677edo: Difference between revisions
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* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] | [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] | [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube] | * "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] | [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] | [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube] | ||
* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] | [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] | [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] – in Scarlattic, 677edo tuning | * "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] | [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] | [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] – in Scarlattic, 677edo tuning | ||
* "Make Gecko Expansion" from ''I Want To'' (2025) – [https://open.spotify.com/track/5dbEP5zQQrrO00f3XZiELV Spotify] | [https://francium223.bandcamp.com/track/make-gecko-expansion Bandcamp] | [https://www.youtube.com/watch?v=D55Y0-p_mWU YouTube] – in Genzelic, 677edo tuning | |||
Revision as of 12:42, 5 February 2025
| ← 676edo | 677edo | 678edo → |
Theory
While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several metallic ratios. Among those, it tunes acoustic phi (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.03 | +0.10 | +0.75 | -0.06 | -0.35 | -0.38 | +0.27 | -0.80 |
| Relative (%) | +0.0 | -2.0 | +5.5 | +42.1 | -3.5 | -19.8 | -21.2 | +15.3 | -45.1 | |
| Steps (reduced) |
677 (0) |
1073 (396) |
1572 (218) |
1901 (547) |
2342 (311) |
2505 (474) |
2767 (59) |
2876 (168) |
3062 (354) | |
Subsets and supersets
677edo is the 123rd prime EDO.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1073 677⟩ | [⟨677 1073]] | +0.0110 | 0.0110 | 0.62 |
| 2.3.5 | [38 -2 -15⟩, [-31 43 -16⟩ | [⟨677 1073 1572]] | -0.0066 | 0.0264 | 1.49 |
| 2.3.5.7 | 703125/702464, 589824/588245, 14348907/14336000 | [⟨677 1073 1572 1901]] | -0.0714 | 0.1145 | 6.46 |
| 2.3.5.7.11 | 3025/3024, 24057/24010, 131072/130977, 759375/758912 | [⟨677 1073 1572 1901 2342]] | -0.0535 | 0.1084 | 6.12 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced)* |
Cents (reduced)* |
Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 109\677 | 193.21 | 262144/234375 | Luna |
| 1 | 125\677 | 221.57 | 8388608/7381125 | Fortune |
| 1 | 281\677 | 498.08 | 4/3 | Counterschismic |
Music
- "From the Ears of the Eel" from Scoop (2024) – Spotify | Bandcamp | YouTube
- "The Scallop Disco Accident" from The Scallop Disco Accident (2025) – Spotify | Bandcamp | YouTube – in Scarlattic, 677edo tuning
- "Make Gecko Expansion" from I Want To (2025) – Spotify | Bandcamp | YouTube – in Genzelic, 677edo tuning