607edo: Difference between revisions
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| Line 26: | Line 26: | ||
| {{monzo|-962 607}} | | {{monzo|-962 607}} | ||
| {{mapping|607 962}} | | {{mapping|607 962}} | ||
| 0.0451 | | +0.0451 | ||
| 0.0451 | | 0.0451 | ||
| 2.28 | | 2.28 | ||
| Line 33: | Line 33: | ||
| 32805/32768, {{monzo|-58 -63 68}} | | 32805/32768, {{monzo|-58 -63 68}} | ||
| {{mapping|607 962 1409}} | | {{mapping|607 962 1409}} | ||
| 0.1465 | | +0.1465 | ||
| 0.1481 | | 0.1481 | ||
| 7.49 | | 7.49 | ||
| Line 40: | Line 40: | ||
| 32805/32768, 420175/419904, 244140625/243045684 | | 32805/32768, 420175/419904, 244140625/243045684 | ||
| {{mapping|607 962 1409 1704}} | | {{mapping|607 962 1409 1704}} | ||
| 0.1212 | | +0.1212 | ||
| 0.1355 | | 0.1355 | ||
| 6.85 | | 6.85 | ||
| Line 47: | Line 47: | ||
| 3025/3024, 6250/6237, 32805/32768, 420175/419904 | | 3025/3024, 6250/6237, 32805/32768, 420175/419904 | ||
| {{mapping|607 962 1409 1704 2100}} | | {{mapping|607 962 1409 1704 2100}} | ||
| 0.0827 | | +0.0827 | ||
| 0.1437 | | 0.1437 | ||
| 7.27 | | 7.27 | ||
| Line 54: | Line 54: | ||
| 2080/2079, 625/624, 3025/3024, 78975/78848, 218700/218491 | | 2080/2079, 625/624, 3025/3024, 78975/78848, 218700/218491 | ||
| {{mapping|607 962 1409 1704 2100 2246}} | | {{mapping|607 962 1409 1704 2100 2246}} | ||
| 0.0838 | | +0.0838 | ||
| 0.1312 | | 0.1312 | ||
| 6.64 | | 6.64 | ||
| Line 61: | Line 61: | ||
| 2080/2079, 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831 | | 2080/2079, 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831 | ||
| {{mapping|607 962 1409 1704 2100 2246 2481}} | | {{mapping|607 962 1409 1704 2100 2246 2481}} | ||
| 0.0780 | | +0.0780 | ||
| 0.1222 | | 0.1222 | ||
| 6.18 | | 6.18 | ||
| Line 82: | Line 82: | ||
| [[Helmholtz]] | | [[Helmholtz]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Complete Edition" from ''You Are A...'' (2024) | * "Complete Edition" from ''You Are A...'' (2024) – [https://open.spotify.com/track/3U1YP47z0bmKZ76DzXEDTG Spotify] | [https://francium223.bandcamp.com/track/complete-edition Bandcamp] | [https://www.youtube.com/watch?v=PTpp4HPi98A YouTube] – countertertiaschis[15] in 607edo tuning | ||
* "TAKE THE NIGHT WITH YOU" from ''CAPSLOCK'' (2024) | * "TAKE THE NIGHT WITH YOU" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3xjT48PIa0OjNL7yTBWwVF Spotify] | [https://francium223.bandcamp.com/track/take-the-night-with-you Bandcamp] | [https://www.youtube.com/watch?v=5fzzB753wfM YouTube] | ||
* "Sweep Away" from ''Take Advantage'' (2024) | * "Sweep Away" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/3W9U6apb2cfKHtUXsmILDE Spotify] | [https://francium223.bandcamp.com/track/sweep-away Bandcamp] | [https://www.youtube.com/watch?v=5Q-aQnStoaA YouTube] | ||
* "In the Field of Vodka" from ''Scoop'' (2024) | * "In the Field of Vodka" from ''Scoop'' (2024) – [https://open.spotify.com/track/79JeaYC5nBpz4fG6pPgkEe Spotify] | [https://francium223.bandcamp.com/track/in-the-field-of-vodka Bandcamp] | [https://www.youtube.com/watch?v=j_tkNX986sU YouTube] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 18:52, 15 January 2025
| ← 606edo | 607edo | 608edo → |
Theory
607edo is consistent to the 9-odd-limit. Using the patent val, the equal temperament tempers out 32805/32768, 420175/419904 and 244140625/243045684 in the 7-limit; 3025/3024, 6250/6237, 32805/32768 and 420175/419904 in the 11-limit. It supports countertertiaschis. Essentially tempered chords available in 607et include baladismic chords and xenismic chords.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.143 | -0.811 | -0.127 | +0.247 | -0.330 | -0.178 | -0.973 | +0.391 | +0.406 | -0.390 |
| Relative (%) | +0.0 | -7.2 | -41.0 | -6.4 | +12.5 | -16.7 | -9.0 | -49.2 | +19.8 | +20.6 | -19.7 | |
| Steps (reduced) |
607 (0) |
962 (355) |
1409 (195) |
1704 (490) |
2100 (279) |
2246 (425) |
2481 (53) |
2578 (150) |
2746 (318) |
2949 (521) |
3007 (579) | |
Subsets and supersets
607edo is the 111th prime EDO.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-962 607⟩ | [⟨607 962]] | +0.0451 | 0.0451 | 2.28 |
| 2.3.5 | 32805/32768, [-58 -63 68⟩ | [⟨607 962 1409]] | +0.1465 | 0.1481 | 7.49 |
| 2.3.5.7 | 32805/32768, 420175/419904, 244140625/243045684 | [⟨607 962 1409 1704]] | +0.1212 | 0.1355 | 6.85 |
| 2.3.5.7.11 | 3025/3024, 6250/6237, 32805/32768, 420175/419904 | [⟨607 962 1409 1704 2100]] | +0.0827 | 0.1437 | 7.27 |
| 2.3.5.7.11.13 | 2080/2079, 625/624, 3025/3024, 78975/78848, 218700/218491 | [⟨607 962 1409 1704 2100 2246]] | +0.0838 | 0.1312 | 6.64 |
| 2.3.5.7.11.13.17 | 2080/2079, 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831 | [⟨607 962 1409 1704 2100 2246 2481]] | +0.0780 | 0.1222 | 6.18 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 252\607 | 498.188 | 4/3 | Helmholtz |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct
Music
- "Complete Edition" from You Are A... (2024) – Spotify | Bandcamp | YouTube – countertertiaschis[15] in 607edo tuning
- "TAKE THE NIGHT WITH YOU" from CAPSLOCK (2024) – Spotify | Bandcamp | YouTube
- "Sweep Away" from Take Advantage (2024) – Spotify | Bandcamp | YouTube
- "In the Field of Vodka" from Scoop (2024) – Spotify | Bandcamp | YouTube