Opossum: Difference between revisions

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| '''8/7'''
| '''8/7'''
|}
|}
<nowiki/>* In 11-limit CWE tuning, octave reduced
<nowiki/>* In 15edo tuning, octave reduced


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

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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