User:Lériendil/Sandbox: Difference between revisions

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== Notation ==
== Notation ==
Bohlen-Pierce theory possesses a [[nonoctave]] notation system for [[EDT]]s and no-twos music, which is well-established<ref>[https://en.wikipedia.org/wiki/Bohlen%E2%80%93Pierce_scale#Intervals_and_scale_diagrams]</ref>. 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.
Bohlen-Pierce theory possesses a well-established<ref>[https://en.wikipedia.org/wiki/Bohlen%E2%80%93Pierce_scale#Intervals_and_scale_diagrams]</ref> [[nonoctave]] notation system for [[EDT]]s and no-twos music, which is based on this MOS scale as generated by approximately [[7/3]], relating it to [[Bohlen-Pierce-Stearns|BPS]] temperament, where two 7/3 generators are equated to 27/5. The preferred generator for any edt is its patent val approximation of 7/3.


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.
This notation uses 9 nominals: E F G H J A B C D E as presented in the E Cassiopeian (sLsLsLsLs) mode, and represented by a circle of generators going as follows: ...C# - A# - H# - F# - D - B - J - G - E - C - A - H - F - Db - Bb - Jb - Gb...


=== Examples ===
=== Examples ===
[[11edt]] (equalized):
[[9edt]] (equalized):
{|class="wikitable article-table"
{|class="wikitable article-table"
|-
|-
Line 18: Line 18:
!8
!8
!9
!9
!10
!11
|-
|-
|C
|D
|E
|E
|F
|F
Line 28: Line 24:
|H
|H
|J
|J
|K
|L
|A
|A
|B
|B
|C
|C
|D
|E
|-
|-
|P0
|P0
Line 44: Line 40:
|P8
|P8
|P9
|P9
|P10
|P11
|}
|}


Line 67: Line 61:
!13
!13
|-
|-
|C
|E
|Db
|F
|D, Eb
|F#, Gb
|E, Fb
|G
|F, Gb
|G, Hb
|H
|H
|H#, Jb
|J
|J
|J#, Kb
|A
|K
|A#, Bb
|L, Ab
|A, Bb
|B
|B
|C
|C
|Db, C#
|D
|E
|-
|-
|P0
|P0
|m1
|m1
|M1, m2
|M1
|M2, m3
|P2
|m3
|M3, m4
|M3, m4
|M4, d5
|M4
|P5
|m5
|P6
|M5, m6
|A6, m7
|M6
|M7
|P7
|M8, m9
|m8
|M9, m10
|M8
|M10
|P9
|P11
|}
|}


[[24edt]]:
[[30edt]]:


{|class="wikitable article-table"
{|class="wikitable article-table"
Line 127: Line 121:
!23
!23
!24
!24
!25
!26
!27
!28
!29
!30
|-
|-
|C
|C#, Dbb
|Db
|D
|Eb
|E
|E
|Fb
|D#, Gbb
|F
|F
|E#
|Gb
|Gb
|F#
|Hb
|G
|G
|G#, Hb
|Fx, Jbb
|H
|H
|H#, Jb
|G#
|Jb
|H#
|Ab
|J
|J
|J#, Kbb
|Hx, Bbb
|Kb
|K
|Lb
|L
|Ab
|A
|A
|J#
|Bb
|Bb
|A#
|Cb
|B
|B
|B#, Cb
|Ax, Dbb
|C
|C
|B#
|Db
|C#
|Eb
|D
|Fb, Cx
|E
|-
|-
|P0
|P0
|A0, d1
|MM8, dd2
|m1
|m1
|A0
|d2
|M1
|M1
|m2
|mm3
|M2
|P2
|MM1, mm4
|m3
|m3
|A2
|m4
|M3
|M3
|m4
|mm5
|M4
|M4
|A4, d5
|MM3, mm6
|P5
|m5
|A5, d6
|MM4
|P6
|m6
|A6, d7
|M5
|m7
|d7
|M7
|M6
|MM5, mm8
|P7
|MM6
|m8
|m8
|A7
|d9
|M8
|M8
|m9
|mm1, AA7
|M9
|P9
|m10
|M10
|A10, d11
|P11
|}
|}

Revision as of 23:17, 22 August 2024

Notation

Bohlen-Pierce theory possesses a well-established[1] nonoctave notation system for EDTs and no-twos music, which is based on this MOS scale as generated by approximately 7/3, relating it to BPS temperament, where two 7/3 generators are equated to 27/5. The preferred generator for any edt is its patent val approximation of 7/3.

This notation uses 9 nominals: E F G H J A B C D E as presented in the E Cassiopeian (sLsLsLsLs) mode, and represented by a circle of generators going as follows: ...C# - A# - H# - F# - D - B - J - G - E - C - A - H - F - Db - Bb - Jb - Gb...

Examples

9edt (equalized):

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

13edt (Bohlen-Pierce):

0 1 2 3 4 5 6 7 8 9 10 11 12 13
E F F#, Gb G H H#, Jb J A A#, Bb B C Db, C# D E
P0 m1 M1 P2 m3 M3, m4 M4 m5 M5, m6 M6 P7 m8 M8 P9

30edt:

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 25 26 27 28 29 30
E D#, Gbb F E# Gb F# Hb G Fx, Jbb H G# Jb H# Ab J Hx, Bbb A J# Bb A# Cb B Ax, Dbb C B# Db C# Eb D Fb, Cx E
P0 MM8, dd2 m1 A0 d2 M1 mm3 P2 MM1, mm4 m3 A2 m4 M3 mm5 M4 MM3, mm6 m5 MM4 m6 M5 d7 M6 MM5, mm8 P7 MM6 m8 A7 d9 M8 mm1, AA7 P9
  1. ↑ [1]
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