3L 2s (8/5-equivalent): Difference between revisions

(3 intermediate revisions by the same user not shown)

Line 5:

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 is a minor sixth-repeating ~~equivalent of diatonic~~, each tone has an 8/5 minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This ~~diatonic~~ also has two diminished 7th chords, making it a warped melodic minor scale.

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]] ~~diatonic~~ is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].

[[Basic]] 3L 2s<8/5> is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].

==Notation==

There are 2 main ways to notate ~~the diatonic~~ 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.

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"

|+

Line 1,188:

[[Optimal ET sequence]]: 5ed8/5, 8ed8/5, 13ed8/5

~~==='''Aeolianic-Superpyth'''===~~

~~[[Subgroup]]: 14/9.4/3.3/2~~

~~[[Comma]] list: [[64/63]]~~

~~[[POL2]] generator: ~7/6 = 276.0795~~

~~[[Mapping]]: [{{val|1 1 2}}, {{val|0 -1 -3}}]~~

~~[[Optimal ET sequence]]: 3ed14/9, 11ed14/9, 14ed14/9~~

==Scale tree==

@@ Line 5: / Line 5: @@
 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 is a minor sixth-repeating equivalent of diatonic, each tone has an 8/5 minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This diatonic also has two diminished 7th chords, making it a warped melodic minor scale.
+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]] diatonic is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
+[[Basic]] 3L 2s<8/5> is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
 ==Notation==
-There are 2 main ways to notate the diatonic 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.
+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"
 |+
@@ Line 1,188: / Line 1,188: @@
 [[Optimal ET sequence]]: 5ed8/5, 8ed8/5, 13ed8/5
-==='''Aeolianic-Superpyth'''===
-[[Subgroup]]: 14/9.4/3.3/2
-[[Comma]] list: [[64/63]]
-[[POL2]] generator: ~7/6 = 276.0795
-[[Mapping]]:  [{{val|1 1 2}}, {{val|0 -1 -3}}]
-[[Optimal ET sequence]]: 3ed14/9, 11ed14/9, 14ed14/9
 ==Scale tree==