User:Aura/1905370edo: Difference between revisions
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Prime factorization
2 × 5 × 190537
Step size
0.000629799 ¢
Fifth
1114570\1905370 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2)
180510:143260 (113.7 ¢ : 90.22 ¢)
Consistency limit
17
Distinct consistency limit
17
m Mark as niche. Cleanup. Wrap the harmonics table |
m Text replacement - "{{Infobox ET}}" to "{{Infobox ET|debug=1}}" |
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{{ | {{Mathematical interest}} | ||
{{Infobox ET}} | {{Infobox ET|debug=1}} | ||
{{ED intro}} | {{ED intro}} | ||
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1905370|columns=9 | {{Harmonics in equal|1905370|columns=9}} | ||
{{Harmonics in equal|1905370|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 1905370edo (continued)}} | {{Harmonics in equal|1905370|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 1905370edo (continued)}} | ||
Latest revision as of 16:53, 20 August 2025
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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. |
| ← 1905369edo | 1905370edo | 1905371edo → |
1905370 equal divisions of the octave (abbreviated 1905370edo or 1905370ed2), also called 1905370-tone equal temperament (1905370tet) or 1905370 equal temperament (1905370et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1905370 equal parts of about 0.00063 ¢ each. Each step represents a frequency ratio of 21/1905370, or the 1905370th root of 2.
This edo has a consistency limit of 17, but seems to be at its best in the 2.3.5.7.13.17 subgroup. It tempers out the archangelic comma in the 3-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000000 | +0.000000 | -0.000084 | +0.000096 | -0.000141 | +0.000110 | -0.000047 | +0.000223 | -0.000154 |
| Relative (%) | +0.0 | +0.0 | -13.4 | +15.2 | -22.3 | +17.4 | -7.4 | +35.4 | -24.4 | |
| Steps (reduced) |
1905370 (0) |
3019940 (1114570) |
4424132 (613392) |
5349050 (1538310) |
6591497 (875387) |
7050707 (1334597) |
7788129 (166649) |
8093874 (472394) |
8619059 (997579) | |
| Harmonic | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.000157 | -0.000015 | -0.000100 | +0.000086 | -0.000048 | +0.000025 | +0.000128 | +0.000260 | -0.000001 |
| Relative (%) | -24.9 | -2.4 | -15.9 | +13.7 | -7.6 | +4.0 | +20.3 | +41.3 | -0.1 | |
| Steps (reduced) |
9256251 (1634771) |
9439577 (1818097) |
9925936 (399086) |
10208119 (681269) |
10339042 (812192) |
10583547 (1056697) |
10913808 (1386958) |
11208612 (1681762) |
11300249 (1773399) | |