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	0	1	2	3	4	5	6	7	8	9
JI intervals represented	1/1	16/15~15/14	8/7	11/9	21/16	7/5	3/2	8/5	12/7	11/6
number of secors	10	11	12	13	14	15	16	17	18	19
JI intervals represented	63/32~55/28~108/55~49/25~96/49~88/45	22/21~21/20	9/8	6/5	9/7	11/8	22/15	11/7	42/25	9/5
number of secors	20	21	22
JI intervals represented	48/25~27/14	33/32	11/10

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.

{{#rreplace: 10 31 41 62 72 82 103 113 144 175|/(\d+)(\D+)?/|\1\2}}

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