15ed4

← 14ed40001/10000

15ed40001/10000

16ed40001/10000 →

Prime factorization	3 × 5
Step size	160.003¢
Octave	7\15ed40001/10000 (1120.02¢) (semiconvergent)
Fifth	4\15ed40001/10000 (640.012¢)
Semitones (A1:m2)	7:-4 (1120¢ : -640¢)
Dual sharp fifth	5\15ed40001/10000 (800.014¢) (→1\3ed40001/10000)
Dual flat fifth	4\15ed40001/10000 (640.012¢)
Dual major 2nd	2\15ed40001/10000 (320.006¢)
Consistency limit	2
Distinct consistency limit	2

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).

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