30edt
30edt (30 equal division of the tritave) is a stretched version of 19edo, but with the 3:1 rather than the 2:1 being just. The octave is about 4.5 cents sharp and the step size about 63.4 cents.
Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.
[edit]
Intervals of 30edt[edit]
| Degrees | Cents | Approximate Ratios | 10-3reduced-limit |
Sigma scale name |
| 0 | 0 | 1/1 | 1/1 | C |
| 1 | 63.3985 | 28/27, 27/26 | C#/Dbb | |
| 2 | 126.797 | 14/13, 15/14, 16/15, 29/27 |
Cx/Db | |
| 3 | 190.1955 | 10/9~9/8 | 9/8, 10/9 |
D |
| 4 | 253.594 | 15/13 | 7/6, 8/7 | D#/Ebb |
| 5 | 316.9925 | 6/5 | 6/5 | Dx/Eb |
| 6 | 380.391 | 5/4 | 5/4 | E |
| 7 | 443.7895 | 9/7 | 9/7 | E#/Fb |
| 8 | 507.188 | 4/3 | 4/3 |
F |
| 9 | 570.5865 | 7/5 | 7/5 | F#/Gbb |
| 10 | 633.985 | 10/7 | Fx/Gb | |
| 11 | 697.3835 | 3/2 | 3/2 | G |
| 12 | 760.782 | 14/9 | G#/Hbb | |
| 13 | 824.1805 |
8/5 |
8/5 | Gx/Hb |
| 14 |
887.579 |
5/3 | 5/3 | H |
| 15 | 950.9775 | 19/11 | 7/4, 12/7 | H#/Jbb |
| 16 | 1014.376 | 9/5 | 9/5 | Hx/Jb |
| 17 | 1077.7745 | 13/7 | 15/8 | J |
| 18 | 1141.173 | 27/14 | J#/Kb | |
| 19 | 1204.5715 | 2/1 | 2/1 | K |
| 20 | 1267.970 | 27/13 | 21/10 | K#/Lbb |
| 21 | 1331.3685 | 28/13 | 15/7 | Kx/Lb |
| 22 | 1394.767 | 9/4 | L | |
| 23 | 1458.1655 | 7/3 | 7/3 | L#/Abb |
| 24 | 1521.564 | 12/5 (6/5 plus an octave) | 12/5 | Lx/Ab |
| 25 | 1584.9625 | 5/2 | 5/2 | A |
|
26 |
1648.361 | 13/5 (13/10 plus an octave) | 18/7, 21/8 | A#/Bb |
| 27 | 1711.7595 | 8/3 | 8/3, 27/10 | B |
| 28 |
1775.158 |
14/5 (7/5 plus an octave) | B#/Cbb | |
| 29 | 1838.5565 | 26/9 | Bx/Cb | |
| 30 | 1901.955 | 3/1 | 3/1 | C |
30edt contains all 19edo intervals within 3/1, all temepered progressively sharper. The accumulation of the .241 cent sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615 cents flatter than that in 6edo.
30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces
MOS with an even number of periods per tritave such as a 6L 6s similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an unfair Sigma scale of 8L 3s and the major scale is LLsLLLsLLsL. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a 4L 9s unfair Superlambda MOS which does not border on being atonal as the 17edt rendition does.
Compositions in 30edt[edit]
- "Room Full Of Steam", Mason Green. In the key of "Eb subminor".