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See [[Trienstonic_clan#Opossum|Trienstonic clan]].
{{Infobox regtemp
| Title = Opossum
| Subgroups = 2.3.5.7, 2.3.5.7.11
| Comma basis = [[28/27]], [[126/125]] (7-limit);<br>[[28/27]], [[55/54]], [[77/75]] (11-limit)
| Edo join 1 = 8d | Edo join 2 = 15
| Mapping = 1; -3 -5 -9 -4
| Generators = 11/10
| Generators tuning = 160.5
| Optimization method = CWE
| MOS scales = [[1L 6s]], [[7L 1s]]
| Odd limit 1 = 7 | Mistuning 1 = 21.0 | Complexity 1 = 15
| Odd limit 2 = 11 | Mistuning 2 = 42.0 | Complexity 2 = 15
}}
'''Opossum''' is an alternative [[extension]] to [[porcupine]]. It is defined by [[tempering out]] [[28/27]] and [[126/125]].  


Gencom: [2 10/9; 28/27 40/39 55/54 66/65]
See [[Porcupine family #Opossum]] for technical data.


Gencom mapping: [{{val|1 2 3 4 4 4}}, {{val|0 -3 -5 -9 -4 -2}}]
== Interval chain ==
In the following table, odd harmonics 1–11 and their inverses are in '''bold'''.


== Tuning spectrum ==
{| class="wikitable center-1 right-2"
|-
! #
! Cents*
! Approximate ratios*
|-
| 0
| 0.0
| '''1/1'''
|-
| 1
| 160.0
| 10/9, 11/10, 12/11, 15/14
|-
| 2
| 320.0
| 6/5, 11/9
|-
| 3
| 480.0
| '''4/3''', 9/7
|-
| 4
| 640.0
| 10/7, '''16/11''', 22/15
|-
| 5
| 800.0
| '''8/5''', 11/7
|-
| 6
| 960.0
| 12/7, '''16/9'''
|-
| 7
| 1120.0
| 40/21, 48/25, 64/33
|-
| 8
| 80.0
| 16/15, 36/35
|-
| 9
| 240.0
| '''8/7'''
|}
<nowiki/>* In 15edo tuning, octave reduced
 
== Tunings ==
=== Norm-based tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~10/9 = 161.306{{c}}
| CWE: ~10/9 = 160.459{{c}}
| POTE: ~10/9 = 159.691{{c}}
|}


{| class="wikitable center-all"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
|-
|-
! | ET<br>generator
! rowspan="2" |  
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! colspan="3" | Euclidean
! | neutral<br>second (¢)
! | comments
|-
|-
| |
! Constrained
| | 15/14
! Constrained & skewed
| | 119.443
! Destretched
| |
|-
|-
| |
! Tenney
| | 13/12
| CTE: ~11/10 = 161.365{{c}}
| | 138.573
| CWE: ~11/10 = 160.464{{c}}
| |
| POTE: ~11/10 = 159.807{{c}}
|}
 
=== Target tunings ===
{| class="wikitable center-1 center-3 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Target tunings
|-
|-
| |
! rowspan="2" | Target
| | 13/11
! colspan="2" | Minimax
| | 144.605
! colspan="2" | Least squares
| |
|-
|-
| |
! Generator
| | 9/7
! Eigenmonzo
| | 145.028
! Generator
| |
! Eigenmonzo
|-
|-
| | 1\8
| 5-odd-limit
| |
| ~10/9 = 162.737{{c}}
| | 150.000
| 5/4
| |
| ~10/9 = 162.996{{c}}
| 262144/234375
|-
| 7-odd-limit
| ~10/9 = 159.019{{c}}
| 7/4
| ~10/9 = 158.732{{c}}
| {{Monzo| 0 -5 3 19 }}
|-
| 9-odd-limit
| ~10/9 = 159.019{{c}}
| 7/4
| ~10/9 = 159.481{{c}}
| {{Monzo| 0 3 2 22 }}
|-
| 11-odd-limit
| ~11/10 = 159.019{{c}}
| 7/4
| ~11/10 = 159.564{{c}}
| {{Monzo| -27 2 1 9 -1 }}
|-
| 13-odd-limit
| ~11/10 = 159.019{{c}}
| 7/4
| ~11/10 = 158.421{{c}}
| {{Monzo| 0 15 6 34 -1 -15 }}
|-
| 15-odd-limit
| ~11/10 = 159.019{{c}}
| 7/4
| ~11/10 = 159.377{{c}}
| {{Monzo| 0 32 23 35 -5 -21 }}
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
|-
| |
! Edo<br>generator
| | 12/11
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
| | 150.637
! Generator (¢)
| |
! Comments
|-
|-
| |
|  
| | 13/10
| 15/14
| | 151.405
| 119.443
| |
|  
|-
|-
| |
|  
| | 14/13
| 13/12
| | 153.100
| 138.573
| |
|  
|-
|-
| |
|  
| | 7/5
| 13/11
| | 154.372
| 144.605
| |
|  
|-
|-
| |
|  
| | 7/6
| 9/7
| | 155.522
| 145.028
| |
|  
|-
|-
| |
| 1\8
| | 14/11
|  
| | 156.498
| 150.000
| |
| 8d val, lower bound of 7-odd-limit diamond monotone
|-
|-
| | 3\23
|  
| |
| 11/6
| | 156.522
| 150.637
| |
|  
|-
|-
| |
|  
| | 6/5
| 13/10
| | 157.821
| 151.405
| |
|  
|-
|-
| |
|  
| | {{vector|0 15 6 34 -1 -15}}
| 13/7
| | 158.421
| 153.100
| | 13 limit least squares
|  
|-
|-
| | 5\38
|  
| |
| 7/5
| | 157.895
| 154.372
| |
|  
|-
|-
| | 7\53
|  
| |
| 7/6
| | 158.491
| 155.522
| |
|  
|-
|-
| |
|  
| | 15/13
| 11/7
| | 158.710
| 156.498
| |
|  
|-
|-
| |
| 3\23
| | {{vector|0 -5 3 19}}
|  
| | 158.732
| 156.522
| | 7 limit least squares
| 23bcf val
|-
|-
| |
|  
| | 8/7
| 5/3
| | 159.019
| 157.821
| | 7, 9, 11, 13 and 15 limit minimax
|  
|-
|-
| |
| 5\38
| | 18/13
|  
| | 159.154
| 157.895
| |
| 38bceff val
|-
|-
| |
| 7\53
| | {{vector|0 32 23 35 -5 -21}}
|  
| | 159.377
| 158.491
| | 15 limit least squares
| 53bcefff val
|-
|-
| |
|  
| | {{vector|0 3 2 22}}
| 15/13
| | 159.481
| 158.710
| | 9 limit least squares
|  
|-
|-
| |
|  
| | 1815912315/1476395008
| 7/4
| | 159.564
| 159.019
| | 11 limit least squares
| 7-, 9-, 11-, 13- and 15-odd-limit minimax
|-
|-
| | 2\15
|  
| |
| 13/9
| | 160.000
| 159.154
| |
|  
|-
|-
| |
| 2\15
| | 11/8
|  
| | 162.171
| 160.000
| |
| Upper bound of 7-odd-limit diamond monotone<br>9- and 11-odd-limit diamond monotone (singleton)
|-
|-
| |
|  
| | 5/4
| 11/8
| | 162.737
| 162.171
| | 5 limit minimax
|  
|-
|-
| |
|  
| | 262144/234375
| 5/4
| | 162.996
| 162.737
| | 5 limit least squares
| 5-odd-limit minimax
|-
|-
| |
|  
| | 16/15
| 15/8
| | 163.966
| 163.966
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 165.004
| 165.004
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 165.762
| 165.762
| |
|  
|-
|-
| |
|  
| | 4/3
| 3/2
| | 166.015
| 166.015
| |
|  
|-
|-
| |
|  
| | 11/9
| 11/9
| | 173.704
| 173.704
| |
|  
|-
|-
| |
|  
| | 16/13
| 13/8
| | 179.736
| 179.736
| |
|  
|-
|-
| |
|  
| | 10/9
| 9/5
| | 182.404
| 182.404
| |
|  
|}
|}


[[Category:Smart redirect]]
[[Category:Opossum| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Exotemperaments]]
[[Category:Porcupine family]]
[[Category:Trienstonic clan]]
[[Category:Starling temperaments]]
Retrieved from "https://en.xen.wiki/w/Opossum"