28/15: Difference between revisions

Interval information
Ratio	28/15
Factorization	22 × 3-1 × 5-1 × 7
Monzo	[2 -1 -1 1⟩
Size in cents	1080.557¢
Names	septimal grave major seventh,; aberschismic diminished octave
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
	https://en.xen.wiki/w/File:Jid_28_15_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

Latest revision as of 10:46, 1 August 2026

28/15 is an interval in 7-limit just intonation measuring about 1080.6 cents, traditionally known as the septimal grave major seventh for its proximity (and conflation in marvel tunings such as septimal meantone) with the classical major seventh 15/8. However, it functions as a diminished octave, as is supported by Sagittal notation, Helmholtz–Ellis notation and the Functional Just System, viewed as the Pythagorean diminished octave flattened by an aberschisma. This gives rise to the more precise name aberschismic diminished octave. It arises from stacking various 9-odd-limit consonances, including the stack consisting of 6/5 and 14/9, of 7/6 and 8/5, and of 7/5 and 4/3.

This interval is well approximated by 10edo (9\10).

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

@@ Line 1: / Line 1: @@
-'''28/15'''
+{{Infobox Interval
-|2 -1 -1 1&gt;
+| Name = septimal grave major seventh, aberschismic diminished octave
+| Color name = zg8, zogu octave
+| Sound = jid_28_15_pluck_adu_dr220.mp3
+}}
+'''28/15''' is an interval in [[7-limit]] [[just intonation]] measuring about 1080.6 [[cent]]s, traditionally known as the '''septimal grave major seventh''' for its proximity (and conflation in [[marvel]] tunings such as septimal [[meantone]]) with the classical major seventh [[15/8]]. However, it functions as a diminished octave, as is supported by [[Sagittal notation]], [[Helmholtz–Ellis notation]] and the [[Functional Just System]], viewed as the [[4096/2187|Pythagorean diminished octave]] flattened by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic diminished octave'''. It arises from stacking various [[9-odd-limit]] consonances, including the stack consisting of [[6/5]] and [[14/9]], of [[7/6]] and [[8/5]], and of [[7/5]] and [[4/3]].
-.5572 cents
+== Approximation ==
+This interval is well approximated by [[10edo]] (9\10).
-[[File:jid_28_15_pluck_adu_dr220.mp3]] [[:File:jid_28_15_pluck_adu_dr220.mp3|sound sample]]      [[Category:todo:expand]]
+{{Interval edo approximation|28/15}}
+== See also ==
+* [[15/14]] – its [[octave complement]]
+* [[Gallery of just intervals]]
+[[Category:Seventh]]
+[[Category:Major seventh]]
+[[Category:Octave]]
+[[Category:Diminished octave]]