15ed4
| ← 13ed4 | 15ed4 | 17ed4 → |
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 (¢) | +80.0 | +18.0 | +0.0 | -66.3 | -62.0 | -8.8 | +80.0 | +36.1 | +13.7 | +8.7 | +18.0 | +39.5 | +71.2 | -48.3 |
| relative (%) | +50 | +11 | +0 | -41 | -39 | -6 | +50 | +23 | +9 | +5 | +11 | +25 | +44 | -30 | |
| Steps (reduced) |
8 (8) |
12 (12) |
15 (0) |
17 (2) |
19 (4) |
21 (6) |
23 (8) |
24 (9) |
25 (10) |
26 (11) |
27 (12) |
28 (13) |
29 (14) |
29 (14) | |
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