br />(98.86)
| 34/27<br>(18/17)
| 34/27<br />(18/17)
| [[World calendar]]
| [[World calendar]]
|}
{{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}}

Revision as of 02:00, 16 November 2024

← 351edo 352edo 353edo →
Prime factorization 25 × 11
Step size 3.40909 ¢ 
Fifth 206\352 (702.273 ¢) (→ 103\176)
Semitones (A1:m2) 34:26 (115.9 ¢ : 88.64 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

Theory

352edo is consistent to the 7-odd-limit. Using the patent val, the equal temperament tempers out 2401/2400, 15625/15552, 390625/388962, and 33554432/33480783 in the 7-limit; 3025/3024, 4375/4356, 14700/14641, 19712/19683, 41503/41472, and 131072/130977 in the 11-limit. It supports newt, world calendar, septiruthenic, enki and fortune.

Prime harmonics

Approximation of prime harmonics in 352edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.32 -1.09 -0.64 +0.95 +1.52 +0.73 -0.92 -1.00 -0.03 +0.42
Relative (%) +0.0 +9.3 -31.9 -18.9 +28.0 +44.5 +21.3 -27.0 -29.4 -0.9 +12.3
Steps
(reduced) 		352
(0) 		558
(206) 		817
(113) 		988
(284) 		1218
(162) 		1303
(247) 		1439
(31) 		1495
(87) 		1592
(184) 		1710
(302) 		1744
(336)

Subsets and supersets

352 factors into 25 × 11, with subset edos 2, 4, 8, 11, 16, 22, 32, 44, 88, and 176.

Regular temperament properties

Template:Comma basis begin |- | 2.3.5 | 15625/15552, [95 -57 -2⟩ | [⟨352 558 817]] | +0.0891 | 0.2801 | 8.22 |- | 2.3.5.7 | 2401/2400, 15625/15552, 33554432/33480783 | [⟨352 558 817 988]] | +0.1242 | 0.2500 | 7.33 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 35\352 | 119.32 | 15/14 | Septidiasemi |- | 1 | 65\352 | 221.59 | 8388608/7381125 | Fortune |- | 1 | 93\352 | 317.05 | 6/5 | Hanson |- | 1 | 103\352 | 351.14 | 49/40 | Newt |- | 4 | 93\352
(5\352) | 317.05
(17.05) | 6/5
(126/125) | Quadritikleismic |- | 4 | 117\352
(29\352) | 398.86
(98.86) | 34/27
(18/17) | World calendar Template:Rank-2 end Template:Orf

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