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1L 3s (3/2-equivalent): Difference between revisions

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| Pattern = LLsLs
| Pattern = LLsLs
}}
}}
'''1L 3s<3/2>''' (or '''neptunian'''), is a fifth-repeating MOS scale with 1 large step and 3 small steps. The name "neptunian" was given by [[User:CompactStar|CompactStar]] in analogy to "uranian" name for [[3L 2s (fifth-equivalent)|3L 2s<3/2>]].
{{MOS intro}} The name "neptunian" was given by [[User:CompactStar|CompactStar]] in analogy to "uranian" name for {{mos scalesig|3L 2s<3/1>|link=1}}.


== Notation ==
== Notation ==
Due to being a tetratonic scale, neptunian interval classes often line up with diatonic interval classes (at least for L/s <u><</u> 2/1) so similar note names can be used. Although, one difference is that there are two types of fourth, a "minor fourth" which ranges from a supermajor third to a perfect fourth, and a "major fourth" which ranges from a perfect fourth to a tritone (or subfifth in extremely improper scales).
Due to being a tetratonic scale, neptunian interval classes often line up with diatonic interval classes (at least for {{nowrap|L/s &le; 2/1}}) so similar note names can be used. Although, one difference is that the "perfect fourth" can go up to a subfifth in the most extreme case.
== Modes ==
 
* 3|0 Lsss "tritonian"
== Scale properties ==
* 2|1 sLss "protean"
{{TAMNAMS use}}
* 1|2 ssLs "nereidian"
 
* 0|3 sssL "larissan"
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
=== Mode names ===
{{MOS modes
| Mode Names=
Tritonian $
Protean $
Nereidian $
Larissan $
}}
 
== Scale tree ==
{{MOS tuning spectrum
| 3/2 = Poseidon and Auk are around here
| 5/2 = Halftone (incomplete)
}}


== Scale tree ==
{| class="wikitable"
|-
!Generator (chroma-positive)
!Cents (chroma-positive)
!L
!s
!L/s
!Comments
|-
|3\[[4edf]]
|526.5
|1
|1
|1.0000
|
|-
|13\[[17edf]]
|536.8
|5
|4
|1.2500
|
|-
|10\[[13edf]]
|540.0
|4
|3
|1.3333
|
|-
|7\[[9edf]]
|546.0
|3
|2
|1.5000
|Poseidon is around here
|
|-
|11\[[14edf]]
|551.5
|5
|3
|1.6667
|
|-
|15\[[19edf]]
|554.2
|7
|4
|1.7500
|
|-
|4\[[5edf]]
|561.6
|2
|1
|2.0000
|
|-
|9\[[11edf]]
|574.3
|5
|2
|2.5000
|
|-
|5\[[6edf]]
|585.0
|3
|1
|3.0000
|
|-
|6\[[7edf]]
|601.7
|4
|1
|4.0000
|
|-
|7\[[8edf]]
|614.2
|5
|1
|5.0000
|
|-
|1\[[1edf]]
|702.0
|1
|0
| -> inf
|
|}
== Temperaments ==
== Temperaments ==
=== Poseidon ===
=== Poseidon ===
This temperament equates 2 [[11/8]] with [[5/4]]. It contains an 8:10:11 triad, which sounds quite similar to a major triad although with increased tension. [[9edf]] (and thus [[Carlos Alpha]]) is a good tuning for this temperament with its accurate 5/4 and 11/8.
This temperament equates two [[11/8]]<nowiki />s with [[5/4]]. It contains an 8:10:11 triad, which sounds quite similar to a major triad although with increased tension. [[9edf]] (and thus [[Carlos Alpha]]) is a good tuning for this temperament with its accurate 5/4 and 11/8.


[[Subgroup]]: 3/2.5/4.11/8
[[Subgroup]]: 3/2.5/4.11/8
Line 126: Line 53:
[[Mapping]]: [{{val|1 1 1}}, {{val|0 2 -1}}]
[[Mapping]]: [{{val|1 1 1}}, {{val|0 2 -1}}]


[[EDF]]s: 9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49
[[Support]]ing [[EDF]]s: 9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49


=== Auk ===
=== Auk ===
''Main article: [[Auk]]''
[[Subgroup]]: 3/2.7.13
[[Subgroup]]: 3/2.7.13


Line 137: Line 66:
[[Mapping]]: [{{val|1 2 -2}}, {{val|0 1 3}}]
[[Mapping]]: [{{val|1 2 -2}}, {{val|0 1 3}}]


[[Val]]s: 5, 9, 13, 14, 6[+13], 17[-7, -13], 7[-7, -13], 22[-7], 19[+13], 23[+13], 11[+13], 21[-7, -13], 31[-7], 25[-7, -13]
[[Support]]ing [[ET]]s: 5, 9, 13, 14, 6[+13], 17[-7, -13], 7[-7, -13], 22[-7], 19[+13], 23[+13], 11[+13], 21[-7, -13], 31[-7], 25[-7, -13]
 
=== Halftone ===
''Main article: [[Halftone]]''
 
[[Subgroup]]: 3/2.5/2.7/2
 
[[Comma list]]: 9604/9375
 
{{Mapping|legend=2| 1 3 4 | 0 -4 -5 }}
 
: sval mapping generators: ~3/2, ~15/14
 
[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 128.783
 
Supporting ETs: *5, *6, *7[+5/2, +7/2], *9[-5/2, --7/2], *11, *16, *17[+5/2], *23[+5/2, +7/2], *21[-7/2], *27, *28[+5/2], *38, *43[-7/2], *49
 
<nowiki />* Wart for 3/2
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