Gallery of 3-SN scales mobile: Difference between revisions

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See [[SN scale]] and [[Rank-3 scale]].

Scales are grouped by their ''germinations'', the sequence of introduction of generators until 3 are reached, at which point the ''primitive'' 3-SN scale is developed (the first listed under each germination), from which all others of that germination evolve. The germination of Pythagorean, Meantone, Superpyth, Mavila, and Father MOS (2-SN) scales is (2/1, 3/2). Germinations are grouped by their subgroup, and within that, by the first comma tempered out in scales evolved from the germination.

Scales are grouped by their ''germinations'', the sequence of introduction of generators until 3 are reached, at which point the ''primitive'' 3-SN scale is developed (the first listed under each germination), from which all others of that germination evolve. The germination of [[Pythagorean]], [[Meantone]], [[Superpyth]], [[Mavila]], and [[Father]] [[MOS scale|MOS]] (2-SN) scales is ([[Octave|2/1]], [[3/2]]). Germinations are grouped by their [[subgroup]], and within that, by the first [[comma]] [[Tempering out|tempered out]] in scales evolved from the germination.

Commas tempered out are shown in their simplest basis set, as per SN labeling conventions.

Commas tempered out are shown in their simplest basis set, as per [[SN scale#Labeling|SN labeling conventions]].

Tempered scales are shown in JI as their simplest symmetric pre-image.

Tempered scales are shown in [[Just intonation|JI]] as their simplest symmetric pre-image.

Scales are written in JI and as step patterns in their symmetric mode (scales of odd cardinality) or, for scales of even cardinality, mostly in the even-symmetric mode: the mode symmetric without 2/1, otherwise in the inverse of the even-symmetric mode (the mode symmetric without 1/1).

Scales are written in [[Just intonation|JI]] and as step patterns in their symmetric mode (scales of odd cardinality) or, for scales of even cardinality, mostly in the even-symmetric mode: the mode symmetric without [[Octave|2/1]], otherwise in the inverse of the even-symmetric mode (the mode symmetric without [[1/1]]).

==2.3.5; Marvel==

===(2/1, 3/2, 5/4)===

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(2, 1, 1) in 29ET; (2, 2, 1) in 31ET; (3, 2, 1) in 41ET; (4, 3, 1) in 53eET; (5, 4, 2) in 72ET

====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-31|(2/1, 3/2, 5/4: 225/224, 441/440)[31] (Prodigy)]]====

====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-31|(2/1, 3/2, 5/4: 225/224, 441/440)[31]]] (Prodigy)====

10L+19m+2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TE

10L 19m 2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TE

~ 50/49 22/21 16/15 12/11 9/8 8/7 7/6 6/5 27/22 5/4 14/11 21/16 4/3 15/11 7/5 10/7 22/15 3/2 32/21 11/7 8/5 44/27 5/3 12/7 7/4 16/9 11/6 15/8 21/11 49/25 2/1

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s = 0 -> LLLLsLLLLL Negri[10]

===((2/1, 3/2)[5], 16/15)===

=== ((2/1, 3/2)[5], 16/15)===

====[[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]]====

2L 5m 3s = (10/9, 16/15, 135/128) = (182.4037c, 111.7313c, 92.1787c)

Line 220:

m = 0 -> LssLsLsLssLsLssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Andromeda[70] MODMOS

==2.3.5; Starling, ~~Luyoyo~~, and Ragismic==

==2.3.5; [[Starling]], [[Ptolemismic temperaments|No-7 Ptolemismic]], and [[Ragismic family#Ragismic|Ragismic]]==

===(2/1, 3/2, 6/5)===

====[[SNS (2/1, 3/2, 6/5)-4|(2/1, 3/2, 6/5)[4]]]====

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L = M -> LsLLLsL Meantone[7]; M = s -> sssLsss Opossum[7]; L = s -> LsLsLsL Flat[7]

=====[[SNS (2/1, 3/2, 6/5: 100/99)-7|(2/1, 3/2, 6/5: 100/99)[7] (~~Luyoyo~~)]]=====

=====[[SNS (2/1, 3/2, 6/5: 100/99)-7|(2/1, 3/2, 6/5: 100/99)[7] (No-7 Ptolemismic)]]=====

1L 4M 2S = (~9/8, 10/9~11/10, 27/25~12/11) = (209.7786c, 174.0549c, 146.6352c) TE

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m = s -> sLLsLsLsLLsL Meanpop[12]; L = m -> sLLsLLLsLLsL MODMOS; s = 0 -> LLLsLLLL

=====[[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12] (~~Luyoyo~~)]]=====

=====[[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12] (No-7 Ptolemismic)]]=====

7L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54) = (146.6352c, 63.1434c, 27.4197c) TE

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m = s -> sssLsssssLsssLsssssLsssssLsssLsssssLsss Hemiamity[39] MODMOS; L = m -> sLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLs; s = 0 -> sLssLsLssLssLsLssLs

==2.3.5; Hemifamity==

==2.3.5; [[Hemifamity family#Hemifamity|Hemifamity]] ==

===((2/1, 3/2)[5], 10/9)===

====[[SNS ((2/1, 3/2)-5, 10/9)-10|((2/1, 3/2)[5], 10/9)[10]]]====

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s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8]

====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-17|((2/1, 3/2)[5], 10/9: 5120/5103)[17] (~~Hemefamity~~)]]====

====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-17|((2/1, 3/2)[5], 10/9: 5120/5103)[17] (Hemifamity)]]====

5L 2m 10s = (~35/32, 256/243~21/20, 81/80~64/63) = (153.2376c, 85.8342c, 24.4931c) TE

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s = 0 -> LsLLLsL Arnold[7]; m = 0 -> ssLssssssLssssLssssLssssssLss

===((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63)===

===((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63) ===

====[[SNS ((2/1, 3/2)-12, 64/63: 5120/5103)-24|((2/1, 3/2)[12], 64/63: 5120/5013)[24] (Hemifamity)]]====

5L 7M 12s = (~135/128, ~28/27, 81/80~64/63) = (95.2825c, 61.3411c, 24.4931c) TE

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s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS

==2.5.9; Marvel==

==2.5.9; Marvel ==

===((2/1, 5/4)[3], 9/8)===

=== ((2/1, 5/4)[3], 9/8)===

====[[SNS ((2/1, 5/4)-3, 9/8)-6|((2/1, 5/4)[3], 9/8)[6]]]====

1L 3M 2s = (256/225, 9/8, 10/9)

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m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL

==2.3.7; ~~Orwellian~~==

==2.3.7; [[Orwellismic family#Orwellismic|Orwellismic]]==

===(2/1, 3/2, 7/6)===

====[[SNS (2/1, 3/2, 7/6)-4|(2/1, 3/2, 7/6)[4]]]====

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L = M -> LsLLLsL Archy[5]; s = 0 -> LLsLL Semaphore[5]

=====[[SNS (2/1, 3/2, 7/6: 1728/1715)-7|(2/1, 3/2, 7/6: 1728/1715)[7] (~~Orwellian~~)]]=====

=====[[SNS (2/1, 3/2, 7/6: 1728/1715)-7|(2/1, 3/2, 7/6: 1728/1715)[7] (Orwellismic)]]=====

4L 1M 2s = (~8/7, ~9/8, 49/48~36/35) = (227.1393c, 204.1935c, 43.334c) TE

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L = M -> LsLLLsL Superpyth[5]; s = 0 -> LLsLL Beep[5]

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-12|(2/1, 3/2, 7/6: 1728/1715)[12] (~~Orwellian~~)]]====

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-12|(2/1, 3/2, 7/6: 1728/1715)[12] (Orwellismic)]]====

4L 1M 7s = (~10/9, 54/49~35/32, 49/48~36/35) = (183.8053c, 160.8595c, 43.334c) TE

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L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-17|(2/1, 3/2, 7/6: 1728/1715)[17] (~~Orwellian~~)]]====

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-17|(2/1, 3/2, 7/6: 1728/1715)[17] (Orwellismic)]]====

4L 1M 12s = (~160/147, ~15/14, 49/48~36/35) = (140.4713c, 117.5255c, 43.334c) TE

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L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-22|(2/1, 3/2, 7/6: 1728/1715)[22] (~~Orwellian~~)]]====

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-22|(2/1, 3/2, 7/6: 1728/1715)[22] (Orwellismic)]]====

4L 1m 17s = (~200/189, ~25/24, 49/48~36/35) = (97.1373c, 74.1915c, 43.334c) TE

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m = s -> ssLssssLsssssssLssssLs Fleetwood[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-27|(2/1, 3/2, 7/6: 1728/1715)[27] (~~Orwellian~~)]]====

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-27|(2/1, 3/2, 7/6: 1728/1715)[27] (Orwellismic)]]====

4L 22M 1s = (~250/243, 49/48~36/35, ~50/49) = (53.8033c, 43.334c, 30.8575c) TE

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s = 0 -> ssLsssssLssssssssLsssssLss Fleetwood[26] MODMOS

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-53|(2/1, 3/2, 7/6: 1728/1715)[53] (~~Orwellian~~)]]====

====[[SNS (2/1, 3/2, 7/6: 1728/1715)-53|(2/1, 3/2, 7/6: 1728/1715)[53] (Orwellismic)]]====

27L 4M 22s = (~50/49, 64/63~245/243, 126/125~2401/2400) = (30.8575c, 22.9458c, 12.4765c) TE

@@ Line 3: / Line 3: @@
 See [[SN scale]] and [[Rank-3 scale]].
-Scales are grouped by their ''germinations'', the sequence of introduction of generators until 3 are reached, at which point the ''primitive'' 3-SN scale is developed (the first listed under each germination), from which all others of that germination evolve. The germination of Pythagorean, Meantone, Superpyth, Mavila, and Father MOS (2-SN) scales is (2/1, 3/2). Germinations are grouped by their subgroup, and within that, by the first comma tempered out in scales evolved from the germination.
+Scales are grouped by their ''germinations'', the sequence of introduction of generators until 3 are reached, at which point the ''primitive'' 3-SN scale is developed (the first listed under each germination), from which all others of that germination evolve. The germination of [[Pythagorean]], [[Meantone]], [[Superpyth]], [[Mavila]], and [[Father]] [[MOS scale|MOS]] (2-SN) scales is ([[Octave|2/1]], [[3/2]]). Germinations are grouped by their [[subgroup]], and within that, by the first [[comma]] [[Tempering out|tempered out]] in scales evolved from the germination.
-Commas tempered out are shown in their simplest basis set, as per SN labeling conventions.
+Commas tempered out are shown in their simplest basis set, as per [[SN scale#Labeling|SN labeling conventions]].
-Tempered scales are shown in JI as their simplest symmetric pre-image.
+Tempered scales are shown in [[Just intonation|JI]] as their simplest symmetric pre-image.
-Scales are written in JI and as step patterns in their symmetric mode (scales of odd cardinality) or, for scales of even cardinality, mostly in the even-symmetric mode: the mode symmetric without 2/1, otherwise in the inverse of the even-symmetric mode (the mode symmetric without 1/1).
+Scales are written in [[Just intonation|JI]] and as step patterns in their symmetric mode (scales of odd cardinality) or, for scales of even cardinality, mostly in the even-symmetric mode: the mode symmetric without [[Octave|2/1]], otherwise in the inverse of the even-symmetric mode (the mode symmetric without [[1/1]]).
 ==2.3.5; Marvel==
 ===(2/1, 3/2, 5/4)===
@@ Line 88: / Line 88: @@
 (2, 1, 1) in 29ET; (2, 2, 1) in 31ET; (3, 2, 1) in 41ET; (4, 3, 1) in 53eET; (5, 4, 2) in 72ET
-====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-31|(2/1, 3/2, 5/4: 225/224, 441/440)[31] (Prodigy)]]====
+====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-31|(2/1, 3/2, 5/4: 225/224, 441/440)[31]]] (Prodigy)====
-L+19m+2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TE
+L 19m 2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TE
 ~ 50/49 22/21 16/15 12/11 9/8 8/7 7/6 6/5 27/22 5/4 14/11 21/16 4/3 15/11 7/5 10/7 22/15 3/2 32/21 11/7 8/5 44/27 5/3 12/7 7/4 16/9 11/6 15/8 21/11 49/25 2/1
@@ Line 151: / Line 151: @@
 s = 0 -> LLLLsLLLLL Negri[10]
-===((2/1, 3/2)[5], 16/15)===
+=== ((2/1, 3/2)[5], 16/15)===
 ====[[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]]====
 L 5m 3s = (10/9, 16/15, 135/128) = (182.4037c, 111.7313c, 92.1787c)
@@ Line 220: / Line 220: @@
 m = 0 -> LssLsLsLssLsLssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Andromeda[70] MODMOS
-==2.3.5; Starling, Luyoyo, and Ragismic==
+==2.3.5; [[Starling]], [[Ptolemismic temperaments|No-7 Ptolemismic]], and [[Ragismic family#Ragismic|Ragismic]]==
 ===(2/1, 3/2, 6/5)===
 ====[[SNS (2/1, 3/2, 6/5)-4|(2/1, 3/2, 6/5)[4]]]====
@@ Line 240: / Line 240: @@
 L = M -> LsLLLsL Meantone[7]; M = s -> sssLsss Opossum[7]; L = s -> LsLsLsL Flat[7]
-=====[[SNS (2/1, 3/2, 6/5: 100/99)-7|(2/1, 3/2, 6/5: 100/99)[7] (Luyoyo)]]=====
+=====[[SNS (2/1, 3/2, 6/5: 100/99)-7|(2/1, 3/2, 6/5: 100/99)[7] (No-7 Ptolemismic)]]=====
 L 4M 2S = (~9/8, 10/9~11/10, 27/25~12/11) = (209.7786c, 174.0549c, 146.6352c) TE
@@ Line 270: / Line 270: @@
 m = s -> sLLsLsLsLLsL Meanpop[12]; L = m -> sLLsLLLsLLsL MODMOS; s = 0 -> LLLsLLLL
-=====[[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12] (Luyoyo)]]=====
+=====[[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12] (No-7 Ptolemismic)]]=====
 L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54) = (146.6352c, 63.1434c, 27.4197c) TE
@@ Line 310: / Line 310: @@
 m = s -> sssLsssssLsssLsssssLsssssLsssLsssssLsss Hemiamity[39] MODMOS; L = m -> sLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLs; s = 0 -> sLssLsLssLssLsLssLs
-==2.3.5; Hemifamity==
+==2.3.5; [[Hemifamity family#Hemifamity|Hemifamity]] ==
 ===((2/1, 3/2)[5], 10/9)===
 ====[[SNS ((2/1, 3/2)-5, 10/9)-10|((2/1, 3/2)[5], 10/9)[10]]]====
@@ Line 320: / Line 320: @@
 s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8]
-====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-17|((2/1, 3/2)[5], 10/9: 5120/5103)[17] (Hemefamity)]]====
+====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-17|((2/1, 3/2)[5], 10/9: 5120/5103)[17] (Hemifamity)]]====
 L 2m 10s = (~35/32, 256/243~21/20, 81/80~64/63) = (153.2376c, 85.8342c, 24.4931c) TE
@@ Line 360: / Line 360: @@
 s = 0 -> LsLLLsL Arnold[7]; m = 0 -> ssLssssssLssssLssssLssssssLss
-===((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63)===
+===((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63) ===
 ====[[SNS ((2/1, 3/2)-12, 64/63: 5120/5103)-24|((2/1, 3/2)[12], 64/63: 5120/5013)[24] (Hemifamity)]]====
 L 7M 12s = (~135/128, ~28/27, 81/80~64/63) = (95.2825c, 61.3411c, 24.4931c) TE
@@ Line 389: / Line 389: @@
 s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS
-==2.5.9; Marvel==
+==2.5.9; Marvel ==
-===((2/1, 5/4)[3], 9/8)===
+=== ((2/1, 5/4)[3], 9/8)===
 ====[[SNS ((2/1, 5/4)-3, 9/8)-6|((2/1, 5/4)[3], 9/8)[6]]]====
 L 3M 2s = (256/225, 9/8, 10/9)
@@ Line 483: / Line 483: @@
 m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL
-==2.3.7; Orwellian==
+==2.3.7; [[Orwellismic family#Orwellismic|Orwellismic]]==
 ===(2/1, 3/2, 7/6)===
 ====[[SNS (2/1, 3/2, 7/6)-4|(2/1, 3/2, 7/6)[4]]]====
@@ Line 497: / Line 497: @@
 L = M -> LsLLLsL Archy[5]; s = 0 -> LLsLL Semaphore[5]
-=====[[SNS (2/1, 3/2, 7/6: 1728/1715)-7|(2/1, 3/2, 7/6: 1728/1715)[7] (Orwellian)]]=====
+=====[[SNS (2/1, 3/2, 7/6: 1728/1715)-7|(2/1, 3/2, 7/6: 1728/1715)[7] (Orwellismic)]]=====
 L 1M 2s = (~8/7, ~9/8, 49/48~36/35) = (227.1393c, 204.1935c, 43.334c) TE
@@ Line 503: / Line 503: @@
 L = M -> LsLLLsL Superpyth[5]; s = 0 -> LLsLL Beep[5]
-====[[SNS (2/1, 3/2, 7/6: 1728/1715)-12|(2/1, 3/2, 7/6: 1728/1715)[12] (Orwellian)]]====
+====[[SNS (2/1, 3/2, 7/6: 1728/1715)-12|(2/1, 3/2, 7/6: 1728/1715)[12] (Orwellismic)]]====
 L 1M 7s = (~10/9, 54/49~35/32, 49/48~36/35) = (183.8053c, 160.8595c, 43.334c) TE
@@ Line 521: / Line 521: @@
 L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS
-====[[SNS (2/1, 3/2, 7/6: 1728/1715)-17|(2/1, 3/2, 7/6: 1728/1715)[17] (Orwellian)]]====
+====[[SNS (2/1, 3/2, 7/6: 1728/1715)-17|(2/1, 3/2, 7/6: 1728/1715)[17] (Orwellismic)]]====
 L 1M 12s = (~160/147, ~15/14, 49/48~36/35) = (140.4713c, 117.5255c, 43.334c) TE
@@ Line 539: / Line 539: @@
 L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs
-====[[SNS (2/1, 3/2, 7/6: 1728/1715)-22|(2/1, 3/2, 7/6: 1728/1715)[22] (Orwellian)]]====
+====[[SNS (2/1, 3/2, 7/6: 1728/1715)-22|(2/1, 3/2, 7/6: 1728/1715)[22] (Orwellismic)]]====
 L 1m 17s = (~200/189, ~25/24, 49/48~36/35) = (97.1373c, 74.1915c, 43.334c) TE
@@ Line 557: / Line 557: @@
 m = s -> ssLssssLsssssssLssssLs Fleetwood[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]
-====[[SNS (2/1, 3/2, 7/6: 1728/1715)-27|(2/1, 3/2, 7/6: 1728/1715)[27] (Orwellian)]]====
+====[[SNS (2/1, 3/2, 7/6: 1728/1715)-27|(2/1, 3/2, 7/6: 1728/1715)[27] (Orwellismic)]]====
 L 22M 1s = (~250/243, 49/48~36/35, ~50/49) = (53.8033c, 43.334c, 30.8575c) TE
@@ Line 581: / Line 581: @@
 s = 0 -> ssLsssssLssssssssLsssssLss Fleetwood[26] MODMOS
-====[[SNS (2/1, 3/2, 7/6: 1728/1715)-53|(2/1, 3/2, 7/6: 1728/1715)[53] (Orwellian)]]====
+====[[SNS (2/1, 3/2, 7/6: 1728/1715)-53|(2/1, 3/2, 7/6: 1728/1715)[53] (Orwellismic)]]====
 L 4M 22s = (~50/49, 64/63~245/243, 126/125~2401/2400) = (30.8575c, 22.9458c, 12.4765c) TE