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

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{{Infobox MOS
{{Infobox MOS}}
| Name = Uranian
'''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).  
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|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):
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|  -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
|}
|}


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== 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
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[[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
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[[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
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[[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==
Line 1,172: Line 1,164:
|0
|0
|→ inf
|→ inf
|Paucitonic
|Collapsed
|}
|}
[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:5-tone scales]]
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