3L 2s (8/5-equivalent): Difference between revisions
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{{Infobox MOS | {{Infobox MOS}} | ||
'''3L 2s<8/5>''' | '''3L 2s<8/5>''' is a minor sixth-repeating MOS scale. The notation "<8/5>" means the period of the MOS is 8/5, disambiguating it from octave-repeating [[3L 2s]]. | ||
The generator range is 240 to 342.9 cents, placing it on the [[6/5|diatonic minor third]], usually representing a minor third of some type (like [[6/5]]). The bright (chroma-positive) generator is, however, its minor sixth complement (480 to 514.3 cents). | The generator range is 240 to 342.9 cents, placing it on the [[6/5|diatonic minor third]], usually representing a minor third of some type (like [[6/5]]). The bright (chroma-positive) generator is, however, its minor sixth complement (480 to 514.3 cents). | ||
Because this | Because this is a minor sixth-repeating scale, each tone has an 8/5 minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This scale also has two diminished 7th chords, making it a warped melodic minor scale. | ||
[[Basic]] | [[Basic]] 3L 2s<8/5> is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]]. | ||
==Notation== | ==Notation== | ||
There are 2 main ways to notate | There are 2 main ways to notate this scale. One method uses a simple sixth repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sixth (diminished eleventh~tenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sixth notation, Greek numerals 1-10 may be used. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
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{| class="wikitable" | {| class="wikitable" | ||
!Generators | !Generators | ||
! | !Sixth notation | ||
!Interval category name | !Interval category name | ||
!Generators | !Generators | ||
| Line 1,024: | Line 1,024: | ||
|0 | |0 | ||
|La | |La | ||
| | |perfect sixth (minor sixth) | ||
|0 | |0 | ||
|La | |La | ||
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| -5 | | -5 | ||
|Lab | |Lab | ||
|diminished | |diminished sixth | ||
|- | |- | ||
|6 | |6 | ||
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|} | |} | ||
==Modes== | ==Modes== | ||
The mode names are based on the | The mode names are based on the modes of the diatonic scale , in order of size: | ||
{| class="wikitable" | {| class="wikitable" | ||
!Mode | !Mode | ||
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|d | |d | ||
|} | |} | ||
==Temperaments== | ==Temperaments== | ||
The most basic rank-2 temperament interpretation of this diatonic is '''Aeolianic''', which has septimal 6:7:9 or pental 10:12:15 chords spelled <code>root-(p-1g)-(3g)</code> (p = the minor sixth, g = the approximate 4/3). The name "Aeolianic" comes from the Aeolian minor mode having the minor sixth as its characteristic interval. | The most basic rank-2 temperament interpretation of this diatonic is '''Aeolianic''', which has septimal 6:7:9 or pental 10:12:15 chords spelled <code>root-(p-1g)-(3g)</code> (p = the minor sixth, g = the approximate 4/3). The name "Aeolianic" comes from the Aeolian minor mode having the minor sixth as its characteristic interval. | ||
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[[Optimal ET sequence]]: 5ed8/5, 8ed8/5, 13ed8/5 | [[Optimal ET sequence]]: 5ed8/5, 8ed8/5, 13ed8/5 | ||
==Scale tree== | ==Scale tree== | ||