202edo
| ← 201edo | 202edo | 203edo → |
The 202 equal temperament divides the octave into 202 equal parts of 5.941 cents each.
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.
| Harmonic | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.965 | -0.175 | -0.509 | +1.157 | -2.904 | +1.975 | -0.483 | +1.429 | -1.854 | +1.499 | -1.839 |
| Relative (%) | -16.2 | -2.9 | -8.6 | +19.5 | -48.9 | +33.3 | -8.1 | +24.0 | -31.2 | +25.2 | -31.0 | |
| Steps (reduced) |
320 (118) |
469 (65) |
567 (163) |
699 (93) |
747 (141) |
826 (18) |
858 (50) |
914 (106) |
981 (173) |
1001 (193) |
1052 (42) | |
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
| 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
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