Arcturus hendecatonic notation: Difference between revisions

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'''Arcturus hendecatonic notation''' is a notation system for [[EDT]]s and no-twos music, developed by [[User:CompactStar|CompactStar]]. It is based on the [[2L 9s (3/1-equivalent)|2L 9s⟨3/1⟩]] MOS scale generated by approximately [[5/3]]. The 5/3 generator connects this MOS to the 3.5 subgroup and (in the soft-hard range) [[Arcturus]] temperament, similar to how the [[5L 2s|diatonic]] scale is connected to the [[3-limit]] and (in the equalized-basic range) [[meantone]] temperament.  The preferred generator for a given EDT is the patent val 5/3, unless it is extremely inaccurate (as is the case in some very small EDTs) and does not generate a 2L 9s⟨3/1⟩ scale.  
'''Arcturus hendecatonic notation''' is a notation system for [[EDT]]s and no-twos music, developed by [[User:CompactStar|CompactStar]]. It is based on the [[2L 9s (3/1-equivalent)|2L 9s⟨3/1⟩]] MOS scale generated by approximately [[5/3]]. The 5/3 generator connects this MOS to the 3.5 subgroup and (in the soft-hard range) [[Arcturus]] temperament, similar to how the [[5L 2s|diatonic]] scale is connected to the [[3-limit]] and (in the equalized-basic range) [[meantone]] temperament.  The preferred generator for a given EDT is the patent val 5/3.


The 9|1 mode of 2L 9s⟨3/1⟩ is represented by 11 naturals CDEFGHJKLAB, and #/b accidentals are used to raise and lower by a chroma (L - s). For relative notation, the [[TAMNAMS]] convention of zero-based indices is used.  Assuming Arcturus temperament where [[7/3]] is mapped to the major 8-step, the chord 3:5:7 is notated as C - H - L (P0 - P5 - M8). To notate larger EDTs, Arcturus hendecatonic notation can be combined with [[ups and downs notation]], with ^/v accidentals raising and lowering by 1 EDTstep.
The 9|1 mode of 2L 9s⟨3/1⟩ is represented by 11 naturals CDEFGHJKLAB, and #/b accidentals are used to raise and lower by a chroma (L - s). For relative notation, the [[TAMNAMS]] convention of zero-based indices is used.  Assuming Arcturus temperament where [[7/3]] is mapped to the major 8-step, the chord 3:5:7 is notated as C - H - L (P0 - P5 - M8). To notate larger EDTs, Arcturus hendecatonic notation can be combined with [[ups and downs notation]], with ^/v accidentals raising and lowering by 1 EDTstep.
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{|class="wikitable article-table"
{|class="wikitable article-table"
|-
|-
!Steps
|0
!Absolute notation
|1
!Relative notation
|2
|3
|4
|5
|6
|7
|8
|9
|10
|11
|-
|-
|0
|C
|C
|perfect 0-step
|-
|1
|D
|D
|perfect 1-step
|-
|2
|E
|E
|perfect 2-step
|-
|3
|F
|F
|perfect 3-step
|-
|4
|G
|G
|perfect 4-step
|-
|5
|H
|H
|perfect 5-step
|-
|6
|J
|J
|perfect 6-step
|-
|7
|K
|K
|perfect 7-step
|-
|8
|L
|L
|perfect 8-step
|-
|9
|A
|A
|perfect 9-step
|-
|10
|B
|B
|perfect 10-step
|C
|-
|-
|11
|P0
|C
|P1
|perfect 11-step
|P2
|P3
|P4
|P5
|P6
|P7
|P8
|P9
|P10
|P11
|}
|}


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{|class="wikitable article-table"
{|class="wikitable article-table"
|-
|-
!Steps
|0
!Absolute notation
|1
!Relative notation
|2
|3
|4
|5
|6
|7
|8
|9
|10
|11
|12
|13
|-
|-
|0
|C
|C
|perfect 0-step
|-
|1
|Db
|Db
|minor 1-step
|-
|2
|D
|D
|major 1-step
|-
|3
|E
|E
|major 2-step
|-
|4
|F
|F
|major 3-step
|-
|5
|G
|G
|major 4-step
|-
|6
|H
|H
|perfect 5-step
|-
|7
|J
|J
|perfect 6-step
|-
|8
|Kb
|Kb
|minor 7-step
|-
|9
|K
|K
|major 7-step
|-
|10
|L
|L
|major 8-step
|-
|11
|A
|A
|major 9-step
|-
|12
|B
|B
|major 10-step
|C
|-
|-
|13
|P0
|C
|m1
|perfect 11-step
|M1
|M2
|M3
|M4
|P5
|P6
|m7
|M7
|M8
|M9
|M10
|P11
|}
|}


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{|class="wikitable article-table"
{|class="wikitable article-table"
|-
!Steps
!Absolute notation
!Relative notation
|-
|-
|0
|0
|C
|perfect 0-step
|-
|1
|1
|C#, Dbb
|augmented 0-step, diminished 1-step
|-
|2
|2
|Db
|minor 1-step
|-
|3
|3
|D
|major 1-step
|-
|4
|4
|Eb
|minor 2-step
|-
|5
|5
|E
|major 2-step
|-
|6
|6
|Fb
|minor 3-step
|-
|7
|7
|F
|major 3-step
|-
|8
|8
|Gb
|minor 4-step
|-
|9
|9
|G
|major 4-step
|-
|10
|10
|Hb
|11
|diminished 5-step
|12
|13
|14
|15
|16
|17
|18
|19
|20
|21
|22
|23
|24
|-
|-
|11
|C
|C#, Dbb
|Db
|D
|Eb
|E
|Fb
|F
|Gb
|G
|G#, Hb
|H
|H
|perfect 5-step
|-
|12
|H#, Jb
|H#, Jb
|augmented 5-step, diminished 6-step
|-
|13
|J
|J
|perfect 6-step
|-
|14
|J#, Kbb
|J#, Kbb
|augmented 6-step, diminished 7-step
|-
|15
|Kb
|Kb
|minor 7-step
|-
|16
|K
|K
|major 7-step
|-
|17
|Lb
|Lb
|minor 8-step
|-
|18
|L
|L
|major 8-step
|-
|19
|Ab
|Ab
|minor 9-step
|-
|20
|A
|A
|major 9-step
|-
|21
|Bb
|Bb
|minor 10-step
|-
|22
|B
|B
|major 10-step
|-
|23
|B#, Cb
|B#, Cb
|augmented 10-step, diminished 11-step
|C
|-
|-
|24
|P0
|C
|A0, d1
|perfect 11-step
|m1
|M1
|m2
|M2
|m3
|M3
|m4
|M4
|A4, d5
|P5
|A5, d6
|P6
|A6, d7
|m7
|M7
|m8
|M8
|m9
|M9
|m10
|M10
|A10, d11
|P11
|}
|}


[[Category:Notation]]
[[Category:Notation]]

Revision as of 06:38, 7 June 2023

Arcturus hendecatonic notation is a notation system for EDTs and no-twos music, developed by CompactStar. It is based on the 2L 9s⟨3/1⟩ MOS scale generated by approximately 5/3. The 5/3 generator connects this MOS to the 3.5 subgroup and (in the soft-hard range) Arcturus temperament, similar to how the diatonic scale is connected to the 3-limit and (in the equalized-basic range) meantone temperament. The preferred generator for a given EDT is the patent val 5/3.

The 9|1 mode of 2L 9s⟨3/1⟩ is represented by 11 naturals CDEFGHJKLAB, and #/b accidentals are used to raise and lower by a chroma (L - s). For relative notation, the TAMNAMS convention of zero-based indices is used. Assuming Arcturus temperament where 7/3 is mapped to the major 8-step, the chord 3:5:7 is notated as C - H - L (P0 - P5 - M8). To notate larger EDTs, Arcturus hendecatonic notation can be combined with ups and downs notation, with ^/v accidentals raising and lowering by 1 EDTstep.

Examples

11edt (equalized):

0 1 2 3 4 5 6 7 8 9 10 11
C D E F G H J K L A B C
P0 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11

13edt (Bohlen-Pierce):

0 1 2 3 4 5 6 7 8 9 10 11 12 13
C Db D E F G H J Kb K L A B C
P0 m1 M1 M2 M3 M4 P5 P6 m7 M7 M8 M9 M10 P11

24edt:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
C C#, Dbb Db D Eb E Fb F Gb G G#, Hb H H#, Jb J J#, Kbb Kb K Lb L Ab A Bb B B#, Cb C
P0 A0, d1 m1 M1 m2 M2 m3 M3 m4 M4 A4, d5 P5 A5, d6 P6 A6, d7 m7 M7 m8 M8 m9 M9 m10 M10 A10, d11 P11
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