202edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
The '''202 equal temperament''' divides the octave into 202 equal parts of 5.941 cents each.
{{EDO intro|202}}


==Theory==
== Theory ==
202et tempers out [[2401/2400]], 19683/19600 and 65625/65536 in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, and the rank-4 rastmic temperament tempering out 243/242.
202et tempers out [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, and the rank-4 rastmic temperament tempering out 243/242.
{{harmonics in equal|202|start=2|prec=3}}


==Regular temperament properties==
=== Prime harmonics ===
{{Harmonics in equal|202}}
 
== 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
|{{monzo|-160 101}}
| {{monzo| -160 101 }}
|{{val|202 320}}
| {{val| 202 320 }}
| 0.3044
| 0.3044
| 0.3045
| 0.3045
| 5.13
| 5.13
|-
|-
|2.3.5
| 2.3.5
|{{monzo|-13 17 -6}}, {{monzo|23 6 -14}}
| {{monzo| -13 17 -6 }}, {{monzo| 23 6 -14 }}
|{{val|202 320 469}}
| {{val| 202 320 469 }}
| 0.2280
| 0.2280
| 0.2710
| 0.2710
| 4.56
| 4.56
|-
|-
|2.3.5.7
| 2.3.5.7
|2401/2400, 19683/19600, 65625/65536
| 2401/2400, 19683/19600, 65625/65536
|{{val|202 320 469 567}}
| {{val| 202 320 469 567 }}
| 0.2164
| 0.2164
| 0.2356
| 0.2356
| 3.97
| 3.97
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|243/242, 441/440, 540/539, 2401/2400
| 243/242, 441/440, 540/539, 2401/2400
|{{val|202 320 469 567 699}}
| {{val| 202 320 469 567 699 }}
| 0.1061
| 0.1061
| 0.3049
| 0.3049
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|+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<br>(Reduced)
! Cents<br>(reduced)
! Cents<br>(Reduced)
! Associated<br>ratio
! Associated<br>Ratio
! Temperaments
! Temperaments
|-
|-
|1
| 1
|13\202
| 13\202
|77.23
| 77.23
|256/245
| 256/245
|[[Tertiaseptal]]
| [[Tertiaseptal]]
|-
|-
|1
| 1
|51\202
| 51\202
|302.97
| 302.97
|25/21
| 25/21
|[[Quinmite]]
| [[Quinmite]]
|-
|-
|1
| 1
|85\202
| 85\202
|504.95
| 504.95
|104976/78125
| 104976/78125
|[[Countermeantone]]
| [[Countermeantone]]
|-
|-
|1
| 1
|87\202
| 87\202
|516.83
| 516.83
|27/20
| 27/20
|[[Gravity]]
| [[Gravity]]
|-
|-
|2
| 2
|12\202
| 12\202
|71.29
| 71.29
|25/24
| 25/24
|[[Vishnu]]
| [[Vishnu]]
|-
|-
|2
| 2
|87\202<br>(14\202)
| 87\202<br>(14\202)
|516.83<br>(83.17)
| 516.83<br>(83.17)
|27/20<br>(21/20)
| 27/20<br>(21/20)
|[[Harry]]
| [[Harry]]
|}
|}


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== Music ==
== Music ==
[https://www.youtube.com/watch?v=_bNbb2o5K80 Home Planet Nostalgia] by Mundoworld
; [[Mundoworld]]
* [https://www.youtube.com/watch?v=_bNbb2o5K80 ''Home Planet Nostalgia'']


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Harry]]
[[Category:Harry]]
[[Category:Tertiaseptal]]
[[Category:Tertiaseptal]]

Revision as of 08:33, 13 October 2023

← 201edo 202edo 203edo →
Prime factorization 2 × 101
Step size 5.94059 ¢ 
Fifth 118\202 (700.99 ¢) (→ 59\101)
Semitones (A1:m2) 18:16 (106.9 ¢ : 95.05 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

Theory

202et tempers out 2401/2400, 19683/19600 and 65625/65536 in the 7-limit, and 243/242, 441/440, 4000/3993 in the 11-limit. It also notably tempers out the quartisma. It is the optimal patent val for the 11-limit rank-2 temperaments harry and tertiaseptal, the rank-3 temperament jove tempering out 243/242 and 441/440, and the rank-4 rastmic temperament tempering out 243/242.

Prime harmonics

Approximation of prime harmonics in 202edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.96 -0.18 -0.51 +1.16 -2.90 +1.98 -0.48 +1.43 -1.85 +1.50
Relative (%) +0.0 -16.2 -2.9 -8.6 +19.5 -48.9 +33.3 -8.1 +24.0 -31.2 +25.2
Steps
(reduced) 		202
(0) 		320
(118) 		469
(65) 		567
(163) 		699
(93) 		747
(141) 		826
(18) 		858
(50) 		914
(106) 		981
(173) 		1001
(193)

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [-160 101⟩ ⟨202 320] 0.3044 0.3045 5.13
2.3.5 [-13 17 -6⟩, [23 6 -14⟩ ⟨202 320 469] 0.2280 0.2710 4.56
2.3.5.7 2401/2400, 19683/19600, 65625/65536 ⟨202 320 469 567] 0.2164 0.2356 3.97
2.3.5.7.11 243/242, 441/440, 540/539, 2401/2400 ⟨202 320 469 567 699] 0.1061 0.3049 5.13

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator
(Reduced) 		Cents
(Reduced) 		Associated
Ratio 		Temperaments
1 13\202 77.23 256/245 Tertiaseptal
1 51\202 302.97 25/21 Quinmite
1 85\202 504.95 104976/78125 Countermeantone
1 87\202 516.83 27/20 Gravity
2 12\202 71.29 25/24 Vishnu
2 87\202
(14\202) 		516.83
(83.17) 		27/20
(21/20) 		Harry

Scales

Music

Mundoworld
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