User:CompactStar/Lefts and rights notation: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
CompactStar (talk | contribs)
5,020 edits
No edit summary
CompactStar (talk | contribs)
5,020 edits
No edit summary
Line 1: Line 1:
WIP (the reason this is in userspace)
WIP (the reason this is in userspace)


Lefts and rights notation is a notation for [[just intonation]] developed by [[User:CompactStar|CompactStar]]. It is a combination of Pythagorean notation and a sequence of lefts (L) and rights (R) that are prepended to a Pythagorean classification based on a {{w|binary search}} to name all non-Pythagorean intervals.
Lefts and rights notation is a notation for [[just intonation]] developed by [[User:CompactStar|CompactStar]]. It is a combination of Pythagorean notation and a sequence of lefts and rights which is based on a {{w|binary search}}.


In order to map all intervals into 3-limit notation, each prime harmonic is mapped to
== Definition ==
In order to map all intervals into Pythagorean intervals, each prime harmonic is mapped to the lowest-complexity Pythagorean interval that is within √([[2187/2048]]) of it (this is similar to the algorithm used by the [[Functional Just System]]). Here are some examples for smaller primes:
{|class="wikitable"
|-
!Prime harmonic
!colspan="3"|Notation
|-
|[[2/1]]
|P8
|perfect octave
|C
|-
|[[3/2]]
|P5
|perfect fifth
|G
|-
|[[5/4]]
|M3
|major third
|E
|-
|[[7/4]]
|m7
|minor seventh
|Bb
|-
|[[11/8]]
|P4
|perfect fourth
|F
|-
|[[13/8]]
|m6
|minor sixth
|Ab
|-
|[[17/16]]
|m2
|minor second
|Db
|-
|[[19/16]]
|m3
|minor third
|Eb
|-
|[[23/16]]
|A4
|augmented fourth
|F#
|-
|[[29/16]]
|m7
|minor seventh
|Bb
|-
|[[31/16]]
|P8
|perfect octave
|C
|-
|[[37/32]]
|M2
|major second
|D
|-
|[[41/32]]
|M3
|major third
|E
|-
|[[43/32]]
|P4
|perfect fourth
|F
|-
|[[47/32]]
|P5
|perfect fifth
|G
|-
|[[53/32]]
|M6
|major sixth
|A
|-
|[[59/32]]
|M7
|major seventh
|B
|-
|[[61/32]]
|M7
|major seventh
|B
|}

Revision as of 03:40, 2 January 2024

WIP (the reason this is in userspace)

Lefts and rights notation is a notation for just intonation developed by CompactStar. It is a combination of Pythagorean notation and a sequence of lefts and rights which is based on a binary search.

Definition

In order to map all intervals into Pythagorean intervals, each prime harmonic is mapped to the lowest-complexity Pythagorean interval that is within √(2187/2048) of it (this is similar to the algorithm used by the Functional Just System). Here are some examples for smaller primes:

Prime harmonic Notation
2/1 P8 perfect octave C
3/2 P5 perfect fifth G
5/4 M3 major third E
7/4 m7 minor seventh Bb
11/8 P4 perfect fourth F
13/8 m6 minor sixth Ab
17/16 m2 minor second Db
19/16 m3 minor third Eb
23/16 A4 augmented fourth F#
29/16 m7 minor seventh Bb
31/16 P8 perfect octave C
37/32 M2 major second D
41/32 M3 major third E
43/32 P4 perfect fourth F
47/32 P5 perfect fifth G
53/32 M6 major sixth A
59/32 M7 major seventh B
61/32 M7 major seventh B
Retrieved from "https://en.xen.wiki/index.php?title=User:CompactStar/Lefts_and_rights_notation&oldid=130317"