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Gallery of 3-SN scales: Difference between revisions

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Line 2,134: Line 2,134:
|.0745
|.0745
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 1)
|+Rank-2 temperings (mode 1)
!Equivalence
! Equivalence
!Step pattern
! Step pattern
!Scale
! Scale
!Comma list
! Comma list
|-
|-
|m = s
| m = s
|[[OTC 2L 8s|ssLsssLsss]]
| [[OTC 2L 8s|ssLsssLsss]]
|[[Srutal]][10] 4M (pentachordal decatonic)
| [[Diaschismic]][10] 4M (pentachordal decatonic)
|2048/2025
| 2048/2025
|-
|-
|L = m
| L = m
|[[7L 3s|sLLLsLLLsL]]
| [[7L 3s|sLLLsLLLsL]]
|[[Dicot family|Dicot]][10] MODMOS
| [[Dicot]][10] modmos
|25/24
| 25/24
|-
|-
|L = s
| L = s
|[[5L 5s|LsLsLsLsLs]]
| [[5L 5s|LsLsLsLsLs]]
|[[Limmic temperaments#5-limit .28blackwood.29|Blackwood]][10]
| [[Blackwood]][10]
|256/243
| 256/243
|-
|-
|L - m = m - s
| L - m = m - s
|sLALsLALsL
| sLALsLALsL
|[[Marvel temperaments#Negri|Negri]][10] MODMOS
| [[Negri]][10] modmos
|16875/16384
| 16875/16384
|-
|-
|s = 0
| s = 0
|[[2L 5s|sLssLss]]
| [[2L 5s|sLssLss]]
|[[Mavila]][7]
| [[Mavila]][7]
|135/128
| 135/128
|-
|-
|m = 0
| m = 0
|[[2L 3s|sLsLs]]
| [[2L 3s|sLsLs]]
|[[Trienstonic clan#Father|Father]][5]
| [[Father]][5]
|16/15
| 16/15
|}
|}
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)]]=====
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)]]=====
{| class="wikitable"
{| class="wikitable"
Line 2,493: Line 2,495:


m = 0 -> LssLsLsLssLsLssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Andromeda[70] MODMOS
m = 0 -> LssLsLsLssLsLssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Andromeda[70] MODMOS
==2.3.5; [[Starling]], [[Ptolemismic temperaments|No-7 Ptolemismic]], and [[Ragismic family#Ragismic|Ragismic]]==
==2.3.5; [[Starling]], [[Ptolemismic temperaments|No-7 Ptolemismic]], [[Supermagic]], and [[Ragismic family#Ragismic|Ragismic]]==
===(2/1, 3/2, 6/5)===
===(2/1, 3/2, 6/5)===
====[[SNS (2/1, 3/2, 6/5)-4|(2/1, 3/2, 6/5)[4]]]====
====[[SNS (2/1, 3/2, 6/5)-4|(2/1, 3/2, 6/5)[4]]]====
Line 4,740: Line 4,742:
|4L 3M 1s
|4L 3M 1s
|10/9, 27/25~35/32, 25/24~36/35
|10/9, 27/25~35/32, 25/24~36/35
|
|176.8769, 144.8100, 59.11533
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 4,850: Line 4,852:
|4L 3M 1s
|4L 3M 1s
|10/9~11/10, 27/25~35/32~12/11, 25/24~36/35~33/32
|10/9~11/10, 27/25~35/32~12/11, 25/24~36/35~33/32
|
|173.1413, 149.5159, 58.8799
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 4,955: Line 4,957:
|4L 3M 1s
|4L 3M 1s
|10/9~11/10, 27/25~35/32~12/11~13/12, 25/24~36/35~33/32~27/26
|10/9~11/10, 27/25~35/32~12/11~13/12, 25/24~36/35~33/32~27/26
|
|176.3227, 145.4708, 58.3927
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 5,037: Line 5,039:
|26
|26
|34
|34
|37
|41
|41
|63
|60
|-
|-
!Step sizes in ET
!Step sizes in ET
Line 5,047: Line 5,048:
|(4, 3, 1)
|(4, 3, 1)
|(5, 4, 2)
|(5, 4, 2)
|(5, 5, 2)
|(6, 5, 2)
|(6, 5, 2)
|(9, 8, 3)
|(9, 7, 3)
|}
|}


Line 5,060: Line 5,060:
|4L 3M 1s
|4L 3M 1s
|10/9, 27/25~13/12, 25/24~27/26
|10/9, 27/25~13/12, 25/24~27/26
|
|180.4645c, 136.7099c, 68.1467c
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 5,142: Line 5,142:
|4L 3M 1s
|4L 3M 1s
|10/9~11/10, 27/25~12/11~13/12, 25/24~33/32~27/26
|10/9~11/10, 27/25~12/11~13/12, 25/24~33/32~27/26
|(175.8918c, 142.7754c, 66.7663c)
|175.8918c, 142.7754c, 66.7663c
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 5,225: Line 5,225:
s = 0 -> ssLsLssLsssL Diminished[12] MODMOS; m = 0 -> sLLsLsL Dicot[7]; L = 0 -> Father[11].
s = 0 -> ssLsLssLsssL Diminished[12] MODMOS; m = 0 -> sLLsLsL Dicot[7]; L = 0 -> Father[11].


15-ET: (1,1,1); 19-ET: (2, 1, 1); 22-ET: (2, 1, 2); 26-ET: (3, 1, 2); 27-ET: (2, 2, 1); 29-ET: (3, 1, 3); 31-ET: (3, 2, 1); 34-ET: (3, 2, 2); 41-ET: (4, 2, 3); 46-ET: (4, 3, 2); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 87-ET: (8, 5, 5)
19-ET: (2, 1, 1); 22-ET: (2, 1, 2); 26-ET: (3, 1, 2); 27-ET: (2, 2, 1); 29-ET: (3, 1, 3); 31-ET: (3, 2, 1); 34-ET: (3, 2, 2); 41-ET: (4, 2, 3); 46-ET: (4, 3, 2); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 87-ET: (8, 5, 5)
 
===== (2/1, 6/5)[4], 10/9: 875/864)[15] Supermagic =====
4L 3m 8s = (16/15, 648/625~21/20, 25/24~36/35)
 
~ 25/24 10/9 8/7 6/5 5/4 4/3 25/18 35/24 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs


===== (2/1, 6/5)[4], 10/9: 225/224)[15] Marvel =====
15-ET: (1,1,1); 19-ET: (2, 1, 1); 22-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 60-ET: (6, 4, 3)
4L 8m 3s = (16/15~15/14, 25/24~28/27, 648/625)


~ 25/24 10/9 125/108 6/5 5/4 4/3 25/18 36/25 3/2 8/5 5/3 216/125 9/5 27/14 2/1
===== (2/1, 6/5)[4], 10/9: 100/99, 385/384)[15] Supermagic =====
4L 3m 8s = (16/15, 648/625~21/20~128/121, 25/24~36/35~33/32)


===== (2/1, 6/5)[4], 10/9: 325/324)[15] (2.3.5.13 Marveltwin) =====
~ 25/24 10/9 8/7 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs
4L 8m 3s = (16/15, 25/24~27/26, 648/625~26/25) = (112.3178, 68.1467, 68.5631)


~ 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1 as mLmsmLmsmLmsmLm
15-ET: (1,1,1); 19-ET: (2, 1, 1); 22-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 63-ET: (6, 5, 3)


15d-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 1, 2); 26-ET: (3, 1, 2); 27-ET: (2, 2, 1); 29-ET: (3, 1, 3); 31-ET: (3, 2, 1); 34-ET: (3, 2, 2); 41-ET: (4, 2, 3); 46-ET: (4, 3, 2); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 87-ET: (8, 5, 5)
===== (2/1, 6/5)[4], 10/9: 100/99, 105/104, 144/143)[15] Supermagic =====
4L 3m 8s = (16/15, 648/625~21/20~128/121~26/25, 25/24~36/35~33/32~27/26)


===== (2/1, 6/5)[4], 10/9: 225/224, 325/324)[15] 2.3.5.7.13 Hecate =====
~ 25/24 10/9 8/7 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs
4L 8m 3s = (16/15~15/14, 25/24~28/27~27/26, 648/625~26/25)


~ 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 9/5 27/14 2/1 as mLmsmLmsmLmsmLm
15-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 60-ET: (6, 4, 3)


15d-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 1, 2); 31f-ET: (3, 2, 1); 34d-ET: (3, 2, 2); 41-ET: (4, 2, 3); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 94-ET: (9, 5, 6)
===== (2/1, 6/5)[4], 10/9: 325/324)[15] (2.3.5.13 Marveltwin) =====
===== (2/1, 6/5)[4], 10/9: 100/99, 144/143)[15] (2.3.5.11.13 Ptolemismic) =====
4L 3m 8s = (16/15, 648/625~26/25, 25/24~27/26) = (112.3178, 68.5631, 68.1467)
4L 8m 3s = (16/15, 25/24~33/32~27/26, 648/625~128/121~26/25) = (109.1256, 76.0091, 66.7663)


~ 25/24 10/9 15/13 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1 as mLmsmLmsmLmsmLm
~ 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1 as sLsmsLsmsLsmsLs


15-ET: (1, 1, 1); 19-ET: (2, 1, 1); 22f-ET: (2, 1, 2); 26-ET: (3, 1, 2); 27e-ET: (2, 2, 1); 29-ET: (3, 1, 3); 34-ET: (3, 2, 2); 41-ET: (4, 2, 3)
15d-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 27-ET: (2, 2, 1); 29-ET: (3, 3, 1); 31-ET: (3, 1, 2); 34-ET: (3, 2, 2); 41-ET: (4, 3, 2); 46-ET: (4, 2, 3); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 87-ET: (8, 5, 5)


===== (2/1, 6/5)[4], 10/9: 100/99, 144/143, 225/224)[15] Apollo =====
===== (2/1, 6/5)[4], 10/9: 105/104, 325/324)[15] 2.3.5.7.13 Supermagic =====
4L 8m 3s = (16/15~15/14, 25/24~28/27~33/32~27/26, 648/625~128/121~26/25)
4L 3m 8s = (16/15, 648/625~21/20~26/25, 25/24~36/35~27/26) = (121.6150, 81.3115, 58.8960)


~ 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 9/5 27/14 2/1 as mLmsmLmsmLmsmLm
~ 25/24 10/9 8/7 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs


15d-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 1, 2); 26d-ET: (3, 1, 2); 29f-ET: (3, 1, 3); 31f-ET: (3, 2, 1); 34d-ET: (3, 2, 2); 41-ET: (4, 2, 3); 53e-ET: (5, 3, 3)
15-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 60-ET: (6, 4, 3)
===== (2/1, 6/5)[4], 10/9: 100/99, 144/143)[15] (2.3.5.11.13 Ptolemismic) =====
4L 3m 8s = (16/15, 648/625~128/121~26/25, 25/24~33/32~27/26) = (109.1256, 76.0091, 66.7663) ⟨109.12557, 76.00911, 66.76626]


===== (2/1, 6/5)[4], 10/9: 225/224, 325/324, 385/384)[15] Hecate =====
~ 25/24 10/9 15/13 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1 as sLsmsLsmsLsmsLs
~ 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 9/5 27/14 2/1 as mLmsmLmsmLmsmLm


15d-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 1, 2); 31f-ET: (3, 2, 1); 34de-ET: (3, 2, 2); 41-ET: (4, 2, 3); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 94-ET: (9, 5, 6)
15-ET: (1, 1, 1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 27e-ET: (2, 1, 2); 29-ET: (3, 3, 1); 34-ET: (3, 2, 2); 41-ET: (4, 3, 2)


==2.3.5; [[Hemifamity family#Hemifamity|Hemifamity]] ==
==2.3.5; [[Hemifamity family#Hemifamity|Hemifamity]] ==
Line 5,714: Line 5,718:
14c-ET: (3, 1, 1); 17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 68-ET: (19, 9, 3); 87-ET: (24,11,4)
14c-ET: (3, 1, 1); 17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 68-ET: (19, 9, 3); 87-ET: (24,11,4)


==== (2/1, 3/2, 9/7: 245/243, 385/384)[10] Sensamagic ====
===== (2/1, 3/2, 9/7: 245/243, 385/384)[10] Sensamagic =====
2L 1m 7s = (~135/112, ~35/32, 28/27~36/35~33/32)
2L 1m 7s = (~135/112, ~35/32, 28/27~36/35~33/32)


Line 5,732: Line 5,736:
14c-ET: (2, 0, 1); 17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)
14c-ET: (2, 0, 1); 17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)


==== (2/1, 3/2, 9/7: 245/243, 385/384)[13] Sensamagic ====
===== (2/1, 3/2, 9/7: 245/243, 385/384)[13] Sensamagic =====
2L 1m 10s = (~75/64, 135/128~35/33, 28/27~36/35~33/32)
2L 1m 10s = (~75/64, 135/128~35/33, 28/27~36/35~33/32)


Line 5,786: Line 5,790:
17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22f-ET: (5, 2, 1) 24-ET: (6, 2, 1); 36-ET: (7, 2, 2); 41-ET: (9, 3, 2); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 94-ET: (19, 6, 5)
17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22f-ET: (5, 2, 1) 24-ET: (6, 2, 1); 36-ET: (7, 2, 2); 41-ET: (9, 3, 2); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 94-ET: (19, 6, 5)


==== (2/1, 3/2, 9/7: 351/350, 676/675)[13] ====
===== (2/1, 3/2, 9/7: 351/350, 676/675)[13] =====
2L 1m 10s = (~169/147, ~117/112, 28/27~27/26~26/25)
2L 1m 10s = (~169/147, ~117/112, 28/27~27/26~26/25)


Line 5,812: Line 5,816:


53-ET: (7, 3, 0); 58-ET: (8, 2, 1); 77-ET: (11, 3, 1); 111-ET: (15, 5, 1); 130-ET: (18, 6, 1)
53-ET: (7, 3, 0); 58-ET: (8, 2, 1); 77-ET: (11, 3, 1); 111-ET: (15, 5, 1); 130-ET: (18, 6, 1)
== 2.3.11 Pentacircle ==
=== ((2/1, 3/2)[5], 12/11) ===
==== ((2/1, 3/2)[5], 12/11)[10] ====
5L 2M 3s = (12/11, 88/81, 33/32)
12/11 9/8 27/22 4/3 16/11 3/2 18/11 27/16 81/44 2/1 as LsLMLsLsLM
==== ((2/1, 3/2)[5], 12/11: 896/891)[10] ====
5L 2M 3s = (12/11, 88/81, 33/32~28/27)
~  12/11 9/8 27/22 4/3 16/11 3/2 18/11 27/16 81/44 2/1 as LsLMLsLsLM
==== ((2/1, 3/2)[5], 12/11: 896/891)[17] ====
5L 2M 10s = (128/121~81/77, 256/243~22/21, 33/32~28/27)
~ 28/27 12/11 9/8 32/27 11/9 9/7 4/3 11/8 16/11 3/2 14/9 18/11 27/16 16/9 11/6 27/14 2/1 as sLsMsLssLssLsMsLs
== 2.3.13 Squbema ==
=== ((2/1, 3/2)[5], 13/12) ===
==== ((2/1, 3/2)[5], 13/12)[10] ====
5L 2M 3s = (13/12, 128/117, 27/26)
13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM
==== ((2/1, 3/2)[5], 13/12: 729/728)[10] ====
5L 2M 3s = (13/12, 128/117, 27/26~28/27)
~ 13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM
===== ((2/1, 3/2)[5], 13/12: 729/728)[17] =====
5L 2M 10s = (91/81, 256/243~96/91, 27/26~28/27)
~ 28/27 13/12 9/8 32/27 16/13 9/7 4/3 18/13 13/9 3/2 14/9 13/8 27/16 16/9 24/13 27/14 2/1 as sLsMsLssLssLsMsLs
===== ((2/1, 3/2)[5], 12/11~13/12: 144/143, 729/728)[17] =====
5L 2M 10s = (91/81~81/77, 256/243~96/91~22/21, 27/26~28/27~33/32)
~ 28/27 12/11 9/8 32/27 11/9 9/7 4/3 11/8 13/9 3/2 14/9 13/8 27/16 16/9 12/11 27/14 2/1 as sLsMsLssLssLsMsLs


{{Navbox scale gallery}}
{{Navbox scale gallery}}
Retrieved from "https://en.xen.wiki/w/Gallery_of_3-SN_scales"