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

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WIP (the reason this is in userspace)
WIP (the reason this is in userspace)


Ordinal interval notation is a notation for [[just intonation]] in which all intervals are represented by a normal interval classification combined with an ordinal number.
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 added to a Pythagorean classification based on a {{w|binary search}} to name all non-Pythagorean intervals.


To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:
In order to map all intervals into 3-limit notation, each prime harmonic is mapped to
{|class="wikitable"
|-
!Prime harmonic
!colspan="2"|Interval classification
|-
|[[2/1]]
|P8
|perfect octave
|-
|[[3/2]]
|P5
|perfect fifth
|-
|[[5/4]]
|M3
|major third
|-
|[[7/4]]
|m7
|minor seventh
|-
|[[11/8]]
|U4
|ultrafourth
|-
|[[13/8]]
|an6
|artoneutral sixth
|-
|[[17/16]]
|m2
|minor second
|-
|[[19/16]]
|m3
|minor third
|-
|[[23/16]]
|i5
|infrafifth
|-
|[[29/16]]
|m7
|minor seventh
|-
|[[31/16]]
|i8
|infraoctave
|-
|[[37/32]]
|UM2
|ultramajor second
|-
|[[41/32]]
|M3
|major third
|-
|[[47/32]]
|i5
|infrafifth
|}

Revision as of 03:29, 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 (L) and rights (R) that are added to a Pythagorean classification based on a binary search to name all non-Pythagorean intervals.

In order to map all intervals into 3-limit notation, each prime harmonic is mapped to

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