1817edo: Difference between revisions
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1817edo is distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16|29]] is worth considering. | |||
In the 5-limit, it is a strong tuning for [[alphatricot]]. It also [[tempering out|tempers out]] {{monzo| 128 13 -64 }}, corresponding to the 323 & 1171 temperament, which divides the [[3/1|third harmonic]] into 64 equal parts, as well as {{monzo| -89 -42 67 }} and {{monzo| -50 -71 70 }}. In the 7-limit, it tempers out [[4375/4374]] (ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments [[heimdall]] and [[bragi]]. In the 13-limit, it tempers out [[4096/4095]], [[6656/6655]], and in the 17-limit, [[12376/12375]] and [[14400/14399]]. | |||
In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (17-limit add-37), the [[patent val]] tunes the [[gold]] temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|1817}} | |||
=== Subsets and supersets === | |||
Since 1817 factors into primes as {{nowrap| 23 × 79 }}, 1817edo contains [[23edo]] and [[79edo]] as subsets. | |||
Latest revision as of 13:42, 16 March 2025
| ← 1816edo | 1817edo | 1818edo → |
1817 equal divisions of the octave (abbreviated 1817edo or 1817ed2), also called 1817-tone equal temperament (1817tet) or 1817 equal temperament (1817et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1817 equal parts of about 0.66 ¢ each. Each step represents a frequency ratio of 21/1817, or the 1817th root of 2.
1817edo is distinctly consistent in the 17-odd-limit, and a fairly strong 17-limit system. Past that, adding the mapping for 29 is worth considering.
In the 5-limit, it is a strong tuning for alphatricot. It also tempers out [128 13 -64⟩, corresponding to the 323 & 1171 temperament, which divides the third harmonic into 64 equal parts, as well as [-89 -42 67⟩ and [-50 -71 70⟩. In the 7-limit, it tempers out 4375/4374 (ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments heimdall and bragi. In the 13-limit, it tempers out 4096/4095, 6656/6655, and in the 17-limit, 12376/12375 and 14400/14399.
In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (17-limit add-37), the patent val tunes the gold temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.081 | +0.037 | +0.024 | +0.141 | +0.199 | +0.053 | -0.320 | -0.206 | +0.032 | +0.149 |
| Relative (%) | +0.0 | +12.3 | +5.7 | +3.6 | +21.3 | +30.1 | +8.0 | -48.4 | -31.2 | +4.9 | +22.5 | |
| Steps (reduced) |
1817 (0) |
2880 (1063) |
4219 (585) |
5101 (1467) |
6286 (835) |
6724 (1273) |
7427 (159) |
7718 (450) |
8219 (951) |
8827 (1559) |
9002 (1734) | |
Subsets and supersets
Since 1817 factors into primes as 23 × 79, 1817edo contains 23edo and 79edo as subsets.