User:Unque/37edo Composition Theory
Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!
If it wasn't clear before, I definitely have a "type" when it comes to selecting tuning systems. 37 Equal Divisions of the Octave is another 11-limit system with a sharp diatonic fifth and supports Porcupine temperament. Being 15 + 22, fans of 15edo and 22edo will likely be drawn to 37edo as a structural extension of the two; additionally, fans of split-prime systems may also be drawn to 37 due to its slightly ambiguous harmonic nature (see Intervals).
As always, this page will be full of personal touches that may not reflect an objective truth or even wide consensus about how to use 37edo; I encourage learning musicians to experiment with different ideas and develop styles that best suit their own needs, rather than to take my word (or anyone else's for that matter) at face value as a great truth of music.
Intervals
37edo is a rather interesting 19-limit system, but it does have some amount of harmonic ambiguity in the 3-limit. The two mappings for 3/2 are respectively a diatonic and antidiatonic generator; I will here use + to indicate JI interpretations that use the diatonic 3-limit, and - to indicate those that use the antidiatonic 3-limit.
| Intervals | Cents | JI Intervals | As a generator | Notation | Notes |
|---|---|---|---|---|---|
| 0\37 | 0.00 | 1/1 | C | ||
| 1\37 | 32.43 | 55/54, 56/55 | D♭ | ||
| 2\37 | 64.86 | 28/27 | Sycamore/Unicorn | Sycamore uses diatonic fifth, Unicorn uses antidiatonic fifth | |
| 3\37 | 97.30 | 17/16 | Passion | Cｷ | |
| 4\37 | 129.73 | 14/13, 16/15 | Negri | Patent val 7 technically doesn't count as Negri, but it's the same structure | |
| 5\37 | 162.16 | 10/9, 9/8- | Porcupine | B♯ | 9/8 using antidiatonic fifth |
| 6\37 | 194.59 | 19/17, 9/8 | Didacus | C♯ | 9/8 using dual fifths |
| 7\37 | 227.03 | 9/8+, 8/7 | Gorgo/Shoe | D | 9/8 using diatonic fifth |
| 8\37 | 259.46 | 15/13 | Barbados | E♭ | |
| 9\37 | 291.89 | 13/11, 19/16 | |||
| 10\37 | 324.32 | 77/64 | Orgone | Dｷ | Not a good 6/5, but 77/64 is rather complex; I just think of it as half of 16/11 |
| 11\37 | 356.76 | 11/9, 16/13 | Beatles | Bisects the diatonic fifth | |
| 12\37 | 389.19 | 5/4 | Wuerschmidt | ||
| 13\37 | 421.62 | 14/11 | Lambeth | D♯ | |
| 14\37 | 454.05 | 9/7, 13/10 | Ammonite | E | |
| 15\37 | 486.49 | 4/3+ | Ultrapyth | F | Diatonic fourth |
| 16\37 | 518.92 | 4/3- | Undecimation | Antidiatonic fourth | |
| 17\37 | 551.35 | 11/8 | Emka | Eｷ | |
| 18\37 | 583.78 | 7/5 | Fｷ | ||
| 19\37 | 616.22 | 10/7 | |||
| 20\37 | 648.65 | 16/11 | Emka | E♯ | |
| 21\37 | 681.08 | 3/2- | Undecimation | F♯ | Antidiatonic fifth |
| 22\37 | 713.51 | 3/2+ | Ultrapyth | G | Diatonic fifth |
| 23\37 | 745.95 | 20/13, 14/9 | Ammonite | ||
| 24\37 | 778.38 | 11/7 | Lambeth | ||
| 25\37 | 810.81 | 8/5 | Wuerschmidt | Gｷ | |
| 26\37 | 843.24 | 13/8, 18/11 | Beatles | ||
| 27\37 | 875.68 | 128/77 | Orgone | ||
| 28\37 | 908.11 | 32/19, 22/13 | G♯ | ||
| 29\37 | 940.54 | 26/15 | Barbados | ||
| 30\37 | 972.97 | 7/4, 16/9+ | Gorgo/Shoe | B♭ | 16/9 using diatonic fourths |
| 31\37 | 1005.41 | 16/9 | Didacus | C♭ | 16/9 using dual fourths |
| 32\37 | 1037.84 | 16/9-, 9/5 | Porcupine | 16/9 using antidiatonic fourths | |
| 33\37 | 1070.27 | 15/8, 13/7 | Negri | Bd | |
| 34\37 | 1102.70 | 32/17 | Passion | Cd | |
| 35\37 | 1135.14 | 27/14 | Sycamore/Unicorn | ||
| 36\37 | 1167.57 | 55/28, 108/55 | B | ||
| 37\37 | 1200.00 | 2/1 | C |