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Gallery of 3-SN scales: Difference between revisions

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VisualWikitext
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autopatrolled, emailconfirmed
1,636 edits
→(2/1, 3/2, 6/5): added tables
Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
Line 1,895: Line 1,895:
!Mode in JI
!Mode in JI
!Step pattern
!Step pattern
!Meantone[7] step pattern
!Meantone[7] UDP
!Diatonic mode
![[Mode height]]
![[Mode height]]
|-
|-
Line 1,900: Line 1,903:
|27/25 6/5 4/3 36/25 8/5 9/5 2/1
|27/25 6/5 4/3 36/25 8/5 9/5 2/1
|sMMsMLM
|sMMsMLM
|sLLsLLL
|<nowiki>0|6</nowiki>
|Lochrian
| -0.0529
| -0.0529
|-
|-
Line 1,905: Line 1,911:
|10/9 6/5 4/3 40/27 8/5 16/9 2/1
|10/9 6/5 4/3 40/27 8/5 16/9 2/1
|MsMMsML
|MsMMsML
|LsLLsLL
|<nowiki>2|4</nowiki>
|Aeolian
|  -0.0316
|  -0.0316
|-
|-
Line 1,910: Line 1,919:
|27/25 6/5 27/20 3/2 81/50 9/5 2/1
|27/25 6/5 27/20 3/2 81/50 9/5 2/1
|sMLMsMM
|sMLMsMM
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|  -0.0213
|  -0.0213
|-
|-
Line 1,915: Line 1,927:
|10/9 6/5 4/3 3/2 5/3 9/5 2/1
|10/9 6/5 4/3 3/2 5/3 9/5 2/1
|MsMLMsM
|MsMLMsM
|LsLLLsL
|<nowiki>3|3</nowiki>
|Dorian
|0
|0
|-
|-
Line 1,920: Line 1,935:
|10/9 100/81 4/3 40/27 5/3 50/27 2/1
|10/9 100/81 4/3 40/27 5/3 50/27 2/1
|MMsMLMs
|MMsMLMs
|LLsLLLs
|<nowiki>5|1</nowiki>
|Ionian
|0.0213
|0.0213
|-
|-
Line 1,925: Line 1,943:
|9/8 5/4 27/20 3/2 5/3 9/5 2/1
|9/8 5/4 27/20 3/2 5/3 9/5 2/1
|LMsMMsM
|LMsMMsM
|LLsLLsL
|<nowiki>4|2</nowiki>
|Mixolydian
|0.0316
|0.0316
|-
|-
Line 1,930: Line 1,951:
|10/9 5/4 25/18 3/2 5/3 50/27 2/1
|10/9 5/4 25/18 3/2 5/3 50/27 2/1
|MLMsMMs
|MLMsMMs
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|0.0529
|0.0529
|}
|}
Line 1,958: Line 1,982:
|[[Bug family|Bug]][5]
|[[Bug family|Bug]][5]
|27/25
|27/25
|}10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM
|}
 
L = M -> LsLLLsL Meantone[7], M = s -> sssLsss Porcupine[7]; L = s -> LsLsLsL Dicot[7]; s = 0 -> ssLss Bug[5]
=====[[SNS (2/1, 3/2, 6/5: 126/125)-7|(2/1, 3/2, 6/5: 126/125)[7] (Starling)]]=====
=====[[SNS (2/1, 3/2, 6/5: 126/125)-7|(2/1, 3/2, 6/5: 126/125)[7] (Starling)]]=====
{| class="wikitable"
{| class="wikitable"
Line 1,975: Line 1,997:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Meantone[7] step pattern
!Meantone[7] UDP
!Diatonic mode
![[Mode height]]
![[Mode height]]
|-
|-
Line 1,980: Line 2,005:
|~ 15/14 6/5 4/3 10/7 8/5 9/5 2/1
|~ 15/14 6/5 4/3 10/7 8/5 9/5 2/1
|sMMsMLM
|sMMsMLM
|sLLsLLL
|<nowiki>0|6</nowiki>
|Lochrian
| -0.0616
| -0.0616
|-
|-
Line 1,985: Line 2,013:
|~ 15/14 6/5 27/20 3/2 45/28 9/5 2/1
|~ 15/14 6/5 27/20 3/2 45/28 9/5 2/1
|sMLMsMM
|sMLMsMM
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|  -0.0314
|  -0.0314
|-
|-
Line 1,990: Line 2,021:
|~ 10/9 6/5 4/3 40/27 8/5 16/9 2/1
|~ 10/9 6/5 4/3 40/27 8/5 16/9 2/1
|MsMMsML
|MsMMsML
|LsLLsLL
|<nowiki>2|4</nowiki>
|Aeolian
| -0.0302
| -0.0302
|-
|-
Line 1,995: Line 2,029:
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|MsMLMsM
|MsMLMsM
|LsLLLsL
|<nowiki>3|3</nowiki>
|Dorian
|0
|0
|-
|-
Line 2,000: Line 2,037:
|~ 9/8 5/4 27/20 3/2 5/3 9/5 2/1
|~ 9/8 5/4 27/20 3/2 5/3 9/5 2/1
|LMsMMsM
|LMsMMsM
|LLsLLsL
|<nowiki>4|2</nowiki>
|Mixolydian
|0.0302
|0.0302
|-
|-
Line 2,005: Line 2,045:
|~ 10/9 56/45 4/3 40/27 5/3 28/15 2/1
|~ 10/9 56/45 4/3 40/27 5/3 28/15 2/1
|MMsMLMs
|MMsMLMs
|LLsLLLs
|<nowiki>5|1</nowiki>
|Ionian
|0.0314
|0.0314
|-
|-
Line 2,010: Line 2,053:
|~ 10/9 5/4 7/5 3/2 5/3 28/15 2/1
|~ 10/9 5/4 7/5 3/2 5/3 28/15 2/1
|MLMsMMs
|MLMsMMs
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|0.0616
|0.0616
|}
|}
Line 2,076: Line 2,122:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Meantone[7] step pattern
!Meantone[7] UDP
!Diatonic mode
![[Mode height]]
![[Mode height]]
|-
|-
Line 2,081: Line 2,130:
|~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1
|~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1
|smmsmLm
|smmsmLm
|sLLsLLL
|<nowiki>0|6</nowiki>
|Lochrian
| -0.0427
| -0.0427
|-
|-
Line 2,086: Line 2,138:
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|msmmsmL
|msmmsmL
|LsLLsLL
|<nowiki>2|4</nowiki>
|Aeolian
|  -0.0374
|  -0.0374
|-
|-
Line 2,091: Line 2,146:
|~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1
|~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1
|smLmsmm
|smLmsmm
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|  -0.0053
|  -0.0053
|-
|-
Line 2,096: Line 2,154:
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|msmLmsm
|msmLmsm
|LsLLLsL
|<nowiki>3|3</nowiki>
|Dorian
|0
|0
|-
|-
Line 2,101: Line 2,162:
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|mmsmLms
|mmsmLms
|LLsLLLs
|<nowiki>5|1</nowiki>
|Ionian
|0.0053
|0.0053
|-
|-
Line 2,106: Line 2,170:
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|Lmsmmsm
|Lmsmmsm
|LLsLLsL
|<nowiki>4|2</nowiki>
|Mixolydian
|0.0374
|0.0374
|-
|-
Line 2,111: Line 2,178:
|~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1
|~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1
|mLmsmms
|mLmsmms
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|0.0427
|0.0427
|}
|}
Line 2,173: Line 2,243:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Meantone[7] step pattern
!Meantone[7] UDP
!Diatonic mode
![[Mode height]]
![[Mode height]]
|-
|-
Line 2,178: Line 2,251:
|~ 12/11 6/5 4/3 10/7 8/5 9/5 2/1
|~ 12/11 6/5 4/3 10/7 8/5 9/5 2/1
|sMMsMLM
|sMMsMLM
|sLLsLLL
|<nowiki>0|6</nowiki>
|Lochrian
| -0.0591
| -0.0591
|-
|-
Line 2,183: Line 2,259:
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|MsMMsML
|MsMMsML
|LsLLsLL
|<nowiki>2|4</nowiki>
|Aeolian
|  -0.0433
|  -0.0433
|-
|-
Line 2,188: Line 2,267:
|~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1
|~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1
|sMLMsMM
|sMLMsMM
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|  -0.0158
|  -0.0158
|-
|-
Line 2,193: Line 2,275:
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|MsMLMsM
|MsMLMsM
|LsLLLsL
|<nowiki>3|3</nowiki>
|Dorian
|0
|0
|-
|-
Line 2,198: Line 2,283:
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|MMsMLMs
|MMsMLMs
|LLsLLLs
|<nowiki>5|1</nowiki>
|Ionian
|0.0158
|0.0158
|-
|-
Line 2,203: Line 2,291:
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|LMsMMsM
|LMsMMsM
|LLsLLsL
|<nowiki>4|2</nowiki>
|Mixolydian
|0.0433
|0.0433
|-
|-
Line 2,208: Line 2,299:
|~ 10/9 5/4 7/5 3/2 5/3 11/6 2/1
|~ 10/9 5/4 7/5 3/2 5/3 11/6 2/1
|MLMsMMs
|MLMsMMs
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|0.0591
|0.0591
|}
|}
Line 2,264: Line 2,358:
!Mode in JI
!Mode in JI
!Step pattern
!Step pattern
!Meantone[12] step pattern
!Meantone[12] UDP
![[Mode height]]
![[Mode height]]
|-
|-
Line 2,269: Line 2,365:
|250/243 10/9 2500/2187 100/81 4/3 1000/729 40/27 125/81 5/3 1250/729 50/27 2/1
|250/243 10/9 2500/2187 100/81 4/3 1000/729 40/27 125/81 5/3 1250/729 50/27 2/1
|sLsLLsLmLsLL
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
| -0.0622
| -0.0622
|-
|-
Line 2,274: Line 2,372:
|250/243 10/9 125/108 5/4 625/486 25/18 3/2 125/81 5/3 1250/729 50/27 2/1
|250/243 10/9 125/108 5/4 625/486 25/18 3/2 125/81 5/3 1250/729 50/27 2/1
|sLmLsLLsLsLL
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
| -0.0587
| -0.0587
|-
|-
Line 2,279: Line 2,379:
|250/243 10/9 6/5 100/81 4/3 1000/729 40/27 8/5 400/243 16/9 50/27 2/1
|250/243 10/9 6/5 100/81 4/3 1000/729 40/27 8/5 400/243 16/9 50/27 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
| -0.0338
| -0.0338
|-
|-
Line 2,284: Line 2,386:
|250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|sLLsLmLsLLsL
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
| -0.0302
| -0.0302
|-
|-
Line 2,289: Line 2,393:
|25/24 9/8 125/108 5/4 27/20 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|25/24 9/8 125/108 5/4 27/20 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|mLsLLsLsLLsL
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|  -0.0267
|  -0.0267
|-
|-
Line 2,294: Line 2,400:
|27/25 10/9 6/5 100/81 4/3 36/25 40/27 8/5 5/3 9/5 50/27 2/1
|27/25 10/9 6/5 100/81 4/3 36/25 40/27 8/5 5/3 9/5 50/27 2/1
|LsLsLLsLmLsL
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|  -0.0018
|  -0.0018
|-
|-
Line 2,299: Line 2,407:
|27/25 10/9 6/5 5/4 27/20 25/18 3/2 81/50 5/3 9/5 50/27 2/1
|27/25 10/9 6/5 5/4 27/20 25/18 3/2 81/50 5/3 9/5 50/27 2/1
|LsLmLsLLsLsL
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|0.0018
|0.0018
|-
|-
Line 2,304: Line 2,414:
|27/25 10/9 6/5 162/125 4/3 36/25 40/27 8/5 216/125 16/9 48/25 2/1
|27/25 10/9 6/5 162/125 4/3 36/25 40/27 8/5 216/125 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|0.0267
|0.0267
|-
|-
Line 2,309: Line 2,421:
|27/25 10/9 6/5 162/125 4/3 36/25 3/2 81/50 5/3 9/5 243/125 2/1
|27/25 10/9 6/5 162/125 4/3 36/25 3/2 81/50 5/3 9/5 243/125 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|0.0302
|0.0302
|-
|-
Line 2,314: Line 2,428:
|27/25 9/8 243/200 5/4 27/20 729/500 3/2 81/50 5/3 9/5 243/125 2/1
|27/25 9/8 243/200 5/4 27/20 729/500 3/2 81/50 5/3 9/5 243/125 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|0.0338
|0.0338
|-
|-
Line 2,319: Line 2,435:
|27/25 729/625 6/5 162/125 4/3 36/25 972/625 8/5 216/125 9/5 243/125 2/1
|27/25 729/625 6/5 162/125 4/3 36/25 972/625 8/5 216/125 9/5 243/125 2/1
|LLsLsLLsLmLs
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|0.0587
|0.0587
|-
|-
Line 2,324: Line 2,442:
|27/25 729/625 6/5 162/125 27/20 729/500 3/2 81/50 2187/1250 9/5 243/125 2/1
|27/25 729/625 6/5 162/125 27/20 729/500 3/2 81/50 2187/1250 9/5 243/125 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|0.0622
|0.0622
|}
|}
Line 2,383: Line 2,503:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Meantone[12] step pattern
!Meantone[12] UDP
![[Mode height]]
![[Mode height]]
|-
|-
Line 2,388: Line 2,510:
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 55/36 5/3 121/72 11/6 2/1
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 55/36 5/3 121/72 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
| -0.0899
| -0.0899
|-
|-
Line 2,393: Line 2,517:
|~ 55/54 10/9 55/48 5/4 121/96 11/8 3/2 55/36 5/3 121/72 11/6 2/1
|~ 55/54 10/9 55/48 5/4 121/96 11/8 3/2 55/36 5/3 121/72 11/6 2/1
|sLmLsLLsLsLL
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
| -0.0819
| -0.0819
|-
|-
Line 2,398: Line 2,524:
|~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
| -0.0510
| -0.0510
|-
|-
Line 2,403: Line 2,531:
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|sLLsLmLsLLsL
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
| -0.0430
| -0.0430
|-
|-
Line 2,408: Line 2,538:
|~ 25/24 9/8 55/48 5/4 15/11 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|~ 25/24 9/8 55/48 5/4 15/11 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|mLsLLsLsLLsL
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|  -0.0349
|  -0.0349
|-
|-
Line 2,413: Line 2,545:
|~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1
|~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1
|LsLsLLsLmLsL
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|  -0.0040
|  -0.0040
|-
|-
Line 2,418: Line 2,552:
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 81/50 5/3 9/5 11/6 2/1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 81/50 5/3 9/5 11/6 2/1
|LsLmLsLLsLsL
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|0.0040
|0.0040
|-
|-
Line 2,423: Line 2,559:
|~ 12/11 10/9 6/5 72/55 4/3 16/11 22/15 8/5 96/55 16/9 48/25 2/1
|~ 12/11 10/9 6/5 72/55 4/3 16/11 22/15 8/5 96/55 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|0.0349
|0.0349
|-
|-
Line 2,428: Line 2,566:
|~ 12/11 10/9 6/5 72/55 4/3 16/11 3/2 81/50 5/3 9/5 108/55 2/1
|~ 12/11 10/9 6/5 72/55 4/3 16/11 3/2 81/50 5/3 9/5 108/55 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|0.0430
|0.0430
|-
|-
Line 2,433: Line 2,573:
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 81/50 5/3 9/5 108/55 2/1
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 81/50 5/3 9/5 108/55 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|0.0510
|0.0510
|-
|-
Line 2,438: Line 2,580:
|~ 12/11 144/121 6/5 72/55 4/3 16/11 192/121 8/5 96/55 9/5 108/55 2/1
|~ 12/11 144/121 6/5 72/55 4/3 16/11 192/121 8/5 96/55 9/5 108/55 2/1
|LLsLsLLsLmLs
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|0.0819
|0.0819
|-
|-
Line 2,443: Line 2,587:
|~ 12/11 144/121 6/5 72/55 15/11 81/55 3/2 81/50 216/121 9/5 108/55 2/1
|~ 12/11 144/121 6/5 72/55 15/11 81/55 3/2 81/50 216/121 9/5 108/55 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|0.0899
|0.0899
|}
|}
Line 2,455: Line 2,601:
|[[7L 5s|sLLsLsLsLLsL]]
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meanenneadecal]][12]
|[[Meanenneadecal]][12]
|81/80
|45/44, 81/80
|-
|-
|L = m
|L = m
|sLLsLLLsLLsL
|sLLsLLLsLLsL
|[[Dimipent family|Diminished]][12] MODMOS
|[[Dimipent family|Diminished]][12] MODMOS
|648/625
|100/99, 128/121
|-
|-
|s = 0
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#Porkypine|Porkypine]][8]
|[[Porcupine family#Porkypine|Porkypine]][8]
|250/243
|55/54, 100/99
|}
|}


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