28/15

Interval information

Ratio	28/15
Factorization	22 × 3-1 × 5-1 × 7
Monzo	[2 -1 -1 1⟩
Size in cents	1080.557¢
Name	septimal grave major seventh
Color name	zg8, zogu octave
FJS name	[math]\displaystyle{ \text{d8}^{7}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.71425
Weil norm (log2 max(n, d))	9.61471
Wilson norm (sopfr(nd))	19
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28/15 is a 7-limit just intonation interval of about 1080.6 cents. It is well approximated by 10edo (9\10).

Terminology

Despite being approximated by the major seventh in systems like septimal meantone, and even being called the septimal grave major seventh by some musicians, 28/15 is a diminished octave in just intonation notation systems such as Sagittal notation, Helmholtz-Ellis notation and the Functional Just System, viewed as the Pythagorean diminished octave (4096/2187) altered by 5120/5103.

Approximation

Edo approximations for 28/15 (1080.56 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
10	9\10	1080.00	-0.56	-0.46
11	10\11	1090.91	+10.35	+9.49
20	18\20	1080.00	-0.56	-0.93
21	19\21	1085.71	+5.16	+9.02
30	27\30	1080.00	-0.56	-1.39
31	28\31	1083.87	+3.31	+8.56
40	36\40	1080.00	-0.56	-1.86
41	37\41	1082.93	+2.37	+8.10
50	45\50	1080.00	-0.56	-2.32
51	46\51	1082.35	+1.80	+7.63
60	54\60	1080.00	-0.56	-2.79
61	55\61	1081.97	+1.41	+7.17
70	63\70	1080.00	-0.56	-3.25
71	64\71	1081.69	+1.13	+6.70
80	72\80	1080.00	-0.56	-3.71

See also

• 15/14 – its octave complement
• Gallery of just intervals