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Miracle: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|-
|-
| | number of secors
! | number of <br>secors
! | JI intervals <br>represented
|-
| | 0
| | 0
| | '''1/1'''
|-
| | 1
| | 1
| | 16/15, 15/14
|-
| | 2
| | 2
| | '''8/7'''
|-
| | 3
| | 3
| | '''11/9'''
|-
| | 4
| | 4
| | 21/16
|-
| | 5
| | 5
| | '''7/5'''
|-
| | 6
| | 6
| | '''3/2'''
|-
| | 7
| | 7
| | '''8/5'''
|-
| | 8
| | 8
| | '''12/7'''
|-
| | 9
| | 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'''
| | '''11/6'''
|-
|-
| | number of secors
| | 10
| | 10
| | 88/45, 96/49, 49/25, <br>108/55, 55/28, 63/32
|-
| | 11
| | 11
| | 22/21, 21/20
|-
| | 12
| | 12
| | '''9/8'''
|-
| | 13
| | 13
| | '''6/5'''
|-
| | 14
| | 14
| | '''9/7'''
|-
| | 15
| | 15
| | '''11/8'''
|-
| | 16
| | 16
| | 22/15
|-
| | 17
| | 17
| | '''11/7'''
|-
| | 18
| | 18
| | 42/25, 27/16
|-
| | 19
| | 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'''
| | '''9/5'''
|-
|-
| | number of secors
| | 20
| | 20
| | 48/25, 27/14
|-
| | 21
| | 21
| | 36/35, 33/32
|-
| | 22
| | 22
| |  
| | '''11/10'''
| |
|-
| |
| | 23
| |
| | 33/28
| |
| |  
| |  
|-
|-
| | JI intervals represented
| | 24
| | 48/25~27/14
| | 44/35
| | 33/32
|-
| | '''11/10'''
| | 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|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.


Miracle can also be thought of as a [[Cluster_temperament|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.
Miracle can also be thought of as a [[Cluster_temperament|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=
=Spectrum of Miracle Tunings by Eigenmonzos=
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|-
|-
| | 10/9
| | 10/9
| | 116.716 (9 and 11 limit minimax, Secor's definition of secor)
| | 116.716 (9 and 11 limit minimax, <br>Secor's definition of secor)
|-
|-
| | 11/8
| | 11/8
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