352edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Newer edit →
VisualWikitext
Francium (talk | contribs)
4,826 edits
Created page with "{{Infobox ET}} {{EDO intro|352}} == Theory == 352et is consistent to the 7-odd-limit. Using the patent val, it tempers out 156250000/155649627, 33554432/33480783, 359..."
 
Review
Line 3: Line 3:


== Theory ==
== Theory ==
352et is consistent to the [[7-odd-limit]]. Using the patent val, it tempers out 156250000/155649627, [[33554432/33480783]], 359661568/358722675 and [[2401/2400]] in the 7-limit; [[214990848/214358881]], 78121827/77948684, 100663296/100656875, 10333575/10307264, 2097152/2096325, 1366875/1362944, 125000/124509, [[536870912/535869675]], 151263/151250, 104857600/104825259, [[131072/130977]], 1265625/1261568, [[200704/200475]], 5788125/5767168, [[19712/19683]], 1479016/1476225, [[3025/3024]], [[41503/41472]], [[532400/531441]] and 67110351/67108864 in the 11-limit. It [[support]]s [[world calendar]], [[septiruthenic]], [[enki]] and [[fortune]].
352edo is [[consistent]] to the [[7-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out|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 [[support]]s [[newt]], [[world calendar]], [[septiruthenic]], [[enki]] and [[fortune]].


=== Prime harmonics ===
=== Prime harmonics ===
Line 9: Line 9:


=== Subsets and supersets ===
=== Subsets and supersets ===
352 factors into 2<sup>5</sup> × 11, with subset edos {{EDOs|2, 4, 8, 11, 16, 22, 32, 44, 88, and 176}}. [[2112edo]], which sextuples it, gives a good correction to the harmonic 11.
352 factors into 2<sup>5</sup> × 11, with subset edos {{EDOs| 2, 4, 8, 11, 16, 22, 32, 44, 88, and 176 }}.  


== 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|279 -176}}
| 15625/15552, {{monzo| 95 -57 -2 }}   
|{{mapping|352 558}}
| {{mapping| 352 558 817 }}
| -0.1002
| 0.1002
| 2.94
|-
|2.3.5
|15625/15552, {{monzo|95 -57 -2}}   
|{{mapping|352 558 817}}
| +0.0891
| +0.0891
| 0.2801
| 0.2801
| 8.22
| 8.22
|-
|-
|2.3.5.7
| 2.3.5.7
|2401/2400, 15625/15552, 359661568/358722675
| 2401/2400, 15625/15552, 33554432/33480783
|{{mapping|352 558 817 988}}
| {{mapping| 352 558 817 988 }}
| +0.1242
| +0.1242
| 0.2500
| 0.2500
Line 48: Line 41:
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator<br>(reduced)*
! Generator*
! Cents<br>(reduced)*
! Cents*
! Associated<br>Ratio*
! Associated<br>Ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|35\352
| 35\352
|119.32
| 119.32
|15/14
| 15/14
|[[Septidiasemi]]
| [[Septidiasemi]]
|-
|-
|1
| 1
|65\352
| 65\352
|221.59
| 221.59
|8388608/7381125
| 8388608/7381125
|[[Fortune]]
| [[Fortune]]
|-
|-
|1
| 1
|93\352
| 93\352
|317.05
| 317.05
|6/5
| 6/5
|[[Hanson]]
| [[Hanson]]
|-
|-
|1
| 1
|103\352
| 103\352
|351.14
| 351.14
|49/40
| 49/40
|[[Newt]]
| [[Newt]]
|-
|-
|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
| 117\352<br>(29\352)
| 398.86<br>(98.86)
| 34/27<br>(18/17)
| [[World calendar]]
|}
|}
<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

Revision as of 11:48, 1 January 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

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
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

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
Ratio* 		Temperaments
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

* 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=352edo&oldid=130251"