Xenharmonic Wiki

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

← Older edit
VisualWikitext
CompactStar (talk | contribs)
5,020 edits
No edit summary
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
 
(27 intermediate revisions by 5 users not shown)
Line 7: Line 7:
| 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.
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=
|13\[[17edf]]
Tritonian $
|536.8
Protean $
|5
Nereidian $
|4
Larissan $
|1.2500
}}
|-
 
|10\[[13edf]]
== Scale tree ==
|540.0
{{MOS tuning spectrum
|4
| 3/2 = Poseidon and Auk are around here
|3
| 5/2 = Halftone (incomplete)
|1.3333
}}
|-
 
|7\[[9edf]]
== Temperaments ==
|546.0
=== Poseidon ===
|3
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.
|2
 
|1.5000
[[Subgroup]]: 3/2.5/4.11/8
|-
 
|11\[[14edf]]
[[Comma list]]: 121/120
|551.5
 
|5
[[Gencom]]: [3/2 12/11; 121/120]
|3
 
|1.6667
[[POTE generator]]: ~[[12/11]] = 158.29
|-
 
|15\[[19edf]]
[[Mapping]]: [{{val|1 1 1}}, {{val|0 2 -1}}]
|554.2
 
|7
[[Support]]ing [[EDF]]s: 9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49
|4
 
|1.7500
=== Auk ===
|-
''Main article: [[Auk]]''
|4\[[5edf]]
 
|561.6
[[Subgroup]]: 3/2.7.13
|2
 
|1
[[Comma list]]: 87808/85293
|2.0000
 
|-
[[CTE tuning|CTE generator]]: ~28/9 = 1950.859
|9\[[11edf]]
 
|574.3
[[Mapping]]: [{{val|1 2 -2}}, {{val|0 1 3}}]
|5
 
|2
[[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]
|2.5000
 
|-
=== Halftone ===
|5\[[6edf]]
''Main article: [[Halftone]]''
|585.0
 
|3
[[Subgroup]]: 3/2.5/2.7/2
|1
 
|3.0000
[[Comma list]]: 9604/9375
|-
 
|6\[[7edf]]
{{Mapping|legend=2| 1 3 4 | 0 -4 -5 }}
|601.7
 
|4
: sval mapping generators: ~3/2, ~15/14
|1
 
|4.0000
[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 128.783
|-
 
|7\[[8edf]]
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
|614.2
 
|5
<nowiki />* Wart for 3/2
|1
|5.0000
|-
|1\[[1edf]]
|702.0
|1
|0
| -> inf
|}
Retrieved from "https://en.xen.wiki/w/1L_3s_(3/2-equivalent)"