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

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{{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]]). It is a [[Warped diatonic|warped diatonic scale]] because it has one extra small step compared to diatonic ([[3L 1s (fifth-equivalent)]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.  


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 52: Line 44:
110.835
110.835
|2\11
|2\11
[[Tel:127.6282|127.6282]]
127.6282
|3\14
|3\14
[[Tel:150.4189|150.4189]]
150.4189
|-
|-
|Bb
|Bb
|Βb
|Βb
|3\18
|3\18
[[Tel:116.9925|116.9925]]
116.9925
|2\13
|2\13
[[Tel:107.9931|107.9931]]
107.9931
|3\21
|3\21
[[Tel:100.2793|100.2793]]
100.2793
|2\19
|2\19
73.89
73.89
Line 76: Line 68:
155.99
155.99
|3\13
|3\13
[[Tel:161.9896|161.9896]]
161.9896
|5\21
|5\21
[[Tel:167.1321|167.1321]]
167.1321
|2\8
|2\8
175.48875
175.48875
Line 84: Line 76:
184.725
184.725
|3\11
|3\11
[[Tel:191.4423|191.4423]]
191.4423
|4\14
|4\14
[[Tel:200.5586|200.5586]]
200.5586
|-
|-
|B#
|B#
|Β#
|Β#
|5\18
|5\18
[[Tel:194.9875|194.9875]]
194.9875
| rowspan="2" |4\13
| rowspan="2" |4\13
[[Tel:215.9862|215.9862]]
215.9862
|7\21
|7\21
[[Tel:233.9851|233.9851]]
233.985
|3\8
|3\8
[[Tel:263.2331|263.2331]]
263.2331
|8\19
|8\19
295.56
295.56
Line 103: Line 95:
319.07045
319.07045
|7\14
|7\14
[[Tel:350.9775|350.9775]]
350.9775
|-
|-
|Cb
|Cb
Line 110: Line 102:
233.985
233.985
|6\21
|6\21
[[Tel:200.5586|200.5586]]
200.5586
|2\8
|2\8
175.48875
175.48875
Line 116: Line 108:
147.78
147.78
|2\11
|2\11
[[Tel:127.6282|127.6282]]
127.6282
|2\14
|2\14
[[Tel:100.2793|100.2793]]
100.2793
|-
|-
|'''C'''
|'''C'''
|'''Γ'''
|'''Γ'''
|'''7\18'''
|'''7\18'''
'''[[Tel:272.9825|272.9825]]'''
'''272.9825'''
|'''5\13'''
|'''5\13'''
'''[[Tel:269.9829|269.9829]]'''
'''269.9829'''
|'''8\21'''
|'''8\21'''
'''[[Tel:267.4114|267.4114]]'''
'''267.4114'''
|'''3\8'''
|'''3\8'''
'''[[Tel:263.2331|263.2331]]'''
'''263.2331'''
|'''7\19'''
|'''7\19'''
'''258.615'''
'''258.615'''
|'''4\11'''
|'''4\11'''
'''[[Tel:255.2564|255.2564]]'''
'''255.2564'''
|'''5\14'''
|'''5\14'''
'''[[Tel:250.6982|250.6982]]'''
'''250.6982'''
|-
|-
|C#
|C#
Line 142: Line 134:
311.98
311.98
|6\13
|6\13
[[Tel:323.9792|323.9792]]
323.9792
|10\21
|10\21
[[Tel:334.2643|334.2643]]
334.2643
| rowspan="2" |4\8
| rowspan="2" |4\8
[[Tel:350.9775|350.9775]]
350.9775
|9\19
|9\19
332.505
332.505
Line 152: Line 144:
382.88455
382.88455
|8\14
|8\14
[[Tel:401.1171|401.1171]]
401.1171
|-
|-
|Db
|Db
Line 159: Line 151:
389.975
389.975
|7\13
|7\13
[[Tel:377.9758|377.9758]]
377.9758
|11\21
|11\21
[[Tel:367.9607|367.9607]]
367.9607
|10\19
|10\19


Line 168: Line 160:
319.07045
319.07045
|6\14
|6\14
[[Tel:300.8379|300.8379]]
300.8379
|-
|-
|'''D'''
|'''D'''
|'''Δ'''
|'''Δ'''
|'''11\18'''
|'''11\18'''
'''[[Tel:428.9725|428.9725]]'''
'''428.9725'''
|'''8\13'''
|'''8\13'''
'''[[Tel:431.9723|431.9723]]'''
'''431.9723'''
|'''13\21'''
|'''13\21'''
'''[[Tel:434.5436|434.5436]]'''
'''434.5436'''
|'''5\8'''
|'''5\8'''
'''[[Tel:438.7219|438.7219]]'''
'''438.7219'''
|'''12\19'''
|'''12\19'''
'''470.285'''
'''470.285'''
|'''7\11'''
|'''7\11'''
'''[[Tel:446.6986|446.6986]]'''
'''446.6986'''
|'''9\14'''
|'''9\14'''
'''[[Tel:451.2568|451.2568]]'''
'''451.2568'''
|-
|-
|D#
|D#
Line 192: Line 184:
467.97
467.97
|9\13
|9\13
[[Tel:485.9688|485.9688]]
485.9688
|15\21
|15\21
[[Tel:501.3964|501.3964]]
501.3964
| rowspan="2" |6\8
| rowspan="2" |6\8
526.46625
526.46625
Line 200: Line 192:
554.175
554.175
|9\11
|9\11
[[Tel:574.3268|574.3268]]
574.3268
|12\14
|12\14
[[Tel:601.6757|601.6757]]
601.6757
|-
|-
|Eb
|Eb
Line 209: Line 201:
545.965
545.965
|10\13
|10\13
[[Tel:539.9653|539.9653]]
539.9653
|16\21
|16\21
[[Tel:534.8229|534.8229]]
534.8229
|14\19
|14\19
516.23
516.23
|8\11
|8\11
[[Tel:510.5128|510.5128]]
510.5128
|10\14
|10\14
[[Tel:501.3964|501.3964]]
501.3964
|-
|-
|E
|E
|Ε
|Ε
|15\18
|15\18
[[Tel:584.9625|584.9625]]
584.9625
|11\13
|11\13
[[Tel:593.9619|593.9619]]
593.9619
|18\21
|18\21
[[Tel:601.6757|601.6757]]
601.6757
|7\8
|7\8
[[Tel:614.2106|614.2106]]
614.2106
|17\19
|17\19
628.065
628.065
|10\11
|10\11
[[Tel:638.1409|638.1409]]
638.1409
|13\14
|13\14
[[Tel:651.8154|651.8154]]
651.8154
|-
|-
|E#
|E#
Line 241: Line 233:
622.96
622.96
| rowspan="2" |12\13
| rowspan="2" |12\13
[[Tel:646.9585|646.9585]]
646.9585
|20\21
|20\21
[[Tel:668.5286|668.5286]]
668.5286
|8\8
|8\8
701.955
701.955
Line 251: Line 243:
765.769
765.769
|16\14
|16\14
[[Tel:802.2343|802.2343]]
802.2343
|-
|-
|Ab
|Ab
|Ϛb/Ϝb
|Ϛb/Ϝb
|17\18
|17\18
[[Tel:662.9575|662.9575]]
662.9575
|19\21
|19\21
[[Tel:635.1021|635.1021]]
635.1021
|7\8
|7\8
[[Tel:614.2106|614.2106]]
614.2106
|16\19
|16\19
591.12
591.12
|9\11
|9\11
[[Tel:574.3268|574.3268]]
574.3268
|11\14
|11\14
551.636
551.636
Line 275: Line 267:
|Ϛ#/Ϝ#
|Ϛ#/Ϝ#
|19\18
|19\18
[[Tel:740.9525|740.9525]]
740.9525
|14\13
|14\13
[[Tel:754.9515|754.9515]]
754.9515
|23\21
|23\21
[[Tel:768.8021|768.8021]]
768.8021
| rowspan="2" |9\8
| rowspan="2" |9\8
[[Tel:789.6994|789.6994]]
789.6994
|22\19
|22\19
812.79
812.79
|13\11
|13\11
[[Tel:829.5832|829.5832]]
829.5832
|17\14
|17\14
[[Tel:852.3739|852.3739]]
852.3739
|-
|-
|Bb
|Bb
|Ζb
|Ζb
|21\18
|21\18
[[Tel:818.9475|818.9475]]
818.9475
|15\13
|15\13
[[Tel:809.9481|809.9481]]
809.9481
|24\21
|24\21
[[Tel:802.2343|802.2343]]
802.2343
|21\19
|21\19
775.845
775.845
Line 302: Line 294:
765.769
765.769
|15\14
|15\14
[[Tel:752.0946|752.0946]]
752.0946
|-
|-
|B
|B
Line 309: Line 301:
857.945
857.945
|16\13
|16\13
[[Tel:862.9446|862.9446]]
862.9446
|26\21
|26\21
[[Tel:868.0871|868.0871]]
868.0871
|10\8
|10\8
877.44375
877.44375
Line 317: Line 309:
886.68
886.68
|14\11
|14\11
[[Tel:893.3973|893.3973]]
893.3973
|18\14
|18\14
[[Tel:902.5136|902.5136]]
902.5136
|-
|-
|B#
|B#
|Ζ#
|Ζ#
|23\18
|23\18
[[Tel:896.9425|896.9425]]
896.9425
| rowspan="2" |17\13
| rowspan="2" |17\13
[[Tel:917.9412|917.9412]]
917.9412
|28\21
|28\21
[[Tel:935.9406|935.9406]]
935.9406
|11\8
|11\8
[[Tel:965.1881|965.1881]]
965.1881
|27\19
|27\19
997.515
997.515
Line 343: Line 335:
935.94
935.94
|27\21
|27\21
[[Tel:902.3156|902.3156]]
902.5136
|10\8
|10\8
877.44375
877.44375
Line 349: Line 341:
849.753
849.753
|13\11
|13\11
[[Tel:829.5832|829.5832]]
829.5832
|16\14
|16\14
[[Tel:802.2343|802.2343]]
802.2343
|-
|-
|'''C'''
|'''C'''
|'''Η'''
|'''Η'''
|'''25\18'''
|'''25\18'''
'''[[Tel:974.9375|974.9375]]'''
'''974.9375'''
|'''18\13'''
|'''18\13'''
'''[[Tel:971.9379|971.9379]]'''
'''971.9379'''
|'''29\21'''
|'''29\21'''
'''[[Tel:969.3664|969.3664]]'''
'''969.3664'''
|'''11\8'''
|'''11\8'''  
'''[[Tel:965.1881|965.1881]]'''
'''965.1881'''
|'''26\19'''
|'''26\19'''
'''960.57'''
'''960.57'''
|'''15\11'''
|'''15\11'''
'''[[Tel:957.2114|957.2114]]'''
'''957.2114'''
|'''19\14'''
|'''19\14'''
'''[[Tel:952.6532|952.6532]]'''
'''952.6532'''
|-
|-
|C#
|C#
Line 525: Line 517:
|1
|1
|C
|C
|perfect mosthird (min third)
|perfect 2-mosstep (min third)
| -1
| -1
|D
|D
|perfect mosfourth (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):
Line 558: Line 550:
|  -5
|  -5
|A#
|A#
|augmented unison (chroma)
|augmented 0-mosstep (chroma)
|-
|-
|6
|6
|Cb
|Cb
|diminished mosthird
|diminished 2-mosstep
|  -6
|  -6
|D#
|D#
|augmented mosfourth
|augmented 3-mosstep
|-
|-
|7
|7
|Ebb
|Ebb
|diminished mosfifth
|diminished 4-mosstep
|  -7
|  -7
|B#
|B#
|augmented mossecond
|augmented 1-mosstep
|}
|}


Line 673: 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 679: Line 671:
[[Comma]] list: [[245/243]]
[[Comma]] list: [[245/243]]


[[POL2]] generator: ~7/6 = [[Tel:262.1728|262.1728]]
[[POL2]] generator: ~7/6 = 262.1728


[[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 689: Line 681:
[[Comma]] list: [[245/243]], [[100/99]]
[[Comma]] list: [[245/243]], [[100/99]]


[[POL2]] generator: ~7/6 = [[Tel:264.3771|264.3771]]
[[POL2]] generator: ~7/6 = 264.3771


[[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 699: Line 691:
[[Comma]] list: [[245/243]], [[441/440]]
[[Comma]] list: [[245/243]], [[441/440]]


[[POL2]] generator: ~7/6 = [[Tel:261.5939|261.5939]]
[[POL2]] generator: ~7/6 = 261.5939


[[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 720: Line 712:
|-
|-
|3\5
|3\5
|
|
|
|
|
|
Line 730: Line 724:
|Equalised
|Equalised
|-
|-
|11\18
|
|
|
|
|
|
|
|
|11\18
|428.973
|428.973
|272.983
|272.983
Line 742: 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
|
|
|
|
|
|
|431.972
|431.972
Line 754: Line 778:
|
|
|
|
|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 764: 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
|
|
|
|
|
|
|
Line 776: 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 1,023:
|
|
|-
|-
|
|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 798: Line 1,064:
|
|
|
|
|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
|
|
|
|
|
|451.257
|451.257
|250.698
|250.698
Line 808: Line 1,154:
|-
|-
|2\3
|2\3
|
|
|
|
|
|
Line 816: 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)"