User:Francium/719edo: Difference between revisions
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Prime factorization
719 (prime)
Step size
1.66898 ¢
Fifth
421\719 (702.643 ¢)
Semitones (A1:m2)
71:52 (118.5 ¢ : 86.79 ¢)
Dual sharp fifth
421\719 (702.643 ¢)
Dual flat fifth
420\719 (700.974 ¢)
Dual major 2nd
122\719 (203.616 ¢)
Consistency limit
3
Distinct consistency limit
3
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== Music == | |||
; [[Francium]] | |||
* "Mar-A-Lago & FBI-Raid" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3NhTTk12RA51RgPqtZ70lc Spotify] | [https://francium223.bandcamp.com/track/mar-a-lago-fbi-raid Bandcamp] | [https://www.youtube.com/watch?v=nE16ZpLWUqo YouTube] – in Marfifths, 719edo tuning | |||
{{todo|inline=1|explain its xenharmonic value}} | {{todo|inline=1|explain its xenharmonic value}} | ||
Revision as of 12:09, 16 January 2025
| ← 718edo | 719edo | 720edo → |
Theory
719edo is only consistent to the 3-odd-limit and the error of its harmonic 3 is quite large. Its harmonics 5 and 7 are also about halfway its steps. It can be used in the 2.9.15.21.11.17.19.23.29 subgroup, tempering out 1701/1700, 3025/3024, 2376/2375, 8625/8624, 21888/21875, 72171/72128, 2001/2000 and 116127/116000. It supports marfifths.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.688 | -0.778 | -0.815 | -0.294 | -0.553 | +0.641 | -0.091 | +0.191 | -0.434 | -0.127 | -0.736 |
| Relative (%) | +41.2 | -46.6 | -48.8 | -17.6 | -33.1 | +38.4 | -5.4 | +11.4 | -26.0 | -7.6 | -44.1 | |
| Steps (reduced) |
1140 (421) |
1669 (231) |
2018 (580) |
2279 (122) |
2487 (330) |
2661 (504) |
2809 (652) |
2939 (63) |
3054 (178) |
3158 (282) |
3252 (376) | |
Subsets and supersets
719edo is the 128th prime EDO. 1438edo, which doubles it, gives a good correction to the harmonics 3, 5 and 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-2279 719⟩ | [⟨719 2279]] | 0.0464 | 0.0464 | 2.78 |
Music
- "Mar-A-Lago & FBI-Raid" from The Scallop Disco Accident (2025) – Spotify | Bandcamp | YouTube – in Marfifths, 719edo tuning
|
Todo: explain its xenharmonic value |