User:Aura/1714833edo: Difference between revisions
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Prime factorization
32 × 190537
Step size
0.000699777 ¢
Fifth
1003113\1714833 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2)
162459:128934 (113.7 ¢ : 90.22 ¢)
Consistency limit
11
Distinct consistency limit
11
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{{ | {{Mathematical interest}} | ||
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{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
This EDO seems to be at its best in the 2.3.5.7.13.17.29 subgroup. | This EDO inherits its fifth from [[190537edo]] and seems to be at its best in the 2.3.5.7.13.17.29 [[subgroup]]. | ||
{{Harmonics in equal|1714833}} | {{Harmonics in equal|1714833}} | ||
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. |
| ← 1714832edo | 1714833edo | 1714834edo → |
1714833 equal divisions of the octave (abbreviated 1714833edo or 1714833ed2), also called 1714833-tone equal temperament (1714833tet) or 1714833 equal temperament (1714833et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1714833 equal parts of about 0.0007 ¢ each. Each step represents a frequency ratio of 21/1714833, or the 1714833rd root of 2.
Theory
This EDO inherits its fifth from 190537edo and seems to be at its best in the 2.3.5.7.13.17.29 subgroup.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000000 | +0.000000 | +0.000055 | +0.000096 | +0.000349 | -0.000100 | -0.000116 | -0.000197 | -0.000224 | -0.000087 | -0.000225 |
| Relative (%) | +0.0 | +0.0 | +7.9 | +13.7 | +49.9 | -14.3 | -16.6 | -28.2 | -32.0 | -12.4 | -32.2 | |
| Steps (reduced) |
1714833 (0) |
2717946 (1003113) |
3981719 (552053) |
4814145 (1384479) |
5932348 (787849) |
6345636 (1201137) |
7009316 (149984) |
7284486 (425154) |
7757153 (897821) |
8330626 (1471294) |
8495619 (1636287) | |