111202edo: Difference between revisions
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Created page with "{{Infobox ET}} The '''111202edo''' divides the octave into 111202 equal parts of 0.0108 cents each. It is the denominator of the next convergent for log<sub>2</sub>3 past 7..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} It is the denominator of the next convergent for log<sub>2</sub>3 past [[79335edo|79335]], before [[190537edo|190537]]. | |||
111202edo has a [[consistency]] limit of only 9, and is a strong 5-limit system, with additional strengths in the 2.3.5.17.19.23 subgroup. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|111202}} | {{Harmonics in equal|111202}} | ||
[[Category: | [[Category:3-limit record edos|######]] <!-- 6-digit number --> | ||
Latest revision as of 16:31, 28 July 2025
| ← 111201edo | 111202edo | 111203edo → |
(convergent)
111202 equal divisions of the octave (abbreviated 111202edo or 111202ed2), also called 111202-tone equal temperament (111202tet) or 111202 equal temperament (111202et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 111202 equal parts of about 0.0108 ¢ each. Each step represents a frequency ratio of 21/111202, or the 111202nd root of 2. It is the denominator of the next convergent for log23 past 79335, before 190537.
111202edo has a consistency limit of only 9, and is a strong 5-limit system, with additional strengths in the 2.3.5.17.19.23 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | -0.00000 | -0.00052 | -0.00520 | +0.00308 | -0.00321 | -0.00046 | -0.00038 | -0.00147 | -0.00219 | +0.00498 |
| Relative (%) | +0.0 | -0.0 | -4.8 | -48.2 | +28.5 | -29.8 | -4.3 | -3.5 | -13.7 | -20.3 | +46.2 | |
| Steps (reduced) |
111202 (0) |
176251 (65049) |
258203 (35799) |
312183 (89779) |
384696 (51090) |
411496 (77890) |
454534 (9726) |
472378 (27570) |
503029 (58221) |
540217 (95409) |
550917 (106109) | |