15ed4
| ← 14ed40001/10000 | 15ed40001/10000 | 16ed40001/10000 → |
(semiconvergent)
15ED4 is the equal division of the double octave into 15 parts of 160 cents each (every second step of 15edo).
Lookalikes: 12edt
Basics
15ED4 is a macrotonal tuning system that divides the double octave (4/1) into 15 equally spaced pitches each 160 cents apart. It can be viewed as a subset of 15 EDO that repeats at two octaves rather than one. It has a big xen appeal as it is nonoctave but at the same time contains the double octave allowing for a sort of best of both worlds approach. 15ED4 doesn't do Just Intonation well for the most part but it does represent 7/4 and 11/10 rather well, so it can be viewed as a 3.4.7.10.11 subgroup temperament tempering out 28/27, 49/48, 55/54, and 77/75 (as well as 12EDT).
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.150 | -0.132 | +0.099 | +0.050 | +0.117 | -0.076 | -0.050 | +0.134 | -0.100 | -0.075 | -0.033 | +0.115 | +0.173 | -0.082 |
| Relative (%) | -37.5 | -33.2 | +25.0 | +12.5 | +29.3 | -19.2 | -12.6 | +33.6 | -25.0 | -18.7 | -8.2 | +28.8 | +43.3 | -20.7 | |
| Steps (reduced) |
3010 (3010) |
4771 (4771) |
6021 (6021) |
6990 (6990) |
7782 (7782) |
8451 (8451) |
9031 (9031) |
9543 (9543) |
10000 (10000) |
10414 (10414) |
10792 (10792) |
11140 (11140) |
11462 (11462) |
11761 (11761) | |
MOS Scales
There are a variety of Mos scales available. William Lynch considers the symmetrical MOS: LsLsLsLs to be the most consonant scale in 15ED4. There is also a LsLLsLLLs scale which is more spacey sounding than the symmetrical MOS. The symmetrical MOS can be harmonized with c