947edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" Tags: Mobile edit Mobile web edit |
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<nowiki />* [[Normal | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Very Long Cat" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/00UsULE1PFkKilmuIoFIvy Spotify] | [https://francium223.bandcamp.com/track/very-long-cat Bandcamp] | [https://www.youtube.com/watch?v=YS-ywj253yw YouTube] | * "Very Long Cat" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/00UsULE1PFkKilmuIoFIvy Spotify] | [https://francium223.bandcamp.com/track/very-long-cat Bandcamp] | [https://www.youtube.com/watch?v=YS-ywj253yw YouTube] | ||
Latest revision as of 13:44, 13 March 2026
| ← 946edo | 947edo | 948edo → |
947 equal divisions of the octave (abbreviated 947edo or 947ed2), also called 947-tone equal temperament (947tet) or 947 equal temperament (947et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 947 equal parts of about 1.27 ¢ each. Each step represents a frequency ratio of 21/947, or the 947th root of 2.
Theory
947edo is consistent to the 9-odd-limit, tempering out 3025/3024, 131072/130977, 2460375/2458624 and 766656/765625 in the 11-limit. It is strong in the 2.3.5.11.17.23 subgroup, tempering out 3520/3519, 557056/556875, 30613/30600, 79488/79475 and 3680721/3680000. Using the 2.3.5.17.19.43 subgroup, it tempers out 29241/29240. It supports squarschmidt.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.051 | +0.170 | +0.551 | -0.104 | -0.401 | +0.219 | +0.269 | +0.237 | +0.623 | +0.477 |
| Relative (%) | +0.0 | +4.1 | +13.4 | +43.5 | -8.2 | -31.6 | +17.3 | +21.3 | +18.7 | +49.2 | +37.6 | |
| Steps (reduced) |
947 (0) |
1501 (554) |
2199 (305) |
2659 (765) |
3276 (435) |
3504 (663) |
3871 (83) |
4023 (235) |
4284 (496) |
4601 (813) |
4692 (904) | |
Subsets and supersets
947edo is the 161st prime edo. 1894edo, which doubles it, gives a good correction to the harmonic 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [1501 -947⟩ | [⟨947 1501]] | −0.0162 | 0.0162 | 1.28 |
| 2.3.5 | [-16 35 -17⟩, [77 -31 -12⟩ | [⟨947 1501 2199]] | −0.0352 | 0.0299 | 2.36 |
| 2.3.5.7 | 2460375/2458624, 78125000/78121827, 2579890176/2573571875 | [⟨947 1501 2199 2659]] | −0.0755 | 0.0744 | 5.87 |
| 2.3.5.7.11 | 3025/3024, 131072/130977, 2460375/2458624, 766656/765625 | [⟨947 1501 2199 2659 3276]] | −0.0544 | 0.0788 | 6.22 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 144\947 | 182.471 | 10/9 | Minortone |
| 1 | 204\947 | 258.501 | [-32 13 5⟩ | Lafa |
| 1 | 313\947 | 396.621 | 98304/78125 | Squarschmidt |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct