3696edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
3696edo is consistent in the 17-odd-limit. | 3696edo is consistent in the 17-odd-limit. It is contorted in the 11-limit, sharing the mapping with [[1848edo]], and provides a satisfactory correction to 1848edo's representation for 13 and 17. Besides that, it is a strong tuning in 2.3.5.7.11.23.29. | ||
It is contorted in the 11-limit, sharing the mapping with [[1848edo]]. | |||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|3696}} | {{Harmonics in equal|3696}} | ||
Latest revision as of 16:59, 20 February 2025
| ← 3695edo | 3696edo | 3697edo → |
3696 equal divisions of the octave (abbreviated 3696edo or 3696ed2), also called 3696-tone equal temperament (3696tet) or 3696 equal temperament (3696et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3696 equal parts of about 0.325 ¢ each. Each step represents a frequency ratio of 21/3696, or the 3696th root of 2.
Theory
3696edo is consistent in the 17-odd-limit. It is contorted in the 11-limit, sharing the mapping with 1848edo, and provides a satisfactory correction to 1848edo's representation for 13 and 17. Besides that, it is a strong tuning in 2.3.5.7.11.23.29.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.007 | +0.050 | +0.005 | -0.019 | +0.057 | -0.085 | -0.110 | -0.028 | -0.032 | +0.094 |
| Relative (%) | +0.0 | -2.1 | +15.4 | +1.6 | -5.9 | +17.5 | -26.3 | -34.0 | -8.5 | -9.8 | +29.0 | |
| Steps (reduced) |
3696 (0) |
5858 (2162) |
8582 (1190) |
10376 (2984) |
12786 (1698) |
13677 (2589) |
15107 (323) |
15700 (916) |
16719 (1935) |
17955 (3171) |
18311 (3527) | |