User:CompactStar/Ordinal interval notation: Difference between revisions

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CompactStar (talk | contribs)
5,020 edits
CompactStar (talk | contribs)
5,020 edits
Quartertone-based names will be adopted, so neutral intervals are correctly expressed.
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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.
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.


== 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:
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"
{|class="wikitable"
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|-
|-
|[[11/8]]
|[[11/8]]
|P4
|U4
|perfect fourth
|ultrafourth
|-
|-
|[[13/8]]
|[[13/8]]
|m6
|an6
|minor sixth
|artoneutral sixth
|-
|-
|[[17/16]]
|[[17/16]]
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|augmented fourth
|augmented fourth
|-
|-
|[[29/16]]
|[[11/616]]
|m7
|an7
|minor seventh
|artoneutral seventh
|-
|-
|[[31/16]]
|[[31/16]]
|P8
|i8
|perfect octave
|infraoctave
|-
|-
|
|
|}
|}

Revision as of 08:54, 30 December 2023

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.

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 U4 ultrafourth
13/8 an6 artoneutral sixth
17/16 m2 minor second
19/16 m3 minor third
23/16 A4 augmented fourth
11/616 an7 artoneutral seventh
31/16 i8 infraoctave
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