202edo: Difference between revisions
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Adopt template: EDO intro; cleanup; -redundant categories |
Correct comma bases; formatting; +links to more scales |
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| Line 21: | Line 21: | ||
| 2.3 | | 2.3 | ||
| {{monzo| -160 101 }} | | {{monzo| -160 101 }} | ||
| {{ | | {{mapping| 202 320 }} | ||
| 0.3044 | | 0.3044 | ||
| 0.3045 | | 0.3045 | ||
| Line 28: | Line 28: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| -13 17 -6 }}, {{monzo| 23 6 -14 }} | | {{monzo| -13 17 -6 }}, {{monzo| 23 6 -14 }} | ||
| {{ | | {{mapping| 202 320 469 }} | ||
| 0.2280 | | 0.2280 | ||
| 0.2710 | | 0.2710 | ||
| Line 35: | Line 35: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 19683/19600, 65625/65536 | | 2401/2400, 19683/19600, 65625/65536 | ||
| {{ | | {{mapping| 202 320 469 567 }} | ||
| 0.2164 | | 0.2164 | ||
| 0.2356 | | 0.2356 | ||
| Line 41: | Line 41: | ||
|- | |- | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 243/242, 441/440, | | 243/242, 441/440, 4000/3993, 65625/65536 | ||
| {{ | | {{mapping| 202 320 469 567 699 }} | ||
| 0.1061 | | 0.1061 | ||
| 0.3049 | | 0.3049 | ||
| Line 79: | Line 79: | ||
| 516.83 | | 516.83 | ||
| 27/20 | | 27/20 | ||
| [[ | | [[Larry]] | ||
|- | |- | ||
| 2 | | 2 | ||
| Line 85: | Line 85: | ||
| 71.29 | | 71.29 | ||
| 25/24 | | 25/24 | ||
| [[ | | [[Narayana]] | ||
|- | |- | ||
| 2 | | 2 | ||
| Line 95: | Line 95: | ||
== Scales == | == Scales == | ||
* [[Jove1]] | * [[Jove1]], [[jove2]], [[jove3]], [[jove4]], [[jove5]], [[jove6]] | ||
* [[ | * [[Elfjove7]], [[elfjove8d]], [[elfjove10]], [[elfjove11c]], [[elfjove12]] | ||
* [[Oktone]] | |||
* [[ | |||
== 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 08:42, 13 October 2023
| ← 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) | |
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, 4000/3993, 65625/65536 | [⟨202 320 469 567 699]] | 0.1061 | 0.3049 | 5.13 |
Rank-2 temperaments
| 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 | Larry |
| 2 | 12\202 | 71.29 | 25/24 | Narayana |
| 2 | 87\202 (14\202) |
516.83 (83.17) |
27/20 (21/20) |
Harry |
Scales
- Jove1, jove2, jove3, jove4, jove5, jove6
- Elfjove7, elfjove8d, elfjove10, elfjove11c, elfjove12
- Oktone
Music
- Home Planet Nostalgia – in Oktone scale