15ed4

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← 13ed415ed417ed4 →
Prime factorization 3 × 5
Step size 160¢
Octave 8\15ed4 (1280¢)
Twelfth 12\15ed4 (1920¢) (→4\5ed4)
Consistency limit 1
Distinct consistency limit 1

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).

Approximation of harmonics in 15ed4
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