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'''Miracle''' is a [[regular temperament]] discovered by [[George Secor]] in 1974 which has as a [[generator]] an interval, called a ''[[secor]]'' (after George), that serves as both [[15/14]] and [[16/15]] semitones.  
'''Miracle''' is a [[regular temperament]] discovered by [[George Secor]] in 1974 which has as a [[generator]] an interval, called a ''[[secor]]'' (after George), 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]] and the [[gamelismic clan]]. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/[[octave]], meaning intervals of the [[11-odd-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 [[#Interval chain]]. At least one inversion of every interval in the 11-odd-limit tonality diamond is represented within 22 secors of the starting value.  
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 [[cent]]s/[[octave]], meaning intervals of the [[11-odd-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 the [[#Interval chain]]. At least one inversion of every interval in the 11-odd-limit tonality diamond is represented within 22 secors of the starting value.  


Some temperaments have [[11/9]] as a "neutral third", meaning it is exactly half of a [[3/2]] (tempering out [[243/242]]), and other temperaments (→ [[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 is exactly half of a [[3/2]] (tempering out [[243/242]]), and other temperaments (→ [[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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== Interval chain ==
== Interval chain ==
11-odd-limit ratios are labeled in '''bold'''.
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! # of<br>secors
! #
! Cents value<ref>in 11-limit [[POTE tuning]]</ref><br>(octave-reduced)
! Cents*
! JI intervals <br>represented
! Approximate Ratios
|-
|-
| 0
| 0
| 0.00
| 0.0
| '''1/1'''
| '''1/1'''
|-
|-
| 1
| 1
| 116.63
| 116.7
| 16/15, 15/14
| 15/14, 16/15
|-
|-
| 2
| 2
| 233.27
| 233.4
| '''8/7'''
| '''8/7'''
|-
|-
| 3
| 3
| 349.90
| 350.1
| '''11/9'''
| '''11/9'''
|-
|-
| 4
| 4
| 466.53
| 466.8
| 21/16
| 21/16
|-
|-
| 5
| 5
| 583.16
| 583.6
| '''7/5'''
| '''7/5'''
|-
|-
| 6
| 6
| 699.80
| 700.3
| '''3/2'''
| '''3/2'''
|-
|-
| 7
| 7
| 816.43
| 817.0
| '''8/5'''
| '''8/5'''
|-
|-
| 8
| 8
| 933.06
| 933.7
| '''12/7'''
| '''12/7'''
|-
|-
| 9
| 9
| 1049.69
| 1050.4
| '''11/6'''
| '''11/6'''
|-
|-
| 10
| 10
| 1166.33
| 1167.1
| 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
| 83.8
| 22/21, 21/20
| 22/21, 21/20
|-
|-
| 12
| 12
| 199.59
| 200.5
| '''9/8'''
| '''9/8'''
|-
|-
| 13
| 13
| 316.23
| 317.2
| '''6/5'''
| '''6/5'''
|-
|-
| 14
| 14
| 432.86
| 434.0
| '''9/7'''
| '''9/7'''
|-
|-
| 15
| 15
| 549.49
| 550.7
| '''11/8'''
| '''11/8'''
|-
|-
| 16
| 16
| 666.12
| 667.4
| 22/15
| 22/15
|-
|-
| 17
| 17
| 782.76
| 784.1
| '''11/7'''
| '''11/7'''
|-
|-
| 18
| 18
| 899.39
| 900.8
| 42/25, 27/16
| 27/16, 42/25
|-
|-
| 19
| 19
| 1016.02
| 1017.5
| '''9/5'''
| '''9/5'''
|-
|-
| 20
| 20
| 1132.65
| 1134.2
| 48/25, 27/14
| 27/14, 48/25
|-
|-
| 21
| 21
| 49.29
| 50.9
| 36/35, 33/32
| 33/32, 36/35
|-
|-
| 22
| 22
| 165.92
| 167.6
| '''11/10'''
| '''11/10'''
|-
|-
| 23
| 23
| 282.55
| 284.4
| 33/28
| 33/28
|-
|-
| 24
| 24
| 399.19
| 401.1
| 44/35
| 44/35
|-
|-
| 25
| 25
| 515.82
| 517.8
| 27/20
| 27/20
|-
|-
| 26
| 26
| 632.45
| 634.5
| 36/25
| 36/25
|-
|-
| 27
| 27
| 749.08
| 751.2
| 54/35, 77/50
| 54/35, 77/50
|-
|-
| 28
| 28
| 865.72
| 867.9
| 33/20
| 33/20
|-
|-
| 29
| 29
| 982.35
| 984.6
| 44/25
| 44/25
|-
|-
| 30
| 30
| 1098.98
| 1101.3
| 66/35
| 66/35
|-
|-
| 31
| 31
| 15.62
| 18.0
| 81/80
| 81/80, 121/120
|}
|}
<references/>
<nowiki>*</nowiki> in 11-limit [[CTE tuning]], octave reduced


== Chords ==
== Chords ==
Retrieved from "https://en.xen.wiki/w/Miracle"