202edo: Difference between revisions
+subsets and supersets |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
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| 0.3049 | | 0.3049 | ||
| 5.13 | | 5.13 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 91: | Line 77: | ||
|- | |- | ||
| 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]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Scales == | == Scales == | ||
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== Music == | == Music == | ||
; [[Mundoworld]] | ; [[Mundoworld]] | ||
* [https://www.youtube.com/watch?v=_bNbb2o5K80 ''Home Planet Nostalgia''] | * [https://www.youtube.com/watch?v=_bNbb2o5K80 ''Home Planet Nostalgia''] – in Oktone scale | ||
[[Category:Harry]] | [[Category:Harry]] | ||
Revision as of 03:16, 16 November 2024
| ← 201edo | 202edo | 203edo → |
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
| 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) | |
Subsets and supersets
Since 202 factors into 2 × 101, 202edo contains 2edo and 101edo as its subsets.
Regular temperament properties
Template:Comma basis begin |- | 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, 4000/3993, 65625/65536 | [⟨202 320 469 567 699]] | 0.1061 | 0.3049 | 5.13 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 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
| Larry
|-
| 2
| 12\202
| 71.29
| 25/24
| Narayana
|-
| 2
| 87\202
(14\202)
| 516.83
(83.17)
| 27/20
(21/20)
| Harry
Template:Rank-2 end
Template:Orf
Scales
- Jove1, jove2, jove3, jove4, jove5, jove6
- Elfjove7, elfjove8d, elfjove10, elfjove11c, elfjove12
- Oktone
Music
- Home Planet Nostalgia – in Oktone scale