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Tags: Mobile edit Mobile web edit |
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| [https://www.youtube.com/watch?v=x4Yesl8n6gc Brusselator Sprouts (by Xotla)] (The main riffs are in this scale, although key changes and notes outside the 9 note subset are used too.) | | [https://www.youtube.com/watch?v=x4Yesl8n6gc Brusselator Sprouts (by Xotla)] (The main riffs are in this scale, although key changes and notes outside the 9 note subset are used too.) |
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| == Decatonic (3L 7s) == | | == Sephiroth heptatonic (3L 4s) == |
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| The decatonic scale is excellent for 4:5:13 triads. It's generated by a major third, and two of them span a 4:5:13 triad, spanning degrees 1-4-8, and three of them span a 4:5:13:21 tetrad. This means that 8 of the 10 degrees have a 4:5:13 triad, and 7 of them in turn have a 4:5:13:21.
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| The following is a sortable table of LsssLssLss. (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain.) If you want an 11/8 instead of a 21/16 you can sharpen the 5th degree to get LssLsssLsss which is the only mode to have a 4:5:9:11:13 on the tonic.
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| {| class="wikitable right-1 right-2 sortable"
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| |-
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| ! style="text-align:right" | Degree
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| ! Cents
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| ! Note name on J
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| ! Approximate ratios
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| ! # generators up
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| |-
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| | 1, 11
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| | 0.00, 1200.00
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| | J
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| | '''1/1''', '''2/1'''
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| | 0
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| |-
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| | 2
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| | 184.62
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| | K
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| | '''9/8''', 10/9, 11/10, 19/17, 21/19
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| | +7
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| |-
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| | 3
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| | 276.92
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| | Lb
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| | 7/6, 13/11, 20/17, '''19/16''', 22/19
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| | +4
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| |-
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| | 4
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| | 369.23
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| | L
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| | '''5/4''', 11/9, 16/13, 26/21
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| | +1
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| |-
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| | 5
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| | 461.54
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| | M
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| | 13/10, 17/13, '''21/16''', 22/17
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| | -2
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| |-
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| | 6
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| | 646.15
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| | N
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| | 16/11, 13/9, 19/13
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| | +5
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| |-
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| | 7
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| | 738.46
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| | Ob
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| | 17/11, 20/13, 26/17, 32/21
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| | +2
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| |-
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| | 8
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| | 830.77
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| | O
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| | 8/5, '''13/8''', 18/11, 21/13
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| | -1
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| |-
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| | 9
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| | 1015.38
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| | P#
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| | 9/5, 16/9, 20/11, 34/19, 38/21
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| | +6
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| |-
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| | 10
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| | 1107.69
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| | Q
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| | 17/9, 19/10, 21/11, 32/17, 36/19, 40/21
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| | +3
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| |}
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| === Melodic properties ===
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| The decatonic scale can be viewed as containing archeotonic or oneirotonic scales with possible chromatic alterations, containing different degrees of some intervals. For example, the LsssLssLss mode can be viewed as:
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| *From a 7-tone POV: P1 - M2 - m3~M3 - m4 - m5~M5 - m6 - m7~M7 - P8
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| *From an 8-tone POV: P1 - M2 - m3~M3 - m4 - Mᴛ - M5 - m6 - m7~M7 - P8 or P1 - M2 - m3~M3 - m4 - Mᴛ - M5~A5 - A6 - M7 - P8, thus containing chromatically altered versions of Dylathian, Ilarnekian, Ultharian, and Celephaïsian
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| The 3113131 subset (P1-A2-M3-m4-M5-m6-M7-P8), is more important from the regular temperament POV, in that you can modulate up by major thirds by using 4:5:13 triads on it. The subset is also melodically interesting and pleasing.
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| == Other stuff == | | == Other stuff == |
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| todo: try added fifths or tritones, describe chords with two additions or more | | todo: try added fifths or tritones, describe chords with two additions or more |