2901533edo: Difference between revisions
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{{Infobox ET|Consistency=131|Distinct consistency=131}} | {{Infobox ET|Consistency=131|Distinct consistency=131}} | ||
{{EDO intro|2901533}} | {{EDO intro|2901533}} | ||
Revision as of 03:57, 9 July 2023
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
| ← 2901532edo | 2901533edo | 2901534edo → |
Template:EDO intro 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.
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 | +0.000025 |
| 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 | +5.9 | |
| 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) |
15545114 (1037449) | |
| Harmonic | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.000104 | +0.000060 | -0.000091 | +0.000027 | -0.000041 | +0.000014 | -0.000086 | -0.000092 | +0.000056 | -0.000118 | -0.000103 | +0.000038 |
| Relative (%) | -25.3 | +14.5 | -22.0 | +6.5 | -9.9 | +3.3 | -20.9 | -22.2 | +13.4 | -28.6 | -24.9 | +9.1 | |
| Steps (reduced) |
15744486 (1236821) |
16116823 (1609158) |
16619750 (2112085) |
17068683 (2561018) |
17208230 (2700565) |
17600958 (191760) |
17843694 (434496) |
17959980 (550782) |
18290628 (881430) |
18497387 (1088189) |
18789554 (1380356) |
19149865 (1740667) | |