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

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{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro|Other Names=saturnian}}  
{{MOS intro|Other Names=saturnian}}  
Due to its minor third generator, this scale contains 2 diminished triads. [[Basic]] saturnian is in [[7edf]], an approximation of [[12edo]], which allows for playing regular music and saturnian music at the same time. 2L 3s⟨3/2⟩ is a parent of the 3/2-repeating [[macrodiatonic and microdiatonic scales|microdiatonic scale]], [[5L 2s (3/2-equivalent)|5L 2s⟨3/2⟩]].
The name ''saturnian'' was coined by [[User:CompactStar|CompactStar]], referring to this MOS being the sister MOS of [[3L 2s (3/2-equivalent)|uranian]].


== Notation ==
This scale contains 2 diminished triads represented by stacks of the minor third generator. [[Basic]] saturnian is in [[7edf]], a very close approximation of [[12edo]], which allows for playing diatonic music and saturnian music at the same time.  2L&nbsp;3s⟨3/2⟩ is the parent of the 3/2-repeating [[macrodiatonic and microdiatonic scales|microdiatonic scale]] ({{mos scalesig|5L 2s<3/1>|link=1}}), and the sister of {{mos scalesig|3L 2s<3/1>|link=1}} (uranian) which is generated by a subminor third rather than a minor third.  
The main way of notating the saturnian scale is using a 3/2-repeating notation consisting of 5 naturals (e.g. A-E for the 2|2 mode).
 
== Scale characteristics ==


=== Intervals ===
=== Intervals ===
{{MOS degrees|Step Ratio=2/1; 3/1; 3/2|Notation=ABCDE;#;b}}
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}


=== Genchain ===
{|class="wikitable"
|-
| -4
| -3
| -2
| -1
|0
|1
|2
|3
|4
|-
|d2ms
|m4ms
|m1ms
|P3ms
|P0ms
|P2ms
|M4ms
|M1ms
|A3ms
|}
== Theory ==
== Theory ==
2L 3s&lang;3/2&rang; can be interpreted as the [[nonoctave]] [[regular temperament]] named [[subgroup temperaments#pythium|pythium]] by [[User:CompactStar]], tempering out [[81/80]] in the 3/2.4.5 subgroup. This is the simplest 3/2-equivalent temperament not containing octaves. Because the 3/2-reduced 5th harmonic of [[40/27]] is conflated with the just perfect fifth, the CTE generator of this temperament is exactly the [[32/27]] Pythagorean minor third. Although the most accurate tunings use near-32/27 generators, pythium can be tuned with minor thirds as sharp as that of [[11edf]]'s (319 cents). The best extension of pythium to the 3/2.4.5.7 subgroup adds [[64/63]] to the comma list, making the CTE generator slightly flatter than 32/27, near [[22edf]]'s minor third of 287 cents.
=== Temperament interpretations ===
From a [[half-prime subgroup]] point of view, 2L 3s⟨3/2⟩ can be interpreted as the [[Sirius B]] [[temperament]] in the 3/2.5/2.7/2 [[subgroup]], where the generator is represented by the minor third ~[[25/21]] and 2 of them make ~[[7/5]]. It may also be interpreted as [[meanquad]] temperament using a period of [[3/2]] rather than [[4/1]], where the generator is represented by [[32/27]]~[[6/5]] (in the [[CTE tuning]], it is exactly 32/27). Both temperaments have very similar generators.


== Modes ==
== Modes ==
The mode names are based on the 5 largest satellites of Saturn.
The mode names were coined by [[User:CompactStar|CompactStar]], based on the 6 largest satellites of Saturn, excluding Titan since the "Titanian" name has been used for the [[3L 2s (3/2-equivalent)|uranian scale]].
{{MOS modes|Mode Names=Titanean; Rhean; Iapetian; Dionian; Tethyian}}
{{MOS modes|Mode Names=Rhean$ Iapetian$ Dionian$ Tethyian$ Enceladean$}}


== Scale tree ==
== Scale tree ==
{{Scale tree|Comments=8/5:Near-just 32/27, pythium is in this region;2/1:Augmented 8-mosdegree is nearly an octave;1/0:Degenerate scale with only 2 tones}}
{{MOS tuning spectrum
| 11/7 = [[CTE tuning]] for Sirius B temperament (293.825{{c}})
| 8/5 = Just 32/27 (294.135{{c}})
}}
 
[[Category:Nonoctave]]
[[Category:5-tone scales]]
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