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 [[nonoctave]] 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]], relating it to [[Arcturus]] 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 perfect 8-step, the chord 3:5:7 is notated as C - H - L (P0 - P5 - M8). To notate large 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.


== Examples ==
== Examples ==
[[11edt]] (equalized):
[[11edt]] (equalized):
{|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
| D
|perfect 0-step
| E
| F
| G
| H
| J
| K
| L
| A
| B
| C
|-
|-
|1
| P0
|D
| P1
|perfect 1-step
| P2
|-
| P3
|2
| P4
|E
| P5
|perfect 2-step
| P6
|-
| P7
|3
| P8
|F
| P9
|perfect 3-step
| P10
|-
| P11
|4
|G
|perfect 4-step
|-
|5
|H
|perfect 5-step
|-
|6
|J
|perfect 6-step
|-
|7
|K
|perfect 7-step
|-
|8
|L
|perfect 8-step
|-
|9
|A
|perfect 9-step
|-
|10
|B
|perfect 10-step
|-
|11
|C
|perfect 11-step
|}
|}


[[13edt]] (Bohlen-Pierce):
[[13edt]] (Bohlen-Pierce):


{|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
| Db
|perfect 0-step
| D, Eb
| E, Fb
| F, Gb
| G, Hb
| H
| J
| J#, Kb
| K
| L, Ab
| A, Bb
| B
| C
|-
|-
|1
| P0
|Db
| m1
|minor 1-step
| M1, m2
|-
| M2, m3
|2
| M3, m4
|D
| M4, d5
|major 1-step
| P5
|-
| P6
|3
| A6, m7
|E
| M7
|major 2-step
| M8, m9
|-
| M9, m10
|4
| M10
|F
| P11
|major 3-step
|}
|-
 
|5
[[24edt]]:
|G
 
|major 4-step
{| class="wikitable article-table"
|-
|6
|H
|perfect 5-step
|-
|7
|J
|perfect 6-step
|-
|8
|Kb
|minor 7-step
|-
|9
|K
|major 7-step
|-
|10
|L
|major 8-step
|-
|-
|11
! 0
|A
! 1
|major 9-step
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
! 17
! 18
! 19
! 20
! 21
! 22
! 23
! 24
|-
|-
|12
| C
|B
| C#, Dbb
|major 10-step
| 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
|-
|-
|13
| 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
|}
|}
{{Navbox notation}}
[[Category:Nonoctave]]
[[Category:Arcturus]]

Latest revision as of 18:30, 11 February 2025

Arcturus hendecatonic notation is a nonoctave 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, relating it to Arcturus 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, Eb E, Fb F, Gb G, Hb H J J#, Kb K L, Ab A, Bb B C
P0 m1 M1, m2 M2, m3 M3, m4 M4, d5 P5 P6 A6, m7 M7 M8, m9 M9, m10 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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Temperaments Chain-of-fifths notation • Stein–Zimmermann–Gould notation • Ups and downs notation • Syntonic–rastmic subchroma notation • Extended meantone notation • Fractional sharp notation
See musical notation for a longer list of systems by category. See Category:Notation for the most complete, comprehensive list, but not sorted by category.
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