2901533edo
| ← 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.
Except for 8 barely-inconsistent interval pairs, it is consistent in the 137-prime-limited no-247's 255-odd-limit (a total of 4067 interval pairs), with primes 151, 157, 163, 173, 181, 197 and 211 being includeable to that odd limit for a tiny penalty of only 3 more barely-inconsistent interval pairs (and for a total of 4830). Including odd 247 adds 8 more inconsistent interval pairs and 90 more consistent interval pairs for a total of 4928 interval pairs (of which 19 interval pairs are inconsistent). Because of its unusual consistency at its size range, it could be a candidate for "miracle edo" (not miracle, the temperament) after 311edo, although this is not entirely certain or clear because a deep exhaustive search of comprehensive odd-limit performance has not been done up until this point, but it is at least significant that it holds a significant amount of records for odd limit consistency as detailed on the page for minimal consistent EDOs. Furthermore, it is consistent up to the 25-OPSL, and is consistent to distance 4 in the 16-OPSL.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000000 | +0.000000 | +0.000004 | +0.000021 | -0.000001 | +0.000018 | -0.000132 | +0.000057 | -0.000121 | -0.000071 | -0.000034 | +0.000061 |
| Relative (%) | +0.0 | +0.0 | +0.9 | +5.1 | -0.3 | +4.3 | -32.0 | +13.8 | -29.3 | -17.1 | -8.3 | +14.8 | |
| Steps (reduced) |
2901533 (0) |
4598821 (1697288) |
6737151 (934085) |
8145633 (2342567) |
10037655 (1333056) |
10736948 (2032349) |
11859908 (253776) |
12325502 (719370) |
13125264 (1519132) |
14095592 (2489460) |
14374764 (2768632) |
15115401 (607736) | |
| Harmonic | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000025 | -0.000104 | +0.000060 | -0.000091 | +0.000027 | -0.000041 | +0.000014 | -0.000086 | -0.000092 | +0.000056 | -0.000118 | -0.000103 |
| Relative (%) | +5.9 | -25.3 | +14.5 | -22.0 | +6.5 | -9.9 | +3.3 | -20.9 | -22.2 | +13.4 | -28.6 | -24.9 | |
| Steps (reduced) |
15545114 (1037449) |
15744486 (1236821) |
16116823 (1609158) |
16619750 (2112085) |
17068683 (2561018) |
17208230 (2700565) |
17600958 (191760) |
17843694 (434496) |
17959980 (550782) |
18290628 (881430) |
18497387 (1088189) |
18789554 (1380356) | |
| Harmonic | 97 | 101 | 103 | 107 | 109 | 113 | 127 | 131 | 137 | 139 | 149 | 151 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000038 | -0.000140 | +0.000027 | +0.000029 | -0.000070 | -0.000135 | -0.000101 | +0.000024 | -0.000134 | -0.000185 | +0.000126 | -0.000090 |
| Relative (%) | +9.1 | -33.8 | +6.6 | +7.1 | -16.8 | -32.5 | -24.5 | +5.8 | -32.4 | -44.8 | +30.5 | -21.9 | |
| Steps (reduced) |
19149865 (1740667) |
19319020 (1909822) |
19401102 (1991904) |
19560589 (2151391) |
19638110 (2228912) |
19788974 (2379776) |
20277899 (2868701) |
20407709 (96978) |
20595174 (284443) |
20655842 (345111) |
20946656 (635925) |
21002470 (691739) | |
| Harmonic | 157 | 163 | 167 | 173 | 179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000072 | -0.000102 | +0.000138 | -0.000060 | -0.000183 | -0.000139 | +0.000083 | +0.000147 | +0.000049 | -0.000143 | -0.000038 | -0.000202 |
| Relative (%) | +17.5 | -24.8 | +33.3 | -14.5 | -44.4 | -33.6 | +20.0 | +35.5 | +11.8 | -34.5 | -9.2 | -48.9 | |
| Steps (reduced) |
21165583 (854852) |
21322577 (1011846) |
21424062 (1113331) |
21571819 (1261088) |
21714538 (1403807) |
21761050 (1450319) |
21986160 (1675429) |
22029765 (1719034) |
22115635 (1804904) |
22157918 (1847187) |
22403024 (2092293) |
22634568 (2323837) | |
Subsets and supersets
2901533 = 433 × 6701, so 2901533edo contains 433edo and 6701edo as subsets.