User:CompactStar/Ordinal interval notation: Difference between revisions

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Indexed interval notation is a notation for [[just intonation]] in which all intervals are represented by a normal interval category combined with a ordinal number or index. An index of 1 is used for the simplest interval in a category, an index of 2 is used for the second-simplest, an index of 3 is used for the third-simplest, and so on.
Indexed interval notation is a notation for [[just intonation]] in which all intervals are represented by a normal interval classification combined with a ordinal number or index. An index of 1 is used for the simplest interval in an interval class (such as [[6/5]] for minor thirds), an index of 2 is used for the second-simplest, an index of 3 is used for the third-simplest, and so on.
 
== Definition ==
To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:
{|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]]
|P4
|perfect fourth
|-
|[[13/8]]
|m6
|minor sixth
|-
|[[17/16]]
|m2
|minor second
|-
|[[19/16]]
|m3
|minor third
|-
|[[23/16]]
|A4
|augmented fourth
|-
|[[29/16]]
|m7
|minor seventh
|-
|[[31/16]]
|P8
|perfect octave
|-
|
|}

Revision as of 02:37, 2 November 2023

Indexed interval notation is a notation for just intonation in which all intervals are represented by a normal interval classification combined with a ordinal number or index. An index of 1 is used for the simplest interval in an interval class (such as 6/5 for minor thirds), an index of 2 is used for the second-simplest, an index of 3 is used for the third-simplest, and so on.

Definition

To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:

Prime harmonic Interval classification
2/1 P8 perfect octave
3/2 P5 perfect fifth
5/4 M3 major third
7/4 m7 minor seventh
11/8 P4 perfect fourth
13/8 m6 minor sixth
17/16 m2 minor second
19/16 m3 minor third
23/16 A4 augmented fourth
29/16 m7 minor seventh
31/16 P8 perfect octave
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