Wollemia

Wollemia

Subgroups	2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
Comma basis	126/125, 2240/2187 (7-limit); 56/55, 100/99, 243/242 (11-limit) 56/55, 91/90, 100/99, 243/242 (13-limit)
Reduced mapping	⟨1; 4 9 19 10 -2]
ET join	27e & 34
Generators (CWE)	~10/9 = 177.1 ¢
MOS scales	6L 1s, 7L 6s, 7L 13s, 7L 20s
Ploidacot	tetracot
Minimax error	9-odd-limit: 14.5 ¢; 13-odd-limit: 21.7 ¢
Target scale size	9-odd-limit: 20 notes; 13-odd-limit: 27 notes

The wollemia temperament is one of the 7-limit extensions of tetracot, the 5-limit temperament tempering out the tetracot comma (20000/19683), and is naturally a full 13-limit temperament.

In addition to the tetracot comma, wollemia tempers out 126/125, making it a starling temperament.

See Tetracot family #Wollemia for technical data.

Todo: expand

Interval chain

#	Cents*	Approximate ratios
0	0.0	1/1
1	177.1	10/9, 11/10
2	354.2	11/9, 16/13
3	531.3	15/11
4	708.4	3/2
5	885.5	5/3
6	1062.6	11/6, 24/13, 28/15
7	39.7	40/39, 45/44, 55/54
8	216.8	9/8
9	393.9	5/4, 14/11
10	570.9	7/5, 11/8, 18/13
11	748.0	14/9, 20/13
12	925.1	22/13
13	1102.2	15/8, 21/11
14	79.3	21/20, 25/24, 27/26
15	256.4	7/6, 15/13
16	433.5	33/26, 35/27
17	610.6	45/32, 63/44
18	787.7	25/16
19	964.8	7/4
20	1141.9	35/18, 49/25

* In 13-limit CWE tuning, octave reduced

Tunings

Tuning spectrum

Edo generator	Eigenmonzo (Unchanged-interval)	Generator (¢)	Comments
	11/10	165.004
1\7		171.429	7d val
	11/9	173.704
	11/6	174.894
	11/8	175.132
	3/2	175.489
	13/11	175.899
	15/8	176.021
	5/4	176.257	5-odd-limit minimax
	13/9	176.338
5\34		176.471	Lower bound of 7- to 13-odd-limit diamond monotone
	15/13	176.516
	5/3	176.872
	13/10	176.890
	13/12	176.905
	7/4	177.307	7-, 9-, 11-, 13- and 15-odd-limit minimax
	13/7	177.538
4\27		177.777	27e val, upper bound of 9- to 13-odd-limit diamond monotone 15-odd-limit diamond monotone (singleton)
	7/6	177.791
	7/5	178.251
	9/7	178.629
	15/11	178.984
	11/7	179.723
	13/8	179.736
3\20		180.000	20cde val, upper bound of 7-odd-limit diamond monotone
	15/14	180.093
	9/5	182.404