673edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 27: | Line 36: | ||
| 0.1521 | | 0.1521 | ||
| 8.53 | | 8.53 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 37: | Line 53: | ||
| 16875/16384 | | 16875/16384 | ||
| [[Escapade]] | | [[Escapade]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "They Unraveled" from ''Scoop'' (2024) – [https://open.spotify.com/track/2VjnkDBShyJekqv4tv7HA8 Spotify] | [https://francium223.bandcamp.com/track/they-unraveled Bandcamp] | [https://www.youtube.com/watch?v=yQCfdPObfKI YouTube] | * "They Unraveled" from ''Scoop'' (2024) – [https://open.spotify.com/track/2VjnkDBShyJekqv4tv7HA8 Spotify] | [https://francium223.bandcamp.com/track/they-unraveled Bandcamp] | [https://www.youtube.com/watch?v=yQCfdPObfKI YouTube] | ||
Revision as of 13:19, 16 November 2024
| ← 672edo | 673edo | 674edo → |
Theory
673edo is consistent to the 5-odd-limit. Using the 2.3.5.17.19.41 subgroup, it tempers out 4624/4617, 131072/130815, 53136/53125, 10584064/10546875 and 19178125/19131876.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.571 | +0.611 | -0.624 | -0.641 | -0.352 | -0.706 | -0.602 | +0.245 | +0.258 | -0.053 | -0.637 |
| Relative (%) | +32.0 | +34.2 | -35.0 | -36.0 | -19.7 | -39.6 | -33.7 | +13.8 | +14.5 | -3.0 | -35.7 | |
| Steps (reduced) |
1067 (394) |
1563 (217) |
1889 (543) |
2133 (114) |
2328 (309) |
2490 (471) |
2629 (610) |
2751 (59) |
2859 (167) |
2956 (264) |
3044 (352) | |
Subsets and supersets
673edo is the 122nd prime EDO. 2019edo, which triples it, gives a good correction to the 7-limit alongside primes 13 and 23.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [1067 -673⟩ | [⟨673 1067]] | -0.1801 | 0.1801 | 10.10 |
| 2.3.5 | [32 -7 -9⟩, [19 -53 28⟩ | [⟨673 1067 1563]] | -0.2077 | 0.1521 | 8.53 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 31\673 | 55.275 | 16875/16384 | Escapade |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct