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Gallery of 3-SN scales: Difference between revisions

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Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
Added a bunch of rank-2 temperings for equivalence of unison vectors
Line 66: Line 66:
|Antitonic[4]
|Antitonic[4]
|9/8
|9/8
|-
|L - M = M - s
|LsLd
|Bug[4] MODMOS
|27/25
|-
|-
|s = 0
|s = 0
Line 145: Line 150:
|[[Enipucrop]][7]
|[[Enipucrop]][7]
|1125/1024
|1125/1024
|-
|L - M = M - s
|sAsLsAs
|Meantone[7] MODMOS
|81/80
|-
|-
| s = 0
| s = 0
Line 224: Line 234:
|[[Enipucrop]][7]
|[[Enipucrop]][7]
| 35/32, 49/45
| 35/32, 49/45
|-
|L - M = M - s
|sAsLsAs
|Meantone[7] MODMOS
|81/80, 126/125
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 384: Line 399:
|16875/16384  
|16875/16384  
|-
|-
|L= s
|L = s
|[[7L 3s|LsLLsLLsLL]]
|[[7L 3s|LsLLsLLsLL]]
|[[Dicot]][10]
|[[Dicot]][10]
|25/24
|25/24
|-
|L - m = m - s
|sLssdssLss
|Ampersand[10] MODMOS
|34171875/33554432
|-
|-
|s = 0
|s = 0
Line 537: Line 557:
|[[Sharp]][10]
|[[Sharp]][10]
|25/24, 28/27
|25/24, 28/27
|-
|L - m = m - s
|sLssdssLss
|Miracle[10] MODMOS
|225/224, 1029/1024
|-
|-
|s = 0
|s = 0
Line 695: Line 720:
|[[Marvel temperaments#Negri|Negri]][10]
|[[Marvel temperaments#Negri|Negri]][10]
|45/44, 49/48, 56/55  
|45/44, 49/48, 56/55  
|-
|L - m = m - s
|sLssdssLss
|Miracle[10] MODMOS
|225/224, 243/242, 385/384
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 846: Line 876:
|[[Negroni]][10]
|[[Negroni]][10]
|49/48, 55/54, 225/224  
|49/48, 55/54, 225/224  
|-
|L - m = m - s
|sLssdssLss
|Miracle[10] MODMOS
|225/224, 243/242, 385/384
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 914: Line 949:
|[[Marvel temperaments#Negri|Negri]][19]
|[[Marvel temperaments#Negri|Negri]][19]
|49/48, 225/224  
|49/48, 225/224  
|-
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|Magic[19] MODMOS
|225/224, 245/243
|-
|-
|s = 0
|s = 0
Line 993: Line 1,033:
|[[Marvel temperaments#Negri|Negri]][19]
|[[Marvel temperaments#Negri|Negri]][19]
|45/44, 49/48, 56/55
|45/44, 49/48, 56/55
|-
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|Magic[19] MODMOS
|100/99, 225/224, 245/243
|-
|-
|s = 0
|s = 0
Line 1,065: Line 1,110:
|[[Marvel temperaments#Negroni|Negroni]][19]
|[[Marvel temperaments#Negroni|Negroni]][19]
|49/48, 55/54, 225/224  
|49/48, 55/54, 225/224  
|-
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|Witchcraft[19] MODMOS
|225/224, 245/243, 441/440
|-
|-
|s = 0
|s = 0
Line 1,393: Line 1,443:
|[[Mavila]][9] MODMOS
|[[Mavila]][9] MODMOS
| 135/128
| 135/128
|-
|L - M = M - s
|sLssAssLs
|Orson[9] MODMOS
|2109375/2097152
|-
|-
|s = 0
|s = 0
Line 1,486: Line 1,541:
|[[Pelogic]][9] MODMOS
|[[Pelogic]][9] MODMOS
| 21/20, 135/128
| 21/20, 135/128
|-
|L - M = M - s
|sLssAssLs
|Orwell[9] MODMOS
|225/224, 1728/1715
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 1,592: Line 1,652:
|[[Marvel temperaments#Negri|Negri]][9]
|[[Marvel temperaments#Negri|Negri]][9]
|45/44, 49/48, 56/55
|45/44, 49/48, 56/55
|-
|L - M = M - s
|sLssAssLs
|Orwell[9] MODMOS
|99/88, 121/120, 176/175
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 1,716: Line 1,781:
|[[Passion family#Septimal passion|Passion]][12]
|[[Passion family#Septimal passion|Passion]][12]
| 64/63, 3125/3087
| 64/63, 3125/3087
|-
|L - M = M - s
|LdLLLsLLLdLL
|Meantone[12] MODMOS
|81/80, 126/125
|-
|-
|s = 0
|s = 0
Line 1,846: Line 1,916:
|[[Passion family#Septimal passion|Passion]][12]
|[[Passion family#Septimal passion|Passion]][12]
| 64/63, 100/99, 1375/1372
| 64/63, 100/99, 1375/1372
|-
|L - M = M - s
|LdLLLsLLLdLL
|Meanpop[12] MODMOS
|81/80, 126/125, 385/384
|-
|-
|s = 0
|s = 0
Line 1,867: Line 1,942:
|(2, 2, 1)
|(2, 2, 1)
|(3, 2, 1)
|(3, 2, 1)
|(4, 3, 1)
|(5, 3, 1)
|(5, 4, 2)
|(7, 5, 2)
|}
|}
{| class="wikitable"
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE tuning)
!Step sizes in cents (TE tuning)
|-
|-
Line 1,912: Line 1,993:
|[[Escapade family#Septimal escapade|Escapade]][22]
|[[Escapade family#Septimal escapade|Escapade]][22]
| 99/98, 176/175, 2560/2541
| 99/98, 176/175, 2560/2541
|-
|L - m = m - s
|sAssAsAsAsLsAsAsAssAsA
|Magic[22] MODMOS
|100/99, 225/224, 245/243
|-
|-
|s = 0
|s = 0
Line 1,941: Line 2,027:
135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm


m = s -> ssLsssLsss Srutal[10] 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; L = s -> LsLsLsLsLs Blackwood[10]; s = 0 -> sLssLss Mavila[9]; m =0 -> sLsLs Father[5]
m = s -> ssLsssLsss Srutal[10] 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; L = s -> LsLsLsLsLs Blackwood[10];
 
L - m = m - s -> sLALsLALsL Negri[10] MODMOS; s = 0 -> sLssLss Mavila[9]; m =0 -> sLsLs Father[5]
=====[[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)]]=====
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20) = (182.9137c, 116.0124c, 84.9028c) TE
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20) = (182.9137c, 116.0124c, 84.9028c) TE
Line 1,947: Line 2,035:
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm


m = s -> ssLsssLsss Pajara[10] 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; s = 0 -> sLssLss Pelogic[9]
m = s -> ssLsssLsss Pajara[10] 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; L - m = m - s -> sLALsLALsL Negri[10] MODMOS; s = 0 -> sLssLss Pelogic[9]
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-10|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[10] (Prodigy)]]=====
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-10|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[10] (Prodigy)]]=====
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20~22/21) = (184.0358c, 116.7669c, 82.9601c) TE
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20~22/21) = (184.0358c, 116.7669c, 82.9601c) TE
Line 1,953: Line 2,041:
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm


m = s -> ssLsssLsss Pajaric[10] 4M (Pentachordal decatonic)
m = s -> ssLsssLsss Pajaric[10] 4M (Pentachordal decatonic); L - m = m - s -> sLALsLALsL Negroni[10] MODMOS
====[[SNS ((2/1, 3/2)-5, 16/15)-17|((2/1, 3/2)[5], 16/15)[17]]]====
====[[SNS ((2/1, 3/2)-5, 16/15)-17|((2/1, 3/2)[5], 16/15)[17]]]====
10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c,
10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c,
Line 1,959: Line 2,047:
135/128 16/15 9/8 32/27 5/4 81/64 4/3 45/32 64/45 3/2 128/81 8/5 27/16 16/9 15/8 256/135 2/1 as LsLMLsLLsLLsLMLsL
135/128 16/15 9/8 32/27 5/4 81/64 4/3 45/32 64/45 3/2 128/81 8/5 27/16 16/9 15/8 256/135 2/1 as LsLMLsLLsLLsLMLsL


L = M -> LsLLLsLLsLLsLLLsL Helmholtz[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS;
L = M -> LsLLLsLLsLLsLLLsL Helmholtz[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS; s = 0 -> LLsLLLLLLsLL Srutal[12] 4M (Hexachordal Dodecatonic); M = 0 -> LsLLsLLsLLsLLsL Blackwood[15]
 
s = 0 -> LLsLLLLLLsLL Srutal[12] 4M (Hexachordal Dodecatonic); M = 0 -> LsLLsLLsLLsLLsL Blackwood[15]
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-17|((2/1, 3/2)[5], 16/15: 225/224)[17] (Marvel)]]=====
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-17|((2/1, 3/2)[5], 16/15: 225/224)[17] (Marvel)]]=====
2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63) = (98.0109c, 84.9028c, 31.1096)  TE
2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63) = (98.0109c, 84.9028c, 31.1096)  TE
Line 1,983: Line 2,069:
m = s -> ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS; L = m -> sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29];
m = s -> ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS; L = m -> sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29];


L = s -> LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS; s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)
L = s -> LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS; L - m = m - s -> Marvolo[29] MODMOS;
 
s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)
====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-41|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[41] (Prodigy)]]====
====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-41|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[41] (Prodigy)]]====
29L 2M 10s = (2048/2025~50/49~64/63~45/44~56/55, 49/48~55/54, ~121/120) = (33.8068c, 33.4621c, 15.3465c) TE
29L 2M 10s = (2048/2025~50/49~64/63~45/44~56/55, 49/48~55/54, ~121/120) = (33.8068c, 33.4621c, 15.3465c) TE
Line 1,990: Line 2,078:


L = M -> LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS; M = s -> LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31];
L = M -> LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS; M = s -> LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31];
L - M = M - s -> Witchcraft[41] MODMOS


s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS; m = 0 -> LsLLLsLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Negroni[39] MODMOS
s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS; m = 0 -> LsLLLsLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Negroni[39] MODMOS
Line 2,000: Line 2,090:


M = s -> LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS;
M = s -> LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS;
L - M = M - s -> Compton MODMOS


s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS;
s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS;
Line 2,185: Line 2,277:
|[[Dicot family|Dicot]][7]
|[[Dicot family|Dicot]][7]
|25/24
|25/24
|-
|L - M = M - s
|LsLALsL
|Tetracot[7] MODMOS
|20000/19683
|-
|-
|s = 0
|s = 0
Line 2,460: Line 2,557:
|[[Dicot family|Flat]][7]
|[[Dicot family|Flat]][7]
|25/24, 33/32
|25/24, 33/32
|-
|L - m = m - s
|LsLALsL
|Tetracot[7] MODMOS
|100/99, 243/242
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 2,751: Line 2,853:
|[[Ripple family|Ripple]][12]
|[[Ripple family|Ripple]][12]
|6561/6250
|6561/6250
|-
|L - m = m - s
|dLLdLsLdLLdL
|Augmented[12] MODMOS
|128/125
|-
|-
|s = 0
|s = 0
Line 2,875: Line 2,982:
|[[Diminished]][12] MODMOS
|[[Diminished]][12] MODMOS
|36/35, 50/49
|36/35, 50/49
|-
|L - m = m - s
|dLLdLsLdLLdL
|Augene[12] MODMOS
|64/63, 126/125
|-
|-
|s = 0
|s = 0
Line 3,159: Line 3,271:
|[[Dimipent family|Diminished]][12] MODMOS
|[[Dimipent family|Diminished]][12] MODMOS
|100/99, 128/121
|100/99, 128/121
|-
|L - m = m - s
|dLLdLsLdLLdL
|Augene[12] MODMOS
|100/99, 128/125
|-
|-
|s = 0
|s = 0
Line 3,303: Line 3,420:
|[[Meantone family#Flattone|Flattone]][12]
|[[Meantone family#Flattone|Flattone]][12]
|45/44, 81/80, 385/384
|45/44, 81/80, 385/384
|-
|L = m
|sLLsLLLsLLsL
|[[Augmented family#Augene|Augene]][12] MODMOS
|56/55, 64/63, 100/99
|-
|-
|s = 0
|s = 0
Line 3,448: Line 3,560:
|[[Meantone family#Flattone|Flattone]][12]
|[[Meantone family#Flattone|Flattone]][12]
|45/44, 65/64, 78/77, 81/80
|45/44, 65/64, 78/77, 81/80
|-
|L = m
|sLLsLLLsLLsL
|[[Augmented family#Augene|Augene]][12] MODMOS
|40/39, 56/55, 64/63, 66/65
|-
|-
|s = 0
|s = 0
Line 3,777: Line 3,884:


m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
L - m = m - s -> Unidec[20] MODMOS


s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Hystrix[8]
s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Hystrix[8]
Line 3,807: Line 3,916:


L = M -> sLLLsLLLsL Dicot[10] MOSMOS; M = s -> sLsLsLsLsL Blackwood[10]; L = s -> ssLsssLsss Supersharp[10] MODMOS;
L = M -> sLLLsLLLsL Dicot[10] MOSMOS; M = s -> sLsLsLsLsL Blackwood[10]; L = s -> ssLsssLsss Supersharp[10] MODMOS;
L - M = M - s -> dLsLdLsLdL Srutal[10] MODMOS


s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8]
s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8]
Line 3,814: Line 3,925:
~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs
~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs


m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss; s = 0 -> LsLLLsL Dominant[7]; m = 0 -> sLssLssLssLssLs
m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss;
 
L - m = m - s -> Garibaldi[17]; s = 0 -> LsLLLsL Dominant[7]; m = 0 -> sLssLssLssLssLs
=====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-17|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[17] (Akea)]]=====
=====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-17|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[17] (Akea)]]=====
5L 2m 10s = (35/32~12/11, 256/243~21/20, 81/80~64/63~55/54) = (156.6236c, 85.7981c, 26.2356c) TE
5L 2m 10s = (35/32~12/11, 256/243~21/20, 81/80~64/63~55/54) = (156.6236c, 85.7981c, 26.2356c) TE
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