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 scale to the 3.5 subgroup (as well as [[Arcturus]] temperament), similar to how the [[5L 2s|diatonic]] scale is connected to the [[3-limit]].  The preferred generator for the scale 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 basic-hard range) [[Arcturus]] temperament, similar to how the [[5L 2s|diatonic]] scale is connected to the [[3-limit]] and (in the soft-basic range) [[meantone]] temperament.  The preferred generator for the scale 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. Most of the generators for larger EDTs are tunings for Arcturus temperament, but some fall sharp or flat analogous


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, [[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 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 perfect 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 ==
The [[13edt]] (Bohlen-Pierce) gamut is as follows:
[[9edt]]:
{|class="wikitable article-table"
|-
!Steps
!Absolute notation
!Relative notation
|-
|0
|C
|perfect 0-step
|-
|1
|D
|perfect 1-step
|-
|2
|E
|perfect 2-step
|-
|3
|E
|major 2-step
|-
|4
|F
|major 3-step
|-
|5
|G
|major 4-step
|-
|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
|A
|major 9-step
|-
|12
|B
|major 10-step
|-
|13
|C
|perfect 11-step
|}
 
[[13edt]] (Bohlen-Pierce):


{|class="wikitable article-table"
{|class="wikitable article-table"

Revision as of 03:40, 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 basic-hard range) Arcturus temperament, similar to how the diatonic scale is connected to the 3-limit and (in the soft-basic range) meantone temperament. The preferred generator for the scale 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. Most of the generators for larger EDTs are tunings for Arcturus temperament, but some fall sharp or flat analogous

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 larger EDTs, Arcturus hendecatonic notation can be combined with ups and downs notation, with ^/v accidentals raising and lowering by 1 EDTstep.

Examples

9edt:

Steps Absolute notation Relative notation
0 C perfect 0-step
1 D perfect 1-step
2 E perfect 2-step
3 E major 2-step
4 F major 3-step
5 G major 4-step
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 A major 9-step
12 B major 10-step
13 C perfect 11-step

13edt (Bohlen-Pierce):

Steps Absolute notation Relative notation
0 C perfect 0-step
1 Db minor 1-step
2 D major 1-step
3 E major 2-step
4 F major 3-step
5 G major 4-step
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 A major 9-step
12 B major 10-step
13 C perfect 11-step
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