4L 5s (3/1-equivalent): Difference between revisions

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== Notation ==
== Notation ==
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.
Bohlen-Pierce theory possesses a well-established [[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.


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...
This notation uses 9 nominals: for compatibility with [[diamond-MOS notation]], the current recommendation is to use the notes J K L M N O P Q R J as presented in the J Cassiopeian (symmetric, sLsLsLsLs) mode, and represented by a circle of generators going as follows: ...Q# - O# - M# - K# - R - P - N - L - J - Q - O - M - K - Rb - Pb - Nb - Lb... However, an alternative convention (as used on Wikipedia <ref>[https://en.wikipedia.org/wiki/Bohlen%E2%80%93Pierce_scale#Intervals_and_scale_diagrams]</ref> and certain articles of this wiki) labels them C D E F G H J A B C in the C Andromedan (LssLsLsLs) mode, which rotates to the E Cassiopeian mode.
An extension of [[ups and downs notation]], in the obvious way, can be found at [[Lambda ups and downs notation]].


=== Examples ===
=== Examples ===
[[9edt]] (equalized):
[[9edt]] (equalized):
{|class="wikitable article-table"
{|Qlass="wikitable article-table"
|-
|-
!0
!0
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!9
!9
|-
|-
|E
|F
|G
|H
|J
|J
|A
|K
|B
|L
|C
|M
|D
|N
|E
|O
|P
|Q
|R
|J
|-
|-
|P0
|P0
Line 65: Line 66:
[[13edt]] (Bohlen-Pierce):
[[13edt]] (Bohlen-Pierce):


{|class="wikitable article-table"
{|Qlass="wikitable article-table"
|-
|-
!0
!0
Line 82: Line 83:
!13
!13
|-
|-
|E
|F
|F#, Gb
|G
|H
|H#, Jb
|J
|J
|A
|K
|A#, Bb
|K#, Gb
|B
|L
|C
|M
|Db, C#
|M#, Jb
|D
|N
|E
|O
|O#, Bb
|P
|Q
|Rb, C#
|R
|J
|-
|-
|P0
|P0
Line 115: Line 116:
[[30edt]]:
[[30edt]]:


{|class="wikitable article-table"
{|Qlass="wikitable article-table"
|-
|-
!0
!0
Line 149: Line 150:
!30
!30
|-
|-
|E
|J
|D#, Gbb
|R#, Gbb
|F
|K
|E#
|J#
|Gb
|Lb
|F#
|K#
|Hb
|Mb
|G
|L
|Fx, Jbb
|Kx, Jbb
|H
|M
|G#
|L#
|Nb
|M#
|Ob
|N
|Mx, Bbb
|O
|N#
|Pb
|O#
|Qb
|P
|Ox, Dbb
|Q
|P#
|Rb
|Q#
|Jb
|Jb
|H#
|R
|Ab
|Kb, Cx
|J
|J
|Hx, Bbb
|A
|J#
|Bb
|A#
|Cb
|B
|Ax, Dbb
|C
|B#
|Db
|C#
|Eb
|D
|Fb, Cx
|E
|-
|-
|P0
|P0