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Gallery of 3-SN scales: Difference between revisions

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Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
Line 2,453: Line 2,453:
|L = m
|L = m
|[[5L 2s|LsLLLsL]]
|[[5L 2s|LsLLLsL]]
|[[Meanenneadecal]][7]
|[[Meanenneadecal]][7] or [[Meantone family#Flattone|Flattone]][7]
|45/44, 81/80
|45/44, 81/80
|-
|-
Line 2,472: Line 2,472:
|[[29edo|29]]
|[[29edo|29]]
|[[34edo|34]]
|[[34edo|34]]
|[[37edo|37]]
|[[41edo|41]]
|[[41edo|41]]
|-
|-
Line 2,483: Line 2,484:
|(5, 4, 4)
|(5, 4, 4)
|(6, 5, 4)
|(6, 5, 4)
|(7, 5, 5)
|(7, 6, 5)
|(7, 6, 5)
|}
|}
Line 3,148: Line 3,150:
|m = s
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meanenneadecal]][12]
|[[Meanenneadecal]][12] or [[Meantone family#Flattone|Flattone]][12]
|45/44, 81/80
|45/44, 81/80
|-
|-
Line 3,171: Line 3,173:
|[[29edo|29]]
|[[29edo|29]]
|[[34edo|34]]
|[[34edo|34]]
|[[37edo|37]]
|[[41edo|41]]
|[[41edo|41]]
|-
|-
Line 3,180: Line 3,183:
|(4, 1, 0)
|(4, 1, 0)
|(4, 2, 1)
|(4, 2, 1)
|(5, 2, 0)
|(5, 2, 1)
|}
=====(2/1, 3/2, 6/5: 100/99, 385/384)[12] ([[Keemic family#Supermagic|Supermagic]])=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(27/25~12/11~35/32, 25/24~33/32, 250/243~55/54~64/63~121/120)
|149.51592c, 58.8799c, 23.6254c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
|  -6
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 32/21 5/3 121/72 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|
|-
|  -5
|~ 55/54 10/9 8/7 5/4 121/96 11/8 3/2 32/21 5/3 121/72 11/6 2/1
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|
|-
|  -4
|~ 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
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|
|-
|  -3
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 32/21 5/3 9/5 11/6 2/1
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|
|-
|  -2
|~ 25/24 9/8 8/7 5/4 15/11 11/8 3/2 32/21 5/3 9/5 11/6 2/1
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|
|-
|  -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
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|
|-
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|
|-
|2
|~ 12/11 10/9 6/5 21/16 4/3 16/11 22/15 8/5 7/4 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|
|-
|3
|~ 12/11 10/9 6/5 21/16 4/3 16/11 3/2 18/11 5/3 9/5 63/32 2/1
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|
|-
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 63/ 2/1
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|
|-
|5
|~ 12/11 144/121 6/5 21/16 4/3 16/11 192/121 8/5 7/4 9/5 63/32 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|
|-
|6
|~ 12/11 144/121 6/5 21/16 15/11 81/55 3/2 18/11 216/121 9/5 63/32 2/1
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|
|}
{| class="wikitable"
|+Rank-2 temperings (mode -3)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meantone family#Flattone|Flattone]][12]
|45/44, 81/80, 385/384
|-
|L = m
|sLLsLLLsLLsL
|[[Augmented family#Augene|Augene]][12] MODMOS
|56/55, 64/63, 100/99
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#Septimal porcupine|Porcupine]][8]
|55/54, 64/63, 100/99
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[15edo|15]]
|[[19edo|19]]
|[[22edo|22]]
|27e
|[[34edo|34]]
|[[37edo|37]]
|[[41edo|41]]
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(3, 1, 0)
|(3, 2, 1)
|(4, 2, 1)
|(5, 2, 0)
|(5, 2, 1)
|(5, 2, 1)
|}
|}
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