Miracle

Miracle is an exceptionally efficient linear temperament which is a member of both the marvel temperaments and the gamelismic clan. It is quite accurate, with TOP error only 0.63 cents/octave, meaning intervals of the 11-limit tonality diamond are represented with only one or two cents of error. Yet it is also very "low complexity" (efficient), as evidenced by the high density of 11-odd-limit ratios (in bold) in the following table:

number of secors	JI intervals represented
0	1/1
1	16/15, 15/14
2	8/7
3	11/9
4	21/16
5	7/5
6	3/2
7	8/5
8	12/7
9	11/6
10	88/45, 96/49, 49/25, 108/55, 55/28, 63/32
11	22/21, 21/20
12	9/8
13	6/5
14	9/7
15	11/8
16	22/15
17	11/7
18	42/25, 27/16
19	9/5
20	48/25, 27/14
21	36/35, 33/32
22	11/10
23	33/28
24	44/35
25	27/20
26	36/25
27	54/35, 77/50
28	33/20
29	44/25
30	66/35
31	81/80

Some temperaments have 11/9 as a "neutral third", meaning it's exactly half of a 3/2 (tempering out 243/242), and other temperaments (in the gamelismic clan) have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a "secor", and it represents both 16/15 and 15/14.

Miracle can also be thought of as a cluster temperament with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44 ~ 49/48 ~ 50/49 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together.

Spectrum of Miracle Tunings by Eigenmonzos

Eigenmonzo	Secor
8/7	115.587
11/9	115.803
5/4	116.241
7/5	116.502
6/5	116.588 (5 and 7 limit minimax)
11/10	116.591
12/11	116.596
14/11	116.617
7/6	116.641
10/9	116.716 (9 and 11 limit minimax, Secor's definition of secor)
11/8	116.755
9/7	116.792
4/3	116.993