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.
'''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 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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== Examples ==
== Examples ==
[[11edt]] (equalized):
[[11edt]] (equalized):
{|class="wikitable article-table"
{| class="wikitable article-table"
|-
|-
!0
! 0
!1
! 1
!2
! 2
!3
! 3
14
! 4
!5
! 5
!6
! 6
!7
! 7
!8
! 8
!9
! 9
!10
! 10
!11
! 11
|-
|-
|C
| C
|D
| D
|E
| E
|F
| F
|G
| G
|H
| H
|J
| J
|K
| K
|L
| L
|A
| A
|B
| B
|C
| C
|-
|-
|P0
| P0
|P1
| P1
|P2
| P2
|P3
| P3
|P4
| P4
|P5
| P5
|P6
| P6
|P7
| P7
|P8
| P8
|P9
| P9
|P10
| P10
|P11
| P11
|}
|}


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


{|class="wikitable article-table"
{| class="wikitable article-table"
|-
|-
!0
! 0
!1
! 1
!2
! 2
!3
! 3
!4
! 4
!5
! 5
!6
! 6
!7
! 7
!8
! 8
!9
! 9
!10
! 10
!11
! 11
!12
! 12
!13
! 13
|-
|-
|C
| C
|Db
| Db
|D
| D, Eb
|E
| E, Fb
|F
| F, Gb
|G
| G, Hb
|H
| H
|J
| J
|Kb
| J#, Kb
|K
| K
|L
| L, Ab
|A
| A, Bb
|B
| B
|C
| C
|-
|-
|P0
| P0
|m1
| m1
|M1
| M1, m2
|M2
| M2, m3
|M3
| M3, m4
|M4
| M4, d5
|P5
| P5
|P6
| P6
|m7
| A6, m7
|M7
| M7
|M8
| M8, m9
|M9
| M9, m10
|M10
| M10
|P11
| P11
|}
|}


[[24edt]]:
[[24edt]]:


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


[[Category:Notation]]
{{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


View • Talk • EditMusical notation
Universal Sagittal notation
Just intonation Functional Just System • Ben Johnston's notation (Johnston–Copper notation) • Helmholtz–Ellis notation • Color notation
MOS scales Diamond-mos notation • KISS notation (Quasi-diatonic MOS notation)
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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