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

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Rework as well as the change of pythium -> meanquad
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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 the parent of the 3/2-repeating [[macrodiatonic and microdiatonic scales|microdiatonic scale]], [[5L 2s (3/2-equivalent)|5L 2s⟨3/2⟩]], and the sister of [[3L 2s (3/2-equivalent)|3L 2s⟨3/2⟩]] (uranian) which is generated by a subminor third rather than a minor third.
 
The name saturnian was coined by [[User:CompactStar|CompactStar]], referring to the sister MOS of [[3L 2s (3/2-equivalent)|uranian]].
 
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 3s⟨3/2⟩ is the parent of the 3/2-repeating [[macrodiatonic and microdiatonic scales|microdiatonic scale]], [[5L 2s (3/2-equivalent)|5L 2s⟨3/2⟩]], and the sister of [[3L 2s (3/2-equivalent)|3L 2s⟨3/2⟩]] (uranian) which is generated by a subminor third rather than a minor third.  


== Notation ==
== Notation ==
The main way of notating the saturnian scale is using a 3/2-repeating notation consisting of 5 naturals. The notation used in this article is J Dionian is the JKLMN.
The main way of notating the saturnian scale is using a 3/2-repeating notation consisting of 5 naturals. The notation used in this article is the [[diamond MOS notation]].


=== Intervals ===
=== Intervals ===
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== Theory ==
== Theory ==
2L 3s⟨3/2⟩ 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. 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, about 286 cents. Although the most accurate pythium generators are near 32/27, pythium can be tuned with minor thirds as sharp as that of [[11edf]]'s (319 cents).
=== Temperament interpretations==
From a [[half-prime subgroup]] point of view, 2L 3s⟨3/2⟩ can be interpreted as the [[Sirius B]] temperament, where the minor third generator is represented by ~[[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 minor third 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 6 largest satellites of Saturn, excluding Titan since the "Titanian" name has been used for the [[3L 2s (3/2-equivalent)|uranian scale]].
The mode names are 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]].
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== Scale tree ==
== Scale tree ==
{{Scale tree|Comments=5/4:Optimal 3/2.4.5.7 pythium around here;8/5:Near-just 32/27, optimal 3/2.4.5 pythium around here;2/1:Augmented 8-mosstep is nearly an octave;1/0:Degenerate scale with only 2 tones}}
{{Scale tree|Comments=11/7: [[CTE tuning]] for Sirius B temperament (293.825¢); 8/5: Pythagorean minor third (294.135¢); }}


[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:5-tone scales]]
[[Category:5-tone scales]]
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