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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]]).  


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
!Annapolis[6L 4s]
!Annapolis
!18edf
!18edf
!13edf
!13edf
Line 39: Line 31:
!14edf
!14edf
|-
|-
! colspan="2" |A#
|A#
|Α#
|1\18
|1\18
38.9975
38.9975
Line 55: Line 48:
150.4189
150.4189
|-
|-
! colspan="2" |Bb
|Bb
|Βb
|3\18
|3\18
116.9925
116.9925
Line 69: Line 63:
50.1396
50.1396
|-
|-
! colspan="2" |B
|B
|Β
|4\18
|4\18
155.99
155.99
Line 85: Line 80:
200.5586
200.5586
|-
|-
! colspan="2" |B#
|B#
|Β#
|5\18
|5\18
194.9875
194.9875
Line 91: Line 87:
215.9862
215.9862
|7\21
|7\21
233.9851
233.985
|3\8
|3\8
263.2331
263.2331
Line 339: Line 335:
935.94
935.94
|27\21
|27\21
902.3156
902.5136
|10\8
|10\8
877.44375
877.44375
Line 357: Line 353:
|'''29\21'''
|'''29\21'''
'''969.3664'''
'''969.3664'''
|'''11\8'''
|'''11\8'''  
'''965.1881'''
'''965.1881'''
|'''26\19'''
|'''26\19'''
Line 433: Line 429:
|-
|-
|Eb
|Eb
|Ιb (Jb)
|Ιb
|32\18
|32\18
1247.92
1247.92
Line 448: Line 444:
|-
|-
|E
|E
|I (J)
|Ι
|33\18
|33\18
1286.9175
1286.9175
Line 465: Line 461:
|-
|-
|E#
|E#
|Ι# (J#)
|Ι#
|34\18
|34\18
1323.915
1323.915
Line 496: Line 492:
1253.591
1253.591
|-
|-
! colspan="2" |A
!A
!Α
! colspan="7" |1403.91
! colspan="7" |1403.91
|}
|}
Line 520: 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 553: 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 668: 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 678: 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 688: 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 698: 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 715: Line 712:
|-
|-
|3\5
|3\5
|
|
|
|
|
|
Line 725: Line 724:
|Equalised
|Equalised
|-
|-
|11\18
|
|
|
|
|
|
|
|
|11\18
|428.973
|428.973
|272.983
|272.983
Line 736: Line 737:
|
|
|-
|-
|
|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 748: 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 759: 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 771: 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 780: 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 793: 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 803: Line 1,154:
|-
|-
|2\3
|2\3
|
|
|
|
|
|
Line 811: 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)"