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User:Moremajorthanmajor/9L 4s (7/2-equivalent): Difference between revisions

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|ね (にb)
|ね (にb)
|diminished eleventh  
|diminished eleventh  
|-
| colspan="6" |The chromatic 22-note MOS (either [[13L 9s (minor fourteenth equivalent)|13L 9s]], [[9L 13s (minor fourteenth equivalent)|9L 13s]] or [[22edXIV]]) also has these intervals
|-
|-
|13
|13
Line 1,336: Line 1,338:
|け (くb)
|け (くb)
|diminished fourteenth  
|diminished fourteenth  
|-
| colspan="6" |The chromatic 22-note MOS (either [[13L 9s (minor fourteenth equivalent)|13L 9s]], [[9L 13s (minor fourteenth equivalent)|9L 13s]] or [[22edXIV]]) also has these intervals
|-
|-
|14
|14
Line 1,394: Line 1,394:
|へb (ひbb)
|へb (ひbb)
|doubly diminished twelfth
|doubly diminished twelfth
|}
== Genchain ==
The generator chain for this scale is as follows:
{| class="wikitable"
|+
|
|
|
|
|
|
|へb (ひbb)
|せb (しbb)
|もb (むbb)
|とb (つbb)
|めb (みbb)
|てb (ちbb)
|けb (ゆbb)
|→
|-
|
|
|
|
|
|
|dd12
|d9
|d6
|d3
|d13
|d10
|d7
|
|-
|の (ぬb)
|け (くb)
|ね (にb)
|ま (きb)
|ほ (ふb)
|そ (すb)
|へ (ひb)
|せ (しb)
|も (むb)
|と (つb)
|め (みb)
|て (ちb)
|け (ゆb)
|→
|-
|d4
|d14
|d11
|d8
|d5
|m2
|d12
|m9
|m6
|m3
|m13
|m10
|m7
|
|-
|ぬ
|く
|に
|き
|ふ
|す
|ひ
|し
|む
|つ
|み
|ち
|ゆ
|→
|-
|N4
|P1
|N11
|P8
|N5
|M2
|N12
|M9
|M6
|M3
|M13
|M10
|M7
|
|-
|な (ぬ#)
|か (く#)
|に#
|き#
|は (ふ#)
|さ (す#)
|に#
|し#
|よ (む#)
|た (つ#)
|
|
|
|
|-
|A4
|A1
|A11
|A8
|A5
|A2
|A12
|A9
|A6
|A3
|
|
|
|
|}
== Modes ==
The mode names are based on the diatonic scale:
{| class="wikitable"
|+
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
|Lydian Dominant  ♮ 11
|LLLsLLsLLsLLs
|<nowiki>12|0</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Major b14
|LLsLLLsLLsLLs
|<nowiki>11|1</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Mixolydian
|LLsLLsLLLsLLs
|<nowiki>10|2</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|M
|P
|P
|M
|-
|Mixolydian b10 (Persian)
|LLsLLsLLsLLLs
|<nowiki>9|3</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|m
|P
|P
|M
|-
|Aeolian Dominant  ♮6
|LLsLLsLLsLLsL
|<nowiki>8|4</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Dorian b13
|LsLLLsLLsLLsL
|<nowiki>7|5</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Minor
|LsLLsLLLsLLsL
|<nowiki>6|6</nowiki>
|M
|m
|P
|P
|m
|m
|P
|M
|m
|P
|P
|m
|-
|Phrygian  ♮2
|LsLLsLLsLLLsL
|<nowiki>5|7</nowiki>
|M
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Locrian  ♮2 ♮5
|LsLLsLLsLLsLL
|<nowiki>4|8</nowiki>
|M
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Locrian  ♮5
|sLLLsLLsLLsLL
|<nowiki>3|9</nowiki>
|m
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Locrian
|sLLsLLLsLLsLL
|<nowiki>2|10</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Locrian b8
|sLLsLLsLLLsLL
|<nowiki>1|11</nowiki>
|m
|m
|P
|d
|m
|m
|d
|m
|m
|P
|d
|m
|-
|Locrian b8 b11
|sLLsLLsLLsLLL
|<nowiki>0|12</nowiki>
|m
|m
|P
|d
|m
|m
|d
|m
|m
|d
|d
|m
|}
== Temperaments ==
The '''Shōsūshī''' temperament spells its major hexad 24:30:36:45:54:64 or 84:108:126:162:189:224 <code>root-2(4g-3p)-(3g-2p)-(11g-8p)-2(3g-2p)-(1g)</code> (p = 18/5 or 7/2, g = 8/3) and its minor hexad 12:14:18:21:27:32 or 60:72:90:108:135:160 <code>root-(-5g-p)-(3g-2p)-(-2g)-2(3g-2p)-(1g)</code> (p = 18/5 or 7/2, g = 8/3).
=== Shōsūshī-Meantone ===
[[Subgroup]]: 18/5.2.3
[[Comma]] list: [[81/80]]
[[POL2]] generator: ~4/3 = 506.8820
[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 -2 -5}}]
[[Vals]]: [[22edXIV]], [[35edXIV]], [[48edXIV]], [[61edXIV]]
=== Shōsūshī-Superpyth ===
[[Subgroup]]: 7/2.2.3
[[Comma]] list: [[64/63]]
[[POL2]] generator: ~4/3 = 486.8323
[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 -2 -5}}]
[[Vals]]: [[22edXIV]], [[31edXIV]], [[40edXIV]], [[49edXIV]]
== Scale tree ==
The spectrum looks like this:
{| class="wikitable"
|+
! colspan="3" |Generator
!Normalized<ref name=":0" />
!''ed22\12<ref name=":0" />''
!L
!s
!L/s
!Comments
|-
|3\13
|
|
|514; 3, 2
|''507; 1, 3, 3''
|1
|1
|1.000
|Equalised
|-
|
|17\74
|
|510
|''505; 2, 2, 7''
|6
|5
|1.200
|
|-
|
|14\61
|
|509.{{Overline|09}}
|''504; 1, 11, 5''
|5
|4
|1.250
|
|-
|
|
|25\109
|508; 2, 9, 3
|''504; 1, 1, 2, 2, 1, 2, 2''
|9
|7
|1.286
|
|-
|
|11\48
|
|507; 1, 3, 3
|''504.1{{Overline|6}}''
|4
|3
|1.333
|
|-
|
|
|19\83
|506.{{Overline|6}}
|''503; 1, 1, 1, 1, 2, 6''
|7
|5
|1.400
|
|-
|
|8\35
|
|505; 3, 1, 4
|''502; 1, 6''
|3
|2
|1.500
|Shōsūshī-Meantone starts here
|-
|
|
|21\92
|504
|''502; 5, 1, 3''
|8
|5
|1.600
|
|-
|
|
|13\57
|503; 4, 2, 3
|''501; 1, 3, 14''
|5
|3
|1.667
|
|-
|
|
|18\79
|502; 3, 14
|''501; 3, 1, 3, 5''
|7
|4
|1.750
|
|-
|
|
|23\101
|501.{{Overline|81}}
|''500.{{Overline|0099}}''
|9
|5
|1.800
|
|-
|
|5\22
|
|500
|''500''
|2
|1
|2.000
|Shōsūshī-Meantone ends, Shōsūshī-Pythagorean begins
|-
|
|
|27\119
|498; 2, 6
|''499; 6, 3, 1, 4''
|11
|5
|2.200
|
|-
|
|
|22\97
|498; 8, 1, 5
|''498; 1, 31, 3''
|9
|4
|2.250
|
|-
|
|
|17\75
|497; 1, 1, 3, 1, 1, 2
|''498.{{Overline|6}}''
|7
|3
|2.333
|
|-
|
|
|12\53
|496; 1, 1, 4, 3
|''498; 8, 1, 5''
|5
|2
|2.500
|Shōsūshī-Neogothic heartland is from here…
|-
|
|
|19\84
|495; 1, 1, 1, 7
|''497; 1, 1, 1, 1, 1, 2''
|8
|3
|2.667
|…to here
|-
|
|7\31
|
|494; 8, 2
|''496; 1, 3, 2, 3''
|3
|1
|3.000
|Shōsūshī-Pythagorean ends, Shōsūshī-Superpyth begins
|-
|
|
|30\133
|493; 6, 1, 1, 1, 3
|''496; 4, 6, 2, 2''
|13
|4
|3.250
|
|-
|
|
|23\102
|492; 1, 5
|''496; 12, 1, 3''
|10
|3
|3.333
|
|-
|
|
|16\71
|492; 3, 4
|''495; 1, 3, 2, 3, 2''
|7
|2
|3.500
|
|-
|
|
|25\111
|491; 1, 4, 12
|''495; 2, 55''
|11
|3
|3.667
|
|-
|
|9\40
|
|490.{{Overline|90}}
|''495''
|4
|1
|4.000
|
|-
|
|
|20\89
|489; 1, 3, 1, 9
|''494; 2, 1, 1, 1, 1, 1, 1, 2''
|9
|2
|4.500
|
|-
|
|11\49
|
|488.{{Overline|8}}
|''493; 1, 7, 6''
|5
|1
|5.000
|Shōsūshī-Superpyth ends
|-
|
|13\58
|
|487.5
|''493; 9, 1, 2''
|6
|1
|6.000
|
|-
|2\9
|
|
|480
|''488.{{Overline|8}}''
|1
|0
|→ inf
|Paucitonic
|}
|}
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