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

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 | 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>]].  There is a "trivial" neptunian scale in every EDF > 4 with L/s = (n-3)/1 but these are generally unusable for larger EDFs due to becoming extremely lopsided.
+{{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 ==
-Due to being a tetratonic scale, neptunian interval classes often line up with diatonic intervals so it can be notated using similar notation.
+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"
-* 2|1 sLss "protean"
-* 1|2 ssLs "nereidian"
-* 0|3 sssL "larissan"
-== Scale tree ==
+== Scale properties ==
-{| class="wikitable"
+{{TAMNAMS use}}
-|-
-!Generator (chroma-positive)
+=== Intervals ===
-!Cents (chroma-positive)
+{{MOS intervals}}
-!L
-!s
+=== Generator chain ===
-!L/s
+{{MOS genchain}}
-|-
-|3\[[4edf]]
+=== Modes ===
-|526.5
+{{MOS mode degrees}}
-|1
-|1
+=== Mode names ===
-|1.0000
+{{MOS modes
-|-
+| Mode Names=
-|10\[[13edf]]
+Tritonian $
-|540.0
+Protean $
-|4
+Nereidian $
-|3
+Larissan $
-|1.3333
+}}
-|-
-|7\[[9edf]]
+== Scale tree ==
-|546.0
+{{MOS tuning spectrum
-|3
+| 3/2 = Poseidon and Auk are around here
-|2
+| 5/2 = Halftone (incomplete)
-|1.5000
+}}
-|-
-|11\[[14edf]]
+== Temperaments ==
-|551.5
+=== Poseidon ===
-|5
+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.
-|3
-|1.6667
+[[Subgroup]]: 3/2.5/4.11/8
-|-
-|4\[[5edf]]
+[[Comma list]]: 121/120
-|561.6
-|2
+[[Gencom]]: [3/2 12/11; 121/120]
-|1
-|2.0000
+[[POTE generator]]: ~[[12/11]] = 158.29
-|-
-|9\[[11edf]]
+[[Mapping]]: [{{val|1 1 1}}, {{val|0 2 -1}}]
-|574.3
-|5
+[[Support]]ing [[EDF]]s: 9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49
-|2
-|2.5000
+=== Auk ===
-|-
+''Main article: [[Auk]]''
-|5\[[6edf]]
-|585.0
+[[Subgroup]]: 3/2.7.13
-|3
-|1
+[[Comma list]]: 87808/85293
-|3.0000
-|-
+[[CTE tuning|CTE generator]]: ~28/9 = 1950.859
-|6\[[7edf]]
-|601.7
+[[Mapping]]: [{{val|1 2 -2}}, {{val|0 1 3}}]
-|4
-|1
+[[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]
-|4.0000
-|}
+=== 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