227edo: Difference between revisions
Jump to navigation
Jump to search
ArrowHead294 (talk | contribs) m Partial undo |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
227edo [[tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case. | |||
227edo is accurate for the [[13/1|13th harmonic]], as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]]. | 227edo is accurate for the [[13/1|13th harmonic]], as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]]. | ||
| Line 31: | Line 31: | ||
| {{monzo| 360 -227 }} | | {{monzo| 360 -227 }} | ||
| {{mapping| 227 360 }} | | {{mapping| 227 360 }} | ||
| | | −0.3561 | ||
| 0.3560 | | 0.3560 | ||
| 6.73 | | 6.73 | ||
| Line 38: | Line 38: | ||
| 15625/15552, {{monzo| 61 -37 -1 }} | | 15625/15552, {{monzo| 61 -37 -1 }} | ||
| {{mapping| 227 360 527 }} | | {{mapping| 227 360 527 }} | ||
| | | −0.1785 | ||
| 0.3842 | | 0.3842 | ||
| 7.27 | | 7.27 | ||
| Line 45: | Line 45: | ||
| 5120/5103, 15625/15552, 117649/116640 | | 5120/5103, 15625/15552, 117649/116640 | ||
| {{mapping| 227 360 527 637 }} | | {{mapping| 227 360 527 637 }} | ||
| | | −0.0071 | ||
| 0.4461 | | 0.4461 | ||
| 8.44 | | 8.44 | ||
| Line 103: | Line 103: | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "little hope" from ''hope in dark times'' (2024) | * "little hope" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] | [https://francium223.bandcamp.com/track/little-hope Bandcamp] | [https://www.youtube.com/watch?v=juMfOpUu25I YouTube] | ||
* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) | * "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] | [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] | [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube] | ||
* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) | * "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] | [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] | [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube] | ||
* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) | * "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] | [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] | [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube] | ||
[[Category:Countercata]] | [[Category:Countercata]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 18:59, 15 January 2025
| ← 226edo | 227edo | 228edo → |
Theory
227edo tempers out 15625/15552 (kleisma) and [61 -37 -1⟩ in the 5-limit; 5120/5103, 65625/65536, and 117649/116640 in the 7-limit, so that it supports countercata. In the 11-limit, it tempers out 385/384, 2200/2187, 3388/3375, and 12005/11979, so that it provides the optimal patent val for 11-limit countercata. In the 13-limit, it tempers out 325/324, 352/351, 625/624, 676/675, and 847/845, and again supplies a good tuning for 13-limit countercata, although 140edo tunes it better in this case.
227edo is accurate for the 13th harmonic, as the denominator of a convergent to log213, after 10 and before 5231.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +1.13 | -0.41 | -1.43 | -1.54 | +0.00 | +0.77 | -1.48 | +0.80 | +1.26 | +2.10 |
| Relative (%) | +0.0 | +21.4 | -7.8 | -27.0 | -29.1 | +0.0 | +14.6 | -28.0 | +15.1 | +23.8 | +39.7 | |
| Steps (reduced) |
227 (0) |
360 (133) |
527 (73) |
637 (183) |
785 (104) |
840 (159) |
928 (20) |
964 (56) |
1027 (119) |
1103 (195) |
1125 (217) | |
Subsets and supersets
227edo is the 49th prime edo.
Intervals
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [360 -227⟩ | [⟨227 360]] | −0.3561 | 0.3560 | 6.73 |
| 2.3.5 | 15625/15552, [61 -37 -1⟩ | [⟨227 360 527]] | −0.1785 | 0.3842 | 7.27 |
| 2.3.5.7 | 5120/5103, 15625/15552, 117649/116640 | [⟨227 360 527 637]] | −0.0071 | 0.4461 | 8.44 |
| 2.3.5.7.11 | 385/384, 2200/2187, 3388/3375, 12005/11979 | [⟨227 360 527 637 785]] | +0.0832 | 0.4380 | 8.29 |
| 2.3.5.7.11.13 | 325/324, 352/351, 385/384, 625/624, 12005/11979 | [⟨227 360 527 637 785 840]] | +0.0693 | 0.4010 | 7.59 |
| 2.3.5.7.11.13.17 | 325/324, 352/351, 385/384, 595/594, 625/624, 3185/3179 | [⟨227 360 527 637 785 840 928]] | +0.0324 | 0.3821 | 7.23 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 25\227 | 132.16 | 121/112 | Kastro |
| 1 | 60\227 | 317.18 | 6/5 | Countercata |
| 1 | 94\227 | 496.92 | 4/3 | Undecental |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct
Music
- "little hope" from hope in dark times (2024) – Spotify | Bandcamp | YouTube
- "Cuckoo Cucumber" from Cursed Cuckoo Creations (2024) – Spotify | Bandcamp | YouTube
- "Did You Put Resistors In My Brain?" from Questions (2024) – Spotify | Bandcamp | YouTube
- "Too Bad Homeboy" from Abbreviations Gone Wrong (2024) – Spotify | Bandcamp | YouTube