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See [[Trienstonic_clan#Opossum|Trienstonic clan]].
'''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 map: [{{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'''.


== Spectrum of Opossum Tunings by Eigenmonzos ==
{| 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


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


[[Category:Smart redirect]]
[[Category:Opossum| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Exotemperaments]]
[[Category:Porcupine family]]
[[Category:Trienstonic clan]]
[[Category:Starling temperaments]]

Latest revision as of 06:56, 21 June 2025

Opossum is an alternative extension to porcupine. It is defined by tempering out 28/27 and 126/125.

See Porcupine family #Opossum for technical data.

Interval chain

In the following table, odd harmonics 1–11 and their inverses are in bold.

# 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

* In 15edo tuning, octave reduced

Tunings

Least-squares tunings
Target Generator Eigenmonzo
5-odd-limit ~10/9 = 162.996 ¢ 262144/234375
7-odd-limit ~10/9 = 158.732 ¢ [0 -5 3 19⟩
9-odd-limit ~12/11 = 159.481 ¢ [0 3 2 22⟩
11-odd-limit ~12/11 = 159.564 ¢ [-27 2 1 9 -1⟩
13-odd-limit ~12/11 = 158.421 ¢ [0 15 6 34 -1 -15⟩
15-odd-limit ~12/11 = 159.377 ¢ [0 32 23 35 -5 -21⟩

Tuning spectrum

Edo
generator 		Unchanged interval
(eigenmonzo) 		Generator (¢) Comments
15/14 119.443
13/12 138.573
13/11 144.605
9/7 145.028
1\8 150.000 8d val, lower bound of 7-odd-limit diamond monotone
11/6 150.637
13/10 151.405
13/7 153.100
7/5 154.372
7/6 155.522
11/7 156.498
3\23 156.522 23bcf val
5/3 157.821
5\38 157.895 38bceff val
7\53 158.491 53bcefff val
15/13 158.710
7/4 159.019 7-, 9-, 11-, 13- and 15-odd-limit minimax
13/9 159.154
2\15 160.000 Upper bound of 7-odd-limit diamond monotone
9- and 11-odd-limit diamond monotone (singleton)
11/8 162.171
5/4 162.737 5-odd-limit minimax
15/8 163.966
11/10 165.004
15/11 165.762
3/2 166.015
11/9 173.704
13/8 179.736
9/5 182.404
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