Miracle: Difference between revisions
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'''Miracle temperament''' is a regular temperament discovered by [[George Secor]] in 1974 which has as a generator an interval, called '''secor''', that serves as both [[15/14]] and [[16/15]] semitones. | |||
Miracle is an exceptionally efficient linear temperament which is a member of both the [[Marvel_temperaments|marvel temperaments]] and the [[Gamelismic_clan|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: | Miracle is an exceptionally efficient linear temperament which is a member of both the [[Marvel_temperaments|marvel temperaments]] and the [[Gamelismic_clan|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: | ||
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|- | |- | ||
! | number of <br>secors | ! | number of <br>secors | ||
! | cents value* <br>(octave-reduced) | |||
! | JI intervals <br>represented | ! | JI intervals <br>represented | ||
|- | |- | ||
| | 0 | | | 0 | ||
| | 0.00 | |||
| | '''1/1''' | | | '''1/1''' | ||
|- | |- | ||
| | 1 | | | 1 | ||
| | 116.63 | |||
| | 16/15, 15/14 | | | 16/15, 15/14 | ||
|- | |- | ||
| | 2 | | | 2 | ||
| | 233.27 | |||
| | '''8/7''' | | | '''8/7''' | ||
|- | |- | ||
| | 3 | | | 3 | ||
| | 349.90 | |||
| | '''11/9''' | | | '''11/9''' | ||
|- | |- | ||
| | 4 | | | 4 | ||
| | 466.53 | |||
| | 21/16 | | | 21/16 | ||
|- | |- | ||
| | 5 | | | 5 | ||
| | 583.16 | |||
| | '''7/5''' | | | '''7/5''' | ||
|- | |- | ||
| | 6 | | | 6 | ||
| | 699.80 | |||
| | '''3/2''' | | | '''3/2''' | ||
|- | |- | ||
| | 7 | | | 7 | ||
| | 816.43 | |||
| | '''8/5''' | | | '''8/5''' | ||
|- | |- | ||
| | 8 | | | 8 | ||
| | 933.06 | |||
| | '''12/7''' | | | '''12/7''' | ||
|- | |- | ||
| | 9 | | | 9 | ||
| | 1049.69 | |||
| | '''11/6''' | | | '''11/6''' | ||
|- | |- | ||
| | 10 | | | 10 | ||
| | 1166.33 | |||
| | 88/45, 96/49, 49/25, <br>108/55, 55/28, 63/32 | | | 88/45, 96/49, 49/25, <br>108/55, 55/28, 63/32 | ||
|- | |- | ||
| | 11 | | | 11 | ||
| | 82.96 | |||
| | 22/21, 21/20 | | | 22/21, 21/20 | ||
|- | |- | ||
| | 12 | | | 12 | ||
| | 199.59 | |||
| | '''9/8''' | | | '''9/8''' | ||
|- | |- | ||
| | 13 | | | 13 | ||
| | 316.23 | |||
| | '''6/5''' | | | '''6/5''' | ||
|- | |- | ||
| | 14 | | | 14 | ||
| | 432.86 | |||
| | '''9/7''' | | | '''9/7''' | ||
|- | |- | ||
| | 15 | | | 15 | ||
| | 549.49 | |||
| | '''11/8''' | | | '''11/8''' | ||
|- | |- | ||
| | 16 | | | 16 | ||
| | 666.12 | |||
| | 22/15 | | | 22/15 | ||
|- | |- | ||
| | 17 | | | 17 | ||
| | 782.76 | |||
| | '''11/7''' | | | '''11/7''' | ||
|- | |- | ||
| | 18 | | | 18 | ||
| | 899.39 | |||
| | 42/25, 27/16 | | | 42/25, 27/16 | ||
|- | |- | ||
| | 19 | | | 19 | ||
| | 1016.02 | |||
| | '''9/5''' | | | '''9/5''' | ||
|- | |- | ||
| | 20 | | | 20 | ||
| | 1132.65 | |||
| | 48/25, 27/14 | | | 48/25, 27/14 | ||
|- | |- | ||
| | 21 | | | 21 | ||
| | 49.29 | |||
| | 36/35, 33/32 | | | 36/35, 33/32 | ||
|- | |- | ||
| | 22 | | | 22 | ||
| | 165.92 | |||
| | '''11/10''' | | | '''11/10''' | ||
|- | |- | ||
| | 23 | | | 23 | ||
| | 282.55 | |||
| | 33/28 | | | 33/28 | ||
|- | |- | ||
| | 24 | | | 24 | ||
| | 399.19 | |||
| | 44/35 | | | 44/35 | ||
|- | |- | ||
| | 25 | | | 25 | ||
| | 515.82 | |||
| | 27/20 | | | 27/20 | ||
|- | |- | ||
| | 26 | | | 26 | ||
| | 632.45 | |||
| | 36/25 | | | 36/25 | ||
|- | |- | ||
| | 27 | | | 27 | ||
| | 749.08 | |||
| | 54/35, 77/50 | | | 54/35, 77/50 | ||
|- | |- | ||
| | 28 | | | 28 | ||
| | 865.72 | |||
| | 33/20 | | | 33/20 | ||
|- | |- | ||
| | 29 | | | 29 | ||
| | 982.35 | |||
| | 44/25 | | | 44/25 | ||
|- | |- | ||
| | 30 | | | 30 | ||
| | 1098.98 | |||
| | 66/35 | | | 66/35 | ||
|- | |- | ||
| | 31 | | | 31 | ||
| | 15.62 | |||
| | 81/80 | | | 81/80 | ||
|} | |} | ||
<span style="font-family: Arial,Helvetica,sans-serif;">*in 11-limit POTE tuning</span> | |||
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|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. | 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|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. | ||
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| | 116.993 | | | 116.993 | ||
|} | |} | ||
[[Category:miracle]] | [[Category:miracle]] | ||
[[Category:temperament]] | [[Category:temperament]] | ||