2901533edo
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| ← 2901532edo | 2901533edo | 2901534edo → |
2901533 equal divisions of the octave (abbreviated 2901533edo or 2901533ed2), also called 2901533-tone equal temperament (2901533tet) or 2901533 equal temperament (2901533et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2901533 equal parts of about 0.000414 ¢ each. Each step represents a frequency ratio of 21/2901533, or the 2901533rd root of 2.
2901533edo is the smallest edo to be consistent in the 79-odd-limit, and is consistent up to the 131-odd-limit. Because of its unusual consistency at its size range, it could be a candidate for "miracle edo" (not miracle, the temperament) after 311edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000000 | +0.000000 | +0.000004 | +0.000021 | -0.000001 | +0.000018 | -0.000132 | +0.000057 | -0.000121 |
| Relative (%) | +0.0 | +0.0 | +0.9 | +5.1 | -0.3 | +4.3 | -32.0 | +13.8 | -29.3 | |
| Steps (reduced) |
2901533 (0) |
4598821 (1697288) |
6737151 (934085) |
8145633 (2342567) |
10037655 (1333056) |
10736948 (2032349) |
11859908 (253776) |
12325502 (719370) |
13125264 (1519132) | |
| Harmonic | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.000071 | -0.000034 | +0.000061 | +0.000025 | -0.000104 | +0.000060 | -0.000091 | +0.000027 | -0.000041 |
| Relative (%) | -17.1 | -8.3 | +14.8 | +5.9 | -25.3 | +14.5 | -22.0 | +6.5 | -9.9 | |
| Steps (reduced) |
14095592 (2489460) |
14374764 (2768632) |
15115401 (607736) |
15545114 (1037449) |
15744486 (1236821) |
16116823 (1609158) |
16619750 (2112085) |
17068683 (2561018) |
17208230 (2700565) | |
| Harmonic | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000014 | -0.000086 | -0.000092 | +0.000056 | -0.000118 | -0.000103 | +0.000038 | -0.000140 | +0.000027 |
| Relative (%) | +3.3 | -20.9 | -22.2 | +13.4 | -28.6 | -24.9 | +9.1 | -33.8 | +6.6 | |
| Steps (reduced) |
17600958 (191760) |
17843694 (434496) |
17959980 (550782) |
18290628 (881430) |
18497387 (1088189) |
18789554 (1380356) |
19149865 (1740667) |
19319020 (1909822) |
19401102 (1991904) | |
| Harmonic | 107 | 109 | 113 | 127 | 131 | 137 | 139 | 149 | 151 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000029 | -0.000070 | -0.000135 | -0.000101 | +0.000024 | -0.000134 | -0.000185 | +0.000126 | -0.000090 |
| Relative (%) | +7.1 | -16.8 | -32.5 | -24.5 | +5.8 | -32.4 | -44.8 | +30.5 | -21.9 | |
| Steps (reduced) |
19560589 (2151391) |
19638110 (2228912) |
19788974 (2379776) |
20277899 (2868701) |
20407709 (96978) |
20595174 (284443) |
20655842 (345111) |
20946656 (635925) |
21002470 (691739) | |
Subsets and supersets
Since 2901533 factors into primes as 433 × 6701, so 2901533edo contains 433edo and 6701edo as subsets.