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3L 2s (3/2-equivalent): Difference between revisions

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Line 1: Line 1:
{{Infobox MOS
{{Infobox MOS}}
| Name =
'''3L 2s<span class="Unicode">&lang;</span>3/2<span class="Unicode">&rang;</span>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<span class="Unicode">&lang;</span>3/2<span class="Unicode">&rang;</span>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version of diatonic ([[3L 1s (3/2-equivalent)|3L 1s<span class="Unicode">&lang;</span>3/2<span class="Unicode">&rang;</span>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.  
| Equave = 3/2
| nLargeSteps = 3
| nSmallSteps = 2
| Equalized = 2
| Paucitonic = 1
| Pattern = LLsLs
}}
'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]).  


The generator range is 234 to 280.8 cents, placing it in between the [[9/8|diatonic major second]] and the [[6/5|diatonic minor third]], usually representing a subminor third of some type (like [[7/6]]). The bright (chroma-positive) generator is, however, its fifth complement (468 to 421.2 cents).  
The generator range is 234 to 280.8 cents, placing it in between the [[9/8|diatonic major second]] and the [[6/5|diatonic minor third]], usually representing a subminor third of some type (like [[7/6]]). The bright (chroma-positive) generator is, however, its fifth complement (468 to 421.2 cents).  
Line 29: Line 21:
!Superhard
!Superhard
|-
|-
!Sesq
!Uranian
!D-Sesq
!Annapolis
!18edf
!18edf
!13edf
!13edf
Line 92: Line 84:
|5\18
|5\18
194.9875
194.9875
|4\13
| rowspan="2" |4\13
215.9862
215.9862
|7\21
|7\21
233.985
233.985
! rowspan="2" |'''3\8'''
|3\8
'''263.2331'''
263.2331
|8\19
|8\19
295.56
295.56
Line 105: Line 97:
350.9775
350.9775
|-
|-
!Cb
|Cb
!Γb
|Γb
!7\18
|6\18
272.9825
233.985
!5\13
|6\21
269.9829
200.5586
!8\21
|2\8
267.4114
175.48875
!7\19
|4\19
258.615
147.78
!4\11
|2\11
255.2564
127.6282
!5\14
|2\14
250.6982
100.2793
|-
|-
|C
|'''C'''
|Γ
|'''Γ'''
|'''7\18'''
'''272.9825'''
|'''5\13'''
'''269.9829'''
|'''8\21'''
'''267.4114'''
|'''3\8'''
'''263.2331'''
|'''7\19'''
'''258.615'''
|'''4\11'''
'''255.2564'''
|'''5\14'''
'''250.6982'''
|-
|C#
|Γ#
|8\18
|8\18
311.98
311.98
Line 128: Line 137:
|10\21
|10\21
334.2643
334.2643
|4\8
| rowspan="2" |4\8
350.9775
350.9775
|10\19
|9\19
369.45
332.505
|6\11
|6\11
382.88455
382.88455
|8\14
|8\14
401.1171
401.1171
|-
|C#
|Γ#
|9\18
350.9775
| rowspan="2" |7\13
377.9758
|12\21
401.1171
|5\8
438.7219
|13\19
470.285
|8\11
510.5128
|11\14
551.536
|-
|-
|Db
|Db
Line 158: Line 150:
|10\18
|10\18
389.975
389.975
|7\13
377.9758
|11\21
|11\21
367.9607
367.9607
|4\8
|10\19
350.9775
 
|9\19
369.45
332.505
|5\11
|5\11
319.07045
319.07045
Line 169: Line 162:
300.8379
300.8379
|-
|-
|D
|'''D'''
|Δ
|'''Δ'''
|11\18
|'''11\18'''
428.9725
'''428.9725'''
|8\13
|'''8\13'''
431.9723
'''431.9723'''
|13\21
|'''13\21'''
434.5436
'''434.5436'''
|5\8
|'''5\8'''
438.7219
'''438.7219'''
|12\19
|'''12\19'''
443.34
'''470.285'''
|7\11
|'''7\11'''
446.6986
'''446.6986'''
|9\14
|'''9\14'''
451.2568
'''451.2568'''
|-
|-
|D#
|D#
Line 205: Line 198:
|Eb
|Eb
|Εb
|Εb
|13\18
|14\18
506.9675
545.965
|10\13
|10\13
539.9653
539.9653
Line 324: Line 317:
|23\18
|23\18
896.9425
896.9425
|17\13
| rowspan="2" |17\13
917.9412
917.9412
|28\21
|28\21
935.94
935.9406
! rowspan="2" |11\8
|11\8
965.1881
965.1881
|27\19
|27\19
Line 337: Line 330:
1052.9235
1052.9235
|-
|-
!Cb
|Cb
!Ηb
|Ηb
!25\18
|24\18
974.9375
935.94
!18\13
|27\21
971.9379
902.5136
!29\21
|10\8
969.3664
877.44375
!26\19
|23\19
960.57
849.753
!15\11
|13\11
957.2114
829.5832
!19\14
|16\14
952.6532
802.2343
|-
|-
|C
|'''C'''
|Η
|'''Η'''
|'''25\18'''
'''974.9375'''
|'''18\13'''
'''971.9379'''
|'''29\21'''
'''969.3664'''
|'''11\8'''
'''965.1881'''
|'''26\19'''
'''960.57'''
|'''15\11'''
'''957.2114'''
|'''19\14'''
'''952.6532'''
|-
|C#
|Η#
|26\18
|26\18
1012.935
1012.935
Line 360: Line 370:
|31\21
|31\21
1036.2193
1036.2193
|12\8
| rowspan="2" |12\8
1052.9235
1052.9235
|29\19
|29\19
Line 368: Line 378:
|22\14
|22\14
1103.0721
1103.0721
|-
|C#
|Η#
|27\18
1052.9325
| rowspan="2" |20\13
1079.9308
|33\21
1103.0721
|13\8
1140.7769
|32\19
1172.24
|19\11
1212.5678
|25\14
1253.4911
|-
|-
|Db
|Db
Line 390: Line 383:
|28\18
|28\18
1091.93
1091.93
|20\13
1079.9308
|32\21
|32\21
1069.9157
1069.9157
|12\8
1052.9235
|28\19
|28\19
1034.46
1034.46
Line 401: Line 394:
1002.7929
1002.7929
|-
|-
|D
|'''D'''
|Θ
|'''Θ'''
|29\18
|'''29\18'''
1130.9275
'''1130.9275'''
|21\13
|'''21\13'''
1133.9273
'''1133.9273'''
|34\21
|'''34\21'''
1136.4986
'''1136.4986'''
|13\8
|'''13\8'''
1140.7769
'''1140.7769'''
|31\19
|'''31\19'''
1145.295
'''1145.295'''
|18\11
|'''18\11'''
1148.6536
'''1148.6536'''
|23\14
|'''23\14'''
1153.2118
'''1153.2118'''
|-
|-
|D#
|D#
Line 437: Line 430:
|Eb
|Eb
|Ιb
|Ιb
|31\18
|32\18
1208.9225
1247.92
|23\13
|23\13
1241.9203
1241.9203
Line 524: Line 517:
|1
|1
|C
|C
|perfect mosthird (min third)
|perfect 2-mosstep (min third)
| -1
| -1
|D
|D
|perfect mos fourth (maj third)
|perfect 3-mosstep (maj third)
|-
|-
|2
|2
|Eb
|Eb
|minor mosfifth
|minor 4-mosstep
| -2
| -2
|B
|B
|major mossecond
|major 1-mosstep
|-
|-
|3
|3
|Bb
|Bb
|minor mossecond
|minor 1-mosstep
| -3
| -3
|E
|E
|major mosfifth
|major 4-mosstep
|-
|-
|4
|4
|Db
|Db
|diminished mosfourth
|diminished 3-mosstep
| -4
| -4
|C#
|C#
|augmented mosthird
|augmented 2-mosstep
|-
|-
| colspan="6" |The chromatic 8-note MOS also has the following intervals (from some root):
| colspan="6" |The chromatic 8-note MOS also has the following intervals (from some root):
|-
|-
|11
|5
|Ab
|Ab
|diminished sesquitave
|diminished sesquitave
| -11
| -5
|A#
|A#
|augmented unison (chroma)
|augmented 0-mosstep (chroma)
|-
|-
|12
|6
|Cb
|Cb
|diminished mosthird
|diminished 2-mosstep
| -12
| -6
|D#
|D#
|augmented mosfourth
|augmented 3-mosstep
|-
|-
|13
|7
|Ebb
|Ebb
|diminished mosfifth
|diminished 4-mosstep
| -13
| -7
|B#
|B#
|augmented mossecond
|augmented 1-mosstep
|}
|}


Line 607: Line 600:
|M2
|M2
|M5
|M5
|a3
|A3
|a1
|A1
|a4
|A4
|a2
|A2
|a5
|A5
|}
|}


Line 672: Line 665:


== Temperaments ==
== Temperaments ==
The most basic rank-2 temperament interpretation of uranian is '''semiwolf''', which has 4:7:10 chords spelled <code>root-(p+1g)-(3p-2g)</code> (p = 3/2, g = the approximate 7/6). The name "semiwolf" comes from two [[7/6]] generators approximating a [[27/20]] wolf fourth. This is further extended to the 11-limit in two interpretations: '''semilupine''' where 2 major mos2nds (LL) equal 11/9, and '''hemilycan''' where 1 major and 2 minor mos2nds (sLs) equal 11/9. Basic 8edf fits both extensions.
The most basic rank-2 temperament interpretation of uranian is '''semiwolf''', which has 4:7:10 chords spelled <code>root-(p+1g)-(3p-2g)</code> (p = 3/2, g = the approximate 7/6). The name "semiwolf" comes from two [[7/6]] generators approximating a [[27/20]] wolf fourth. This is further extended to the 11-limit in two interpretations: '''semilupine''' where 2 major 2-mossteps (LL) equal 11/9, and '''hemilycan''' where 1 major and 2 minor 2-mossteps (sLs) equal 11/9. Basic 8edf fits both extensions.
===Semiwolf===
===Semiwolf===
[[Subgroup]]: 3/2.7/4.5/2
[[Subgroup]]: 3/2.7/4.5/2
Line 682: Line 675:
[[Mapping]]: [{{val|1 1 3}}, {{val|0 1 -2}}]
[[Mapping]]: [{{val|1 1 3}}, {{val|0 1 -2}}]


[[Vals]]: {{val list|8edf, 11edf, 13edf}}
{{Optimal ET sequence|legend=1|8edf, 11edf, 13edf}}
====Semilupine====
====Semilupine====
[[Subgroup]]: 3/2.7/4.5/2.11/4
[[Subgroup]]: 3/2.7/4.5/2.11/4
Line 692: Line 685:
[[Mapping]]: [{{val|1 1 3 4}}, {{val|0 1 -2 -4}}]
[[Mapping]]: [{{val|1 1 3 4}}, {{val|0 1 -2 -4}}]


[[Vals]]: {{val list|8edf, 13edf}}
{{Optimal ET sequence|legend=1|8edf, 13edf}}
====Hemilycan====
====Hemilycan====
[[Subgroup]]: 3/2.7/4.5/2.11/4
[[Subgroup]]: 3/2.7/4.5/2.11/4
Line 702: Line 695:
[[Mapping]]: [{{val|1 1 3 1}}, {{val|0 1 -2 4}}]
[[Mapping]]: [{{val|1 1 3 1}}, {{val|0 1 -2 4}}]


[[Vals]]: {{val list|8edf, 11edf}}
{{Optimal ET sequence|legend=1|8edf, 11edf}}


== Scale tree==
== Scale tree==
The spectrum looks like this:
The spectrum looks like this:
{| class="wikitable"
{| class="wikitable"
! colspan="4" rowspan="2" |Generator
! colspan="6" rowspan="2" |Generator
(bright)
(bright)
! colspan="2" |Cents
! colspan="2" |Cents
Line 719: Line 712:
|-
|-
|3\5
|3\5
|
|
|
|
|
|
Line 729: Line 724:
|Equalised
|Equalised
|-
|-
|11\18
|
|
|
|
|
|
|11\18
|
|428.9725
|
|428.973
|272.983
|272.983
|4
|4
Line 741: Line 738:
|-
|-
|
|
|30\49
|
|
|
|
|429.768
|272.187
|11
|8
|1.375
|
|-
|
|19\31
|
|
|
|
|
|430.2305
|271.7255
|7
|5
|1.400
|
|-
|8\13
|8\13
|
|
|431.9723
|
|
|
|
|431.972
|269.983
|269.983
|3
|3
Line 752: Line 777:
|-
|-
|
|
|
|37\60
|
|
|
|432.872
|269.083
|14
|9
|1.556
|
|-
|
|29\47
|
|
|
|
|
|433.121
|268.834
|11
|7
|1.571
|
|-
|
|21\34
|
|
|
|
|433.56
|268.395
|8
|5
|1.600
|
|-
|
|
|34\55
|
|
|
|433.935
|268.02
|13
|8
|1.625
|
|-
|
|
|13\21
|13\21
|
|
|
|
|435.084
|435.084
|266.871
|266.871
Line 763: Line 842:
|-
|-
|
|
|18\29
|
|
|
|
|435.696
|266.259
|7
|4
|1.750
|
|-
|
|23\37
|
|
|
|
|436.35
|265.605
|9
|5
|1.800
|
|-
|
|28\45
|
|
|
|
|436.772
|265.183
|11
|6
|1.833
|
|-
|
|
|33\53
|
|
|
|437.066
|264.889
|13
|7
|1.857
|
|-
|5\8
|5\8
|
|
|
|
|438.7219
|
|
|
|438.722
|263.233
|263.233
|2
|2
Line 775: Line 908:
|
|
|
|
|
|
|
|47\75
|439.892
|262.063
|19
|9
|2.111
|
|-
|
|
|
|
|42\67
|
|440.031
|261.924
|17
|8
|2.125
|
|-
|
|
|
|37\59
|
|
|440.209
|261.746
|15
|7
|2.143
|
|-
|
|
|32\51
|
|
|
|440.442
|261.513
|13
|6
|2.167
|
|-
|
|27\43
|
|
|
|
|440.762
|261.193
|11
|5
|2.200
|
|-
|
|22\35
|
|
|
|
|441.229
|260.726
|9
|4
|2.250
|
|-
|
|17\27
|
|
|
|
|441.972
|259.973
|7
|3
|2.333
|
|-
|
|
|29\46
|
|
|
|442.537
|259.418
|12
|5
|2.400
|
|-
|
|
|12\19
|12\19
|
|
|
|
|443.34
|443.34
|258.615
|258.615
Line 785: Line 1,024:
|-
|-
|
|
|19\30
|
|
|
|
|444.5715
|257.3835
|8
|3
|2.667
|
|-
|
|26\41
|
|
|
|
|
|445.142
|256.813
|11
|4
|2.750
|
|-
|7\11
|7\11
|
|
|
|
|
|
|446.699
|446.699
Line 796: Line 1,063:
|-
|-
|
|
|
|37\58
|
|
|
|447.799
|254.156
|16
|5
|3.200
|
|-
|
|30\47
|
|
|
|
|
|
|448,056
|253.899
|13
|4
|3.250
|
|-
|
|23\36
|
|
|
|
|448.471
|253.484
|10
|3
|3.333
|
|-
|
|16\25
|
|
|
|
|449.251
|252.704
|7
|2
|3.500
|
|-
|
|25\39
|
|
|
|
|449.971
|251.984
|11
|3
|3.667
|
|-
|
|34\53
|
|
|
|
|450.311
|251.644
|15
|4
|3.750
|
|-
|9\14
|9\14
|451.2568
|
|250.6982
|
|
|
|
|451.257
|250.698
|4
|4
|1
|1
Line 807: Line 1,154:
|-
|-
|2\3
|2\3
|
|
|
|
|
|
Line 815: Line 1,164:
|0
|0
|→ inf
|→ inf
|Paucitonic
|Collapsed
|}
|}
[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:5-tone scales]]
Retrieved from "https://en.xen.wiki/w/3L_2s_(3/2-equivalent)"