2901533edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|2901533}} == Theory == {{Harmonics in equal|2901533}}" |
m Mathematical interest |
||
| (15 intermediate revisions by 8 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Mathematical interest}} | ||
{{ | {{Infobox ET | ||
| Consistency=131 | |||
| Distinct consistency=131 | |||
}} | |||
{{ED intro}} | |||
== | Except for 8 barely in[[consistent]] interval pairs, 2901533edo 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 [[odd prime sum limit|25-OPSL]], and is [[Consistency #Consistency to distance d|consistent to distance 4]] in the 16-OPSL. | ||
{{Harmonics in equal|2901533}} | |||
=== Prime harmonics === | |||
{{Harmonics in equal|2901533|columns=12}} | |||
{{Harmonics in equal|2901533|columns=12|start=13|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}} | |||
{{Harmonics in equal|2901533|columns=12|start=25|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}} | |||
{{Harmonics in equal|2901533|columns=12|start=37|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}} | |||
=== Subsets and supersets === | |||
{{Nowrap|2901533 {{=}} 433 × 6701}}, so 2901533edo contains [[433edo]] and [[6701edo]] as subsets. | |||
Latest revision as of 22:07, 10 August 2025
|
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.
Except for 8 barely inconsistent interval pairs, 2901533edo 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.