2207edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|2207}} == Theory == 2207edo is consistent to the 5-odd-limit, but its harmonic 5 is about halfway its steps. It is strong in th..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
2207edo is [[consistent]] to the [[5-odd-limit]], | 2207edo is only [[consistent]] to the [[5-odd-limit]], and its [[harmonic]] [[5/1|5]] is about halfway between its steps. It is strong in the 2.3.11.17.31 [[subgroup]], [[tempering out]] 1114112/1114047, 133159451283/133143986176, 214374114/214358881 and 748268928/748264639. Using the 2.3.7.11.17.37 subgroup, it tempers out [[3774/3773]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | |- | ||
! rowspan="2" |[[Comma list | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
|- | ! colspan="2" | Tuning error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|-3498 2207}} | | {{monzo|-3498 2207}} | ||
| {{mapping|2207 3498}} | | {{mapping|2207 3498}} | ||
| 0.0021 | | +0.0021 | ||
| 0.0021 | | 0.0021 | ||
| 0.39 | | 0.39 | ||
|} | |} | ||
== Music == | |||
; [[Francium]] | |||
* "I'm Such a "Look at the Moon" Person." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/47wcdZHMpT846xQD5Csnu9 Spotify] | [https://francium223.bandcamp.com/track/im-such-a-look-at-the-moon-person Bandcamp] | [https://www.youtube.com/watch?v=1j-w-De3uOo YouTube] | |||
* "200$ PLEASE" from ''Things to Scream at People'' (2025) – [https://open.spotify.com/track/42KFfiRRhCkF9pmV45AoEC Spotify] | [https://francium223.bandcamp.com/track/200-please Bandcamp] | [https://www.youtube.com/watch?v=vxdXAxbsgE4 YouTube] | |||
Latest revision as of 13:34, 14 October 2025
| ← 2206edo | 2207edo | 2208edo → |
2207 equal divisions of the octave (abbreviated 2207edo or 2207ed2), also called 2207-tone equal temperament (2207tet) or 2207 equal temperament (2207et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2207 equal parts of about 0.544 ¢ each. Each step represents a frequency ratio of 21/2207, or the 2207th root of 2.
Theory
2207edo is only consistent to the 5-odd-limit, and its harmonic 5 is about halfway between its steps. It is strong in the 2.3.11.17.31 subgroup, tempering out 1114112/1114047, 133159451283/133143986176, 214374114/214358881 and 748268928/748264639. Using the 2.3.7.11.17.37 subgroup, it tempers out 3774/3773.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.007 | -0.269 | +0.091 | -0.013 | +0.019 | +0.070 | +0.268 | -0.017 | -0.096 | +0.085 | +0.271 |
| Relative (%) | -1.2 | -49.5 | +16.8 | -2.4 | +3.4 | +13.0 | +49.2 | -3.0 | -17.6 | +15.5 | +49.9 | |
| Steps (reduced) |
3498 (1291) |
5124 (710) |
6196 (1782) |
6996 (375) |
7635 (1014) |
8167 (1546) |
8623 (2002) |
9021 (193) |
9375 (547) |
9694 (866) |
9984 (1156) | |
Subsets and supersets
2207edo is the 329th prime edo. 4414edo, which doubles it, gives a good correction to the harmonic 5.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-3498 2207⟩ | [⟨2207 3498]] | +0.0021 | 0.0021 | 0.39 |