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Gallery of 3-SN scales: Difference between revisions

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1,636 edits
Line 4,739: Line 4,739:
|-
|-
|4L 3M 1s
|4L 3M 1s
|10/9, 27/25, 25/24
|10/9, 27/25~35/32, 25/24~36/35
|(182.4037c, 133.2376c, 70.6724c)
|
|}
|}
{| class="wikitable"
{| class="wikitable"
|+
|+
!Mode number
!Mode number
!Mode in JI (height order)
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Porcupine[8]
!Porcupine[8]
Line 4,753: Line 4,753:
|-
|-
|4
|4
|10/9 6/5 4/3 36/25 8/5 216/125 48/25 2/1
|~ 10/9 6/5 4/3 35/24 8/5 7/4 35/18 2/1
|LMLMLMLs
|LMLMLMLs
|<nowiki>LLLLLLLs 7|0</nowiki>
|<nowiki>LLLLLLLs 7|0</nowiki>
Line 4,759: Line 4,759:
|-
|-
|3
|3
|10/9 6/5 4/3 36/25 8/5 5/3 50/27 2/1
|~ 10/9 6/5 4/3 35/24 8/5 5/3 50/27 2/1
|LMLMLsLM
|LMLMLsLM
|<nowiki>LLLLLsLL 5|2</nowiki>
|<nowiki>LLLLLsLL 5|2</nowiki>
Line 4,765: Line 4,765:
|-
|-
|2
|2
|27/25 6/5 162/125 36/25 972/625 216/125 9/5 2/1
|~ 27/25 6/5 21/16 35/24 63/40 7/4 9/5 2/1
|MLMLMLsL
|MLMLMLsL
|<nowiki>LLLLLLsL 6|1</nowiki>
|<nowiki>LLLLLLsL 6|1</nowiki>
Line 4,771: Line 4,771:
|-
|-
|1
|1
|10/9 6/5 4/3 25/18 125/81 5/3 50/27 2/1
|~ 10/9 6/5 4/3 25/18 32/21 5/3 50/27 2/1
|LMLsLMLM
|LMLsLMLM
|<nowiki>LLLsLLLL 3|4</nowiki>
|<nowiki>LLLsLLLL 3|4</nowiki>
Line 4,777: Line 4,777:
|-
|-
| -1
| -1
|27/25 6/5 162/125 36/25 3/2 5/3 9/5 2/1
|~ 27/25 6/5 21/16 35/24 3/2 5/3 9/5 2/1
|MLMLsLML
|MLMLsLML
|<nowiki>LLLLsLLL 4|3</nowiki>
|<nowiki>LLLLsLLL 4|3</nowiki>
Line 4,783: Line 4,783:
|-
|-
| -2
| -2
|10/9 125/108 625/486 25/18 125/81 5/3 50/27 2/1
|~ 10/9 8/7 80/63 25/18 32/21 5/3 50/27 2/1
|LsLMLMLM
|LsLMLMLM
|<nowiki>LsLLLLLL 1|6</nowiki>
|<nowiki>LsLLLLLL 1|6</nowiki>
Line 4,789: Line 4,789:
|-
|-
| -3
| -3
|27/25 6/5 5/4 25/18 3/2 5/3 9/5 2/1
|~ 27/25 6/5 5/4 25/18 3/2 5/3 9/5 2/1
|MLsLMLML
|MLsLMLML
|<nowiki>LLsLLLLL 2|5</nowiki>
|<nowiki>LLsLLLLL 2|5</nowiki>
Line 4,795: Line 4,795:
|-
|-
| -4
| -4
|25/24 125/108 5/4 25/18 3/2 5/3 9/5 2/1
|~ 25/24 8/7 5/4 25/18 3/2 5/3 9/5 2/1
|sLMLMLML
|sLMLMLML
|<nowiki>sLLLLLLL 0|7</nowiki>
|<nowiki>sLLLLLLL 0|7</nowiki>
Line 4,817: Line 4,817:
|Porcupine[8]
|Porcupine[8]
|250/243, 64/63
|250/243, 64/63
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|15
|19
|22
|26
|34
|37
|41
|60
|-
!Step sizes in ET
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(4, 3, 1)
|(5, 4, 2)
|(5, 5, 2)
|(6, 5, 2)
|(9, 7, 3)
|}
===== ((2/1, 6/5)[4], 10/9: 100/99, 385/384)[8] Supermagic =====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|4L 3M 1s
|10/9~11/10, 27/25~35/32~12/11, 25/24~36/35~33/32
|
|}
{| class="wikitable"
|+
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Porcupine[8]
step pattern and UDP
!Diminished[8]
step pattern and UDP
|-
|4
|~ 10/9 6/5 4/3 16/11 8/5 7/4 35/18 2/1
|LMLMLMLs
|<nowiki>LLLLLLLs 7|0</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|3
|~ 10/9 6/5 4/3 16/11 8/5 5/3 11/6 2/1
|LMLMLsLM
|<nowiki>LLLLLsLL 5|2</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|2
|~ 12/11 6/5 21/16 16/11 63/40 7/4 9/5 2/1
|MLMLMLsL
|<nowiki>LLLLLLsL 6|1</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
|1
|~ 10/9 6/5 4/3 11/8 32/21 5/3 11/6 2/1
|LMLsLMLM
|<nowiki>LLLsLLLL 3|4</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -1
|~ 12/11 6/5 21/16 16/11 3/2 5/3 9/5 2/1
|MLMLsLML
|<nowiki>LLLLsLLL 4|3</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -2
|~ 10/9 8/7 44/35 11/8 32/21 5/3 11/6 2/1
|LsLMLMLM
|<nowiki>LsLLLLLL 1|6</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -3
|~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1
|MLsLMLML
|<nowiki>LLsLLLLL 2|5</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
|-
|M = s
| -4
|LsLsLsLs
|~ 25/24 8/7 5/4 11/8 3/2 5/3 9/5 2/1
|Diminished[8]
|sLMLMLML
|648/625
|<nowiki>sLLLLLLL 0|7</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|}
 
{| class="wikitable"
|+Rank-2 temperings (mode 4)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|-
|L - M = M - s
|L = M
|LsLsLsLd
|LLLLLLLs
|Sensipent[8] MODMOS
|Porcupine[8]
|78732/78125
|55/54, 64/63, 100/99
|}
|}


Line 4,832: Line 4,927:
|+Rank-1 temperings
|+Rank-1 temperings
!ET
!ET
|12
|15
|15
|19
|19
|22
|22
|26
|26
|27
|29
|31
|34
|34
|37
|41
|41
|46
|63
|53
|65
|-
|-
!Step sizes in ET
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(2, 2, 1)
|(3, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(3, 3, 1)
|(4, 3, 1)
|(4, 3, 1)
|(4, 3, 2)
|(4, 4, 1)
|(5, 3, 2)
|(5, 4, 2)
|(5, 4, 2)
|(5, 5, 2)
|(6, 5, 2)
|(6, 5, 2)
|(7, 5, 3)
|(9, 8, 3)
|(8, 6, 3)
|(10, 7, 4)
|}
|}


===== ((2/1, 6/5)[4], 10/9: 100/99)[8] (No-7 Ptolemismic) =====
===== ((2/1, 6/5)[4], 10/9: 100/99, 105/104, 144/143)[8] Supermagic =====
{| class="wikitable"
{| class="wikitable"
!Step signature
!Step signature
Line 4,869: Line 4,954:
|-
|-
|4L 3M 1s
|4L 3M 1s
|10/9~11/10, 27/25~12/11, 25/24~33/32
|10/9~11/10, 27/25~35/32~12/11~13/12, 25/24~36/35~33/32~27/26
|(174.0549c, 146.6353c, 63.1433c)
|
|}
|}
{| class="wikitable"
|+
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Porcupine[8]
step pattern and UDP
!Diminished[8]
step pattern and UDP
|-
|4
|~ 10/9 6/5 4/3 13/9 8/5 7/4 35/18 2/1
|LMLMLMLs
|<nowiki>LLLLLLLs 7|0</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|3
|~ 10/9 6/5 4/3 13/9 8/5 5/3 11/6 2/1
|LMLMLsLM
|<nowiki>LLLLLsLL 5|2</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|2
|~ 12/11 6/5 13/10 13/9 39/25 7/4 9/5 2/1
|MLMLMLsL
|<nowiki>LLLLLLsL 6|1</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
|1
|~ 10/9 6/5 4/3 11/8 20/13 5/3 11/6 2/1
|LMLsLMLM
|<nowiki>LLLsLLLL 3|4</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -1
|~ 12/11 6/5 13/10 13/9 3/2 5/3 9/5 2/1
|MLMLsLML
|<nowiki>LLLLsLLL 4|3</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -2
|~ 10/9 8/7 44/35 11/8 20/13 5/3 11/6 2/1
|LsLMLMLM
|<nowiki>LsLLLLLL 1|6</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -3
|~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1
|MLsLMLML
|<nowiki>LLsLLLLL 2|5</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -4
|~ 25/24 8/7 5/4 11/8 3/2 5/3 9/5 2/1
|sLMLMLML
|<nowiki>sLLLLLLL 0|7</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 4)
|+Rank-2 temperings (mode 4)
Line 4,878: Line 5,022:
!Scale
!Scale
!Comma list
!Comma list
|-
|s = 0
|LsLsLsL
|Flat[7]
|25/24, 33/32
|-
|-
|L = M
|L = M
|LLLLLLLs
|LLLLLLLs
|Porkypine[8]
|Porcupine[8]
|55/54, 100/99
|40/39, 55/54, 64/63, 66/65
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-1 temperings
|+Rank-1 temperings
!ET
!ET
|12
|15
|15
|19
|19
|22
|22f
|26
|26
|27e
|29
|34
|34
|37
|41
|41
|63
|-
|-
!Step sizes in ET
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(2, 2, 1)
|(3, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(3, 3, 1)
|(4, 3, 1)
|(4, 3, 1)
|(4, 3, 2)
|(4, 4, 1)
|(5, 4, 2)
|(5, 4, 2)
|(5, 5, 2)
|(6, 5, 2)
|(6, 5, 2)
|(9, 8, 3)
|}
|}


Line 4,938: Line 5,076:
|-
|-
|2
|2
|~ 12/11 6/5 13/10 13/9 39/25 26/15 9/5 2/1
|~ 13/12 6/5 13/10 13/9 39/25 26/15 9/5 2/1
|MLMLMLsL
|MLMLMLsL
|-
|-
Line 4,946: Line 5,084:
|-
|-
| -1
| -1
|~ 12/11 6/5 13/10 13/9 3/2 5/3 9/5 2/1
|~ 13/12 6/5 13/10 13/9 3/2 5/3 9/5 2/1
|MLMLsLML
|MLMLsLML
|-
|-
Line 4,954: Line 5,092:
|-
|-
| -3
| -3
|~ 12/11 6/5 5/4 18/13 3/2 5/3 9/5 2/1
|~ 13/12 6/5 5/4 18/13 3/2 5/3 9/5 2/1
|MLsLMLML
|MLsLMLML
|-
|-
Retrieved from "https://en.xen.wiki/w/Gallery_of_3-SN_scales"