User:CompactStar/Ordinal interval notation: Difference between revisions

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'''Indexed interval notation''' is a notation for [[just intonation]] devised by [[User:CompactStar|CompactStar]].
'''Indexed interval notation''' is a notation for [[just intonation]] devised by [[User:CompactStar|CompactStar]].


Intervals are represented by a conventional interval category and an index. The index is 1 for the simplest (with respect [[Tenney height]) interval in a category, 2 for the second-simplest, 3 for the third-simplest and so on. For example, [[6/5]] is the 1st minor 3rd and [[7/6]] is the 2nd minor 3rd. To get the category of an interval, multiply the categories of the prime harmonics which it factors into, which are predefined as follows:
Intervals are represented by a normal interval category (like minor 3rd, perfect 4th or etc.) and an index. The index is 1 for the simplest (with respect [[Tenney height]]) interval in a category, 2 for the second-simplest, 3 for the third-simplest and so on. For example, [[6/5]] is the 1st minor 3rd (1m3) and [[7/6]] is the 2nd minor 3rd (2m3). Note names work the same way, using A as the reference pitch, so the C which is 6/5 above A (528 Hz) is notated as 1C.
{|class="wikitable"
|-
!Prime harmonic
!colspan="3"|Notation
|-
|[[2/1]]
|P8
|perfect octave
|C
|-
|[[3/2]]
|P5
|perfect 5th
|G
|-
|[[5/4]]
|M3
|major 3rd
|E
|-
|[[7/4]]
|m7
|minor 7th
|Bb
|-
|[[11/8]]
|P4
|perfect 4th
|F
|-
|[[13/8]]
|m6
|minor 6th
|Ab
|-
|[[17/16]]
|m2
|minor 2nd
|Db
|-
|[[19/16]]
|m3
|minor 3rd
|Eb
|-
|[[23/16]]
|A4
|augmented 4th
|F#
|-
|[[29/16]]
|m7
|minor 7th
|Bb
|-
|[[31/16]]
|P8
|perfect octave
|C
|-
|[[37/32]]
|M2
|major 2nd
|D
|-
|[[41/32]]
|M3
|major 3rd
|E
|-
|[[43/32]]
|P4
|perfect 4th
|F
|-
|[[47/32]]
|P5
|perfect 5th
|G
|-
|[[53/32]]
|M6
|major 6th
|A
|-
|[[61/32]]
|M7
|major 7th
|B
|-
|[[67/64]]
|m2
|minor 2nd
|Db
|-
|[[71/64]]
|M2
|major 2nd
|D
|-
|[[73/64]]
|M2
|major 2nd
|D
|-
|[[79/64]]
|M3
|major 3rd
|E
|-
|[[83/64]]
|P4
|perfect 4th
|F
|-
|[[89/64]]
|d5
|diminished 5th
|Gb
|-
|[[97/64]]
|P5
|perfect 5th
|G
|}

Revision as of 23:51, 1 December 2023

Indexed interval notation is a notation for just intonation devised by CompactStar.

Intervals are represented by a normal interval category (like minor 3rd, perfect 4th or etc.) and an index. The index is 1 for the simplest (with respect Tenney height) interval in a category, 2 for the second-simplest, 3 for the third-simplest and so on. For example, 6/5 is the 1st minor 3rd (1m3) and 7/6 is the 2nd minor 3rd (2m3). Note names work the same way, using A as the reference pitch, so the C which is 6/5 above A (528 Hz) is notated as 1C.

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