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Mavila temperament modal harmony: Difference between revisions

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=Introduction=
== Introduction ==


Mavila is the regular temperament eliminating [[135/128|135/128]]. As a consequence, this means that it will have a generator significantly flat of 3/2 so that 4 of them add up to a minor third. For any decent tuning of mavila, another consequence of this tempering is that we end up with an "antidiatonic" 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see [[2L_5s|2L 5s]]) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note "superdiatonic" MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see[[7L_2s| 7L 2s]]) These correspondences can be harnessed to create an intuitive naming system for the modes of mavila[7] and mavila[9] which reference the names of the existing familiar modes of meantone[7].
Mavila is the regular temperament eliminating [[135/128]]. As a consequence, this means that it will have a generator significantly flat of 3/2 so that 4 of them add up to a minor third. For any decent tuning of mavila, another consequence of this tempering is that we end up with an "antidiatonic" 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see [[2L 5s]]) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note "superdiatonic" MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see [[7L 2s]]) These correspondences can be harnessed to create an intuitive naming system for the modes of mavila[7] and mavila[9] which reference the names of the existing familiar modes of meantone[7].


===How to read these charts===
=== How to read these charts ===
<ul><li>The 6|0, 5|1, 4|2 markings are an instance of [[Modal_UDP_Notation|Modal UDP Notation]].</li><li>Unless otherwise specified, all transversals occur in the 2.3.5.7.11 extension of Mavila which tempers out 135/128, 36/35, 45/44, 33/32, called 11-limit Armodue temperament.</li><li>Additionally, "diatonic" names make use of the following abbreviations:<ul><li>SM - Supermajor</li><li>M - Major</li><li>N - Neutral</li><li>m - Minor</li><li>sm - Subminor</li></ul></li></ul>
* The 6|0, 5|1, 4|2 markings are an instance of [[Modal UDP Notation]].
* Unless otherwise specified, all transversals occur in the 2.3.5.7.11 extension of Mavila which tempers out 135/128, 36/35, 45/44, 33/32, called 11-limit Armodue temperament.
* Additionally, "diatonic" names make use of the following abbreviations:
** SM - Supermajor
** M - Major
** N - Neutral
** m - Minor
** sm - Subminor


=2L3s Pentatonic MOS: Pentic=
== 2L3s Pentatonic MOS: Pentic ==
4|0 - LsLss - Patet deng
4|0 - LsLss - Patet deng


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In cyclic permutational order: Patet ding | Patet dong | Patet deng | Patet dung | Patet dang
In cyclic permutational order: Patet ding | Patet dong | Patet deng | Patet dung | Patet dang


===Transversal===
=== Transversal ===


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==="Diatonic" Names===
=== "Diatonic" Names ===


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=2L5s Heptatonic MOS: Antidiatonic=
== 2L 5s Heptatonic MOS: Antidiatonic ==


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<span style="line-height: 1.5;">In cyclic permutational order: Ionian | Dorian | Phrygian | Lydian | Mixolydian | Aeolian | Locrian</span>
<span style="line-height: 1.5;">In cyclic permutational order: Ionian | Dorian | Phrygian | Lydian | Mixolydian | Aeolian | Locrian</span>


===Transversal===
=== Transversal ===


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==="Diatonic" Names===
=== "Diatonic" Names ===


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=7L2s Nonatonic MOS: Superdiatonic=
== 7L 2s Nonatonic MOS: Superdiatonic ==


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In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian
In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian


===Transversal===
=== Transversal ===


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==="Diatonic" Names===
=== "Diatonic" Names ===


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===Superdiatonic Qualities===
=== Superdiatonic Qualities ===
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=Notes on Naming=
== Notes on Naming ==


The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the "Anti-" prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the "Super" prefix (e.g. Superionian, Superaeolian, etc.). The "anti" and "super" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.
The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the "Anti-" prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the "Super" prefix (e.g. Superionian, Superaeolian, etc.). The "anti" and "super" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.
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As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -&gt; Corinthian -&gt; Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.
As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -&gt; Corinthian -&gt; Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.


[[Category:modes]]
[[Category:Mavila]]
[[Category:Modes]]
[[Category:Essays]]
[[Category:Essays]]
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