2207edo: Difference between revisions
Jump to navigation
Jump to search
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..." |
m →Theory: cleanup |
||
| Line 3: | Line 3: | ||
== 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]]. Using the 2.3.7.11.17.37 subgroup, it [[tempering out|tempers out]] [[3774/3773]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
Revision as of 16:51, 17 January 2025
| ← 2206edo | 2207edo | 2208edo → |
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. 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 |