Opossum

Opossum

Subgroups	2.3.5.7, 2.3.5.7.11
Comma basis	28/27, 126/125 (7-limit); 28/27, 55/54, 77/75 (11-limit)
Reduced mapping	⟨1; -3 -5 -9 -4]
ET join	8d & 15
Generators (CWE)	~11/10 = 160.5 ¢
MOS scales	1L 6s, 7L 1s
Ploidacot	omega-tricot
Minimax error	7-odd-limit: 21.0 ¢; 11-odd-limit: 42.0 ¢
Target scale size	7-odd-limit: 15 notes; 11-odd-limit: 15 notes

Opossum is an alternative extension to porcupine. It is defined by tempering out 28/27 and 126/125.

See Porcupine family #Opossum for technical data.

Interval chain

In the following table, odd harmonics 1–11 and their inverses are in bold.

#	Cents*	Approximate ratios*
0	0.0	1/1
1	160.0	10/9, 11/10, 12/11, 15/14
2	320.0	6/5, 11/9
3	480.0	4/3, 9/7
4	640.0	10/7, 16/11, 22/15
5	800.0	8/5, 11/7
6	960.0	12/7, 16/9
7	1120.0	40/21, 48/25, 64/33
8	80.0	16/15, 36/35
9	240.0	8/7

* In 15edo tuning, octave reduced

Tunings

Least-squares tunings

Target	Generator	Eigenmonzo
5-odd-limit	~10/9 = 162.996 ¢	262144/234375
7-odd-limit	~10/9 = 158.732 ¢	[0 -5 3 19⟩
9-odd-limit	~12/11 = 159.481 ¢	[0 3 2 22⟩
11-odd-limit	~12/11 = 159.564 ¢	[-27 2 1 9 -1⟩
13-odd-limit	~12/11 = 158.421 ¢	[0 15 6 34 -1 -15⟩
15-odd-limit	~12/11 = 159.377 ¢	[0 32 23 35 -5 -21⟩

Tuning spectrum

Edo generator	Unchanged interval (eigenmonzo)	Generator (¢)	Comments
	15/14	119.443
	13/12	138.573
	13/11	144.605
	9/7	145.028
1\8		150.000	8d val, lower bound of 7-odd-limit diamond monotone
	11/6	150.637
	13/10	151.405
	13/7	153.100
	7/5	154.372
	7/6	155.522
	11/7	156.498
3\23		156.522	23bcf val
	5/3	157.821
5\38		157.895	38bceff val
7\53		158.491	53bcefff val
	15/13	158.710
	7/4	159.019	7-, 9-, 11-, 13- and 15-odd-limit minimax
	13/9	159.154
2\15		160.000	Upper bound of 7-odd-limit diamond monotone 9- and 11-odd-limit diamond monotone (singleton)
	11/8	162.171
	5/4	162.737	5-odd-limit minimax
	15/8	163.966
	11/10	165.004
	15/11	165.762
	3/2	166.015
	11/9	173.704
	13/8	179.736
	9/5	182.404