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Interval region: Difference between revisions

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rewrote first paragraph. →Schulter system: grouped subregions by region
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It is well-known that there are infinite possible intervals, even if one confines one's view to a single octave. This includes the rational intervals of [[just intonation]] and the irrational intervals of [[EDO]]s, [[edonoi]]s, and other systems. However, it is helpful to consider '''interval regions''' (or '''interval categories'''), which there may be a finite number to consider.
There are infinite possible intervals (both tempered and just), even within a single octave. It can be helpful to group these intervals into a finite number of '''interval regions''' (or '''interval categories''').


== Extended-diatonic interval names ==
== Extended-diatonic interval names ==
Line 18: Line 18:
|-
|-
! | Interval Category
! | Interval Category
! | Associated Ranges of Cents Values (borders are "fuzzy")
! | Approx. Cents Ranges
! colspan="2" |sub-category
|-
|-
| | [[Unison|Pure Unison]] (1:1)
| | [[Unison|Pure Unison]] (1:1)
| | 0
| | 0
|
|
|-
|-
| | [[Comma]]s
| | [[Comma]]s
| | 0-30
| | 0-30
|
|
|-
|-
| | [[Diesis|Dieses]]
| | [[Diesis|Dieses]]
| | 30-60
| | 30-60
|
|
|-
|-
| | [[Minor second|Minor Second]]s
| rowspan="3"| [[Minor second|Minor Second]]s
| | 60-125
| rowspan="3"| 60-125
|small
|60-80
|-
|-
| | *small
|middle
| | 60-80
|80-100
|-
|-
| | *middle
|large
| | 80-100
|100-125
|-
|-
| | *large
| rowspan="3"|[[Neutral second|Neutral Second]]s
| | 100-125
| rowspan="3"| 125-170
|small
|125-135
|-
|-
| | [[Neutral second|Neutral Second]]s
|middle
| | 125-170
|135-160
|-
|-
| | *small
|large
| | 125-135
|160-170
|-
|-
| | *middle
| |[[Equable heptatonic|Equable Heptatonic]]
| | 135-160
|-
| | *large
| | 160-170
|-
| | [[Equable heptatonic|Equable Heptatonic]]
| | 160-182
| | 160-182
|
|
|-
|-
| | [[Major second|Major Second]]s
| rowspan="3"|[[Major second|Major Second]]s
| | 180-240
| rowspan="3"| 180-240
|-
|small
| | *small
|180-200
| | 180-200
|-
|-
| | *middle
|middle
| | 200-220
|200-220
|-
|-
| | *large
|large
| | 220-240
|220-240
|-
|-
| | [[Interseptimal interval|Interseptimal]] (Maj2-min3)
| |[[Interseptimal interval|Interseptimal]] (Maj2-min3)
| | 240-260
| | 240-260
|
|
|-
|-
| | [[Minor third|Minor Third]]s
| rowspan="3"|[[Minor third|Minor Third]]s
| | 260-330
| rowspan="3"| 260-330
|-
|small
| | *small
|260-280
| | 260-280
|-
| | *middle
| | 280-300
|-
| | *large
| | 300-330
|-
|-
| | [[Neutral third|Neutral Third]]s
|middle
| | 330-372
|280-300
|-
|-
| | *small
|large
| | 330-342
|300-330
|-
|-
| | *middle
| rowspan="3"| [[Neutral third|Neutral Third]]s
| | 342-360
|  rowspan="3"| 330-372
|small
|330-342
|-
|-
| | *large
|middle
| | 360-372
|342-360
|-
|-
| | [[Major third|Major Third]]s
|large
| | 372-440
|360-372
|-
|-
| | *small
| rowspan="3"|[[Major third|Major Third]]s
| | 372-400
|  rowspan="3"| 372-440
|small
|372-400
|-
|-
| | *middle
|middle
| | 400-423
|400-423
|-
|-
| | *large
|large
| | 423-440
|423-440
|-
|-
| | [[Interseptimal interval|Interseptimal]] (Maj3-4)
| |[[Interseptimal interval|Interseptimal]] (Maj3-4)
| | 440-468
| | 440-468
|
|
|-
|-
| | [[Perfect fourth|Perfect Fourth]]s
| rowspan="3"|[[Perfect fourth|Perfect Fourth]]s
| | 468-528
| rowspan="3"| 468-528
|-
|small
| | *small
|468-491
| | 468-491
|-
|-
| | *middle
|middle
| | 491-505
|491-505
|-
|-
| | *large
|large
| | 505-528
|505-528
|-
|-
| | [[Superfourth]]s
| |[[Superfourth]]s
| | 528-560
| | 528-560
|
|
|-
|-
| | [[Tritone|Tritonic Region]]
| rowspan="3"|[[Tritone|Tritonic Region]]
| | 560-640
| rowspan="3"| 560-640
|-
|small
| | *small
|560-577
| | 560-577
|-
|-
| | *middle
|middle
| | 577-623
|577-623
|-
|-
| | *large
|large
| | 623-640
|623-640
|-
|-
| | [[Subfifth]]s
| |[[Subfifth]]s
| | 640-672
| | 640-672
|
|
|-
|-
| | [[Perfect fifth|Perfect Fifth]]s
| rowspan="3"|[[Perfect fifth|Perfect Fifth]]s
| | 672-732
| rowspan="3"| 672-732
|-
|small
| | *small
|672-695
| | 672-695
|-
|-
| | *middle
|middle
| | 695-709
|695-709
|-
|-
| | *large
|large
| | 709-732
|709-732
|-
|-
| | [[Interseptimal interval|Interseptimal]] (5-min6)
| | [[Interseptimal interval|Interseptimal]] (5-min6)
| | 732-760
| | 732-760
|
|
|-
|-
| | [[Minor sixth|Minor Sixth]]s
| rowspan="3"|[[Minor sixth|Minor Sixth]]s
| | 760-828
| rowspan="3"| 760-828
|-
|small
| | *small
|760-777
| | 760-777
|-
| | *middle
| | 777-800
|-
| | *large
| | 800-828
|-
|-
| | [[Neutral sixth|Neutral Sixth]]s
|middle
| | 828-870
|777-800
|-
|-
| | *small
|large
| | 828-840
|800-828
|-
|-
| | *middle
| rowspan="3"|[[Neutral sixth|Neutral Sixth]]s
| | 840-858
|  rowspan="3"| 828-870
|small
|828-840
|-
|-
| | *large
|middle
| | 858-870
|840-858
|-
|-
| | [[Major sixth|Major Sixth]]s
|large
| | 870-940
|858-870
|-
|-
| | *small
| rowspan="3"|[[Major sixth|Major Sixth]]s
| | 870-900
|  rowspan="3"| 870-940
|small
|870-900
|-
|-
| | *middle
|middle
| | 900-920
|900-920
|-
|-
| | *large
|large
| | 920-940
|920-940
|-
|-
| | [[Interseptimal interval|Interseptimal]] (Maj6-min7)
| | [[Interseptimal interval|Interseptimal]] (Maj6-min7)
| | 940-960
| | 940-960
|
|
|-
|-
| | [[Minor seventh|Minor Seventh]]s
| rowspan="3"|[[Minor seventh|Minor Seventh]]s
| | 960-1025
| rowspan="3"| 960-1025
|-
|small
| | *small
|960-987
| | 960-987
|-
|-
| | *middle
|middle
| | 987-1000
|987-1000
|-
|-
| | *large
|large
| | 1000-1025
|1000-1025
|-
|-
| | [[Equable heptatonic|Equable Heptatonic]]
| | [[Equable heptatonic|Equable Heptatonic]]
| | 1018-1040
| | 1018-1040
|
|
|-
|-
| | [[Neutral seventh|Neutral Seventh]]s
| rowspan="3"|[[Neutral seventh|Neutral Seventh]]s
| | 1030-1075
| rowspan="3"| 1030-1075
|-
|small
| | *small
|1030-1043
| | 1030-1043
|-
| | *middle
| | 1043-1065
|-
|-
| | *large
|middle
| | 1065-1075
|1043-1065
|-
|-
| | [[Major seventh|Major Seventh]]s
|large
| | 1075-1140
|1065-1075
|-
|-
| | *small
| rowspan="3"| [[Major seventh|Major Seventh]]s
| | 1075-1100
|  rowspan="3"| 1075-1140
|small
|1075-1100
|-
|-
| | *middle
|middle
| | 1100-1120
|1100-1120
|-
|-
| | *large
|large
| | 1120-1140
|1120-1140
|-
|-
| | Octave less diesis
| | Octave less diesis
| | 1140-1170
| | 1140-1170
|
|
|-
|-
| | Octave less comma
| | Octave less comma
| | 1170-1200
| | 1170-1200
|
|
|-
|-
| | [[Octave|Pure Octave]] (2:1)
| | [[Octave|Pure Octave]] (2:1)
| | 1200
| | 1200
|
|
|}
|}


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