32436edo
| ← 32435edo | 32436edo | 32437edo → |
32436 equal divisions of the octave (abbreviated 32436edo or 32436ed2), also called 32436-tone equal temperament (32436tet) or 32436 equal temperament (32436et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 32436 equal parts of about 0.037 ¢ each. Each step represents a frequency ratio of 21/32436, or the 32436th root of 2.
32436edo is consistent in the 5-limit, but only this far. However, it is useful as an interval size measure as it contains many notable EDOs, for example: 12, 17, 34, 36, 53, 306, 612, 901, 954. It expands upon 16218edo which it doubles, trading off consistency for greater amount of divisors.
Other than that, harmonically, by 15% error cutoff it is a strong 2.5.11.17 subgroup tuning, and by 20% cutoff, 32436edo is a satisfactory 2.3.5.11.17.37.53.71 subgroup tuning.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0058 | -0.0022 | -0.0135 | -0.0046 | -0.0171 | +0.0020 | +0.0083 | -0.0095 | -0.0174 | -0.0115 | +0.0063 |
| Relative (%) | +0.0 | +15.6 | -6.0 | -36.4 | -12.4 | -46.3 | +5.5 | +22.3 | -25.6 | -47.2 | -31.2 | +17.1 | |
| Steps (reduced) |
32436 (0) |
51410 (18974) |
75314 (10442) |
91059 (26187) |
112210 (14902) |
120027 (22719) |
132581 (2837) |
137786 (8042) |
146726 (16982) |
157573 (27829) |
160694 (30950) |
168974 (6794) | |
| Harmonic | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0164 | -0.0120 | +0.0132 | +0.0064 | -0.0152 | -0.0147 | +0.0122 | -0.0073 | -0.0055 | -0.0160 | +0.0082 | +0.0041 |
| Relative (%) | +44.3 | -32.4 | +35.6 | +17.2 | -41.0 | -39.6 | +33.1 | -19.8 | -14.9 | -43.2 | +22.1 | +11.0 | |
| Steps (reduced) |
173778 (11598) |
176006 (13826) |
180169 (17989) |
185791 (23611) |
190809 (28629) |
192369 (30189) |
196760 (2144) |
199473 (4857) |
200773 (6157) |
204469 (9853) |
206781 (12165) |
210047 (15431) | |
Subsets and supersets
32436edo has subset edos 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 53, 68, 102, 106, 153, 159, 204, 212, 306, 318, 477, 612, 636, 901, 954, 1802, 1908, 2703, 3604, 5406, 8109, 10812, 16218.
Its abundancy index is approximately 1.73, which may not be as impressive as highly composite EDOs, but 32436edo has a high density of xenharmonically notable EDOs, which opens up potentials for it being used as an interval size measure or a MIDI tuning unit.
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