Arcturus hendecatonic notation
Arcturus hendecatonic notation is a notation system for EDTs and no-twos music, developed by CompactStar. It is based on the 2L 9s⟨3/1⟩ MOS scale generated by approximately 5/3. The 5/3 generator connects this MOS to the 3.5 subgroup and (in the soft-hard range) Arcturus temperament, similar to how the diatonic scale is connected to the 3-limit and (in the equalized-basic range) meantone temperament. The preferred generator for a given EDT is the patent val 5/3, unless it is extremely inaccurate (as is the case in some very small EDTs) and does not generate a 2L 9s⟨3/1⟩ scale.
The 9|1 mode of 2L 9s⟨3/1⟩ is represented by 11 naturals CDEFGHJKLAB, and #/b accidentals are used to raise and lower by a chroma (L - s). For relative notation, the TAMNAMS convention of zero-based indices is used. Assuming Arcturus temperament where 7/3 is mapped to the major 8-step, the chord 3:5:7 is notated as C - H - L (P0 - P5 - M8). To notate larger EDTs, Arcturus hendecatonic notation can be combined with ups and downs notation, with ^/v accidentals raising and lowering by 1 EDTstep.
Examples
11edt (equalized):
| Steps | Absolute notation | Relative notation |
|---|---|---|
| 0 | C | perfect 0-step |
| 1 | D | perfect 1-step |
| 2 | E | perfect 2-step |
| 3 | F | perfect 3-step |
| 4 | G | perfect 4-step |
| 5 | H | perfect 5-step |
| 6 | J | perfect 6-step |
| 7 | K | perfect 7-step |
| 8 | L | perfect 8-step |
| 9 | A | perfect 9-step |
| 10 | B | perfect 10-step |
| 11 | C | perfect 11-step |
13edt (Bohlen-Pierce):
| Steps | Absolute notation | Relative notation |
|---|---|---|
| 0 | C | perfect 0-step |
| 1 | Db | minor 1-step |
| 2 | D | major 1-step |
| 3 | E | major 2-step |
| 4 | F | major 3-step |
| 5 | G | major 4-step |
| 6 | H | perfect 5-step |
| 7 | J | perfect 6-step |
| 8 | Kb | minor 7-step |
| 9 | K | major 7-step |
| 10 | L | major 8-step |
| 11 | A | major 9-step |
| 12 | B | major 10-step |
| 13 | C | perfect 11-step |
| Steps | Absolute notation | Relative notation |
|---|---|---|
| 0 | C | perfect 0-step |
| 1 | C#, Dbb | augmented 0-step, diminished 1-step |
| 2 | Db | minor 1-step |
| 3 | D | major 1-step |
| 4 | Eb | minor 2-step |
| 5 | E | major 2-step |
| 6 | Fb | minor 3-step |
| 7 | F | major 3-step |
| 8 | Gb | minor 4-step |
| 9 | G | major 4-step |
| 10 | Hb | diminished 5-step |
| 11 | H | perfect 5-step |
| 12 | H#, Jb | augmented 5-step, diminished 6-step |
| 13 | J | perfect 6-step |
| 14 | J#, Kbb | augmented 6-step, diminished 7-step |
| 15 | Kb | minor 7-step |
| 16 | K | major 7-step |
| 17 | Lb | minor 8-step |
| 18 | L | major 8-step |
| 19 | Ab | minor 9-step |
| 20 | A | major 9-step |
| 21 | Bb | minor 10-step |
| 22 | B | major 10-step |
| 23 | B#, Cb | augmented 10-step, diminished 11-step |
| 24 | C | perfect 11-step |