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Created page with "{{Infobox ET}} {{EDO intro|469}} == Theory == 469et is only consistent to the 5-odd-limit and the error of the harmonic 3 is quite large. It can be considered..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
469et is only consistent to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is quite large. It can be considered for the 2.9.5.7.13.17 [[subgroup]], tempering out [[2601/2600]], 7616/7605, [[5832/5831]], 60112/60025 and 265625/264992. It [[support]]s [[gravity | 469et is only [[consistent]] to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is quite large. It can be considered for the 2.9.5.7.13.17 [[subgroup]], tempering out [[2601/2600]], 7616/7605, [[5832/5831]], 60112/60025 and 265625/264992. It [[support]]s [[gravity]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
469 factors into 7 × 67, | Since 469 factors into 7 × 67, 469edo has [[7edo]] and [[67edo]] as its subset edos. [[938edo]], which doubles it, gives a good correction to the harmonics 3 and 5. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
|2.9 | ! rowspan="2" | [[Subgroup]] | ||
|{{monzo|1487 -469}} | ! rowspan="2" | [[Comma list]] | ||
|{{mapping|469 1487}} | ! rowspan="2" | [[Mapping]] | ||
| | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.9 | |||
| {{monzo| 1487 -469 }} | |||
| {{mapping| 469 1487 }} | |||
| −0.1232 | |||
| 0.1232 | | 0.1232 | ||
| 4.82 | | 4.82 | ||
|- | |- | ||
|2.9.5 | | 2.9.5 | ||
|{{monzo|38 -1 -15}}, {{monzo|13 -29 34}} | | {{monzo| 38 -1 -15 }}, {{monzo| 13 -29 34 }} | ||
|{{mapping|469 1487 1089}} | | {{mapping| 469 1487 1089 }} | ||
| | | −0.0879 | ||
| 0.1122 | | 0.1122 | ||
| 4.39 | | 4.39 | ||
|} | |} | ||
Latest revision as of 16:42, 16 August 2026
| ← 468edo | 469edo | 470edo → |
469 equal divisions of the octave (abbreviated 469edo or 469ed2), also called 469-tone equal temperament (469tet) or 469 equal temperament (469et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 469 equal parts of about 2.56 ¢ each. Each step represents a frequency ratio of 21/469, or the 469th root of 2.
Theory
469et is only consistent to the 5-odd-limit and the error of the harmonic 3 is quite large. It can be considered for the 2.9.5.7.13.17 subgroup, tempering out 2601/2600, 7616/7605, 5832/5831, 60112/60025 and 265625/264992. It supports gravity.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.89 | +0.04 | +0.90 | +0.78 | -1.21 | +1.26 | -0.85 | -0.05 | -0.71 | +0.01 | +1.15 |
| Relative (%) | -34.7 | +1.6 | +35.1 | +30.5 | -47.3 | +49.4 | -33.2 | -2.0 | -27.8 | +0.3 | +44.9 | |
| Steps (reduced) |
743 (274) |
1089 (151) |
1317 (379) |
1487 (80) |
1622 (215) |
1736 (329) |
1832 (425) |
1917 (41) |
1992 (116) |
2060 (184) |
2122 (246) | |
Subsets and supersets
Since 469 factors into 7 × 67, 469edo has 7edo and 67edo as its subset edos. 938edo, which doubles it, gives a good correction to the harmonics 3 and 5.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [1487 -469⟩ | [⟨469 1487]] | −0.1232 | 0.1232 | 4.82 |
| 2.9.5 | [38 -1 -15⟩, [13 -29 34⟩ | [⟨469 1487 1089]] | −0.0879 | 0.1122 | 4.39 |