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| There are infinite possible intervals (both tempered and just), even within a single [[2/1|octave]]. It can be helpful to group these intervals into a finite number of '''interval regions''' or '''interval categories'''. | | 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'''. |
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| == Concrete regions vs abstract categories == | | == Concrete regions vs abstract categories == |
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| {{Main|Extended-diatonic interval names}} | | {{Main|Extended-diatonic interval names}} |
| Many interval naming systems extend the diatonic interval names by adding new [[interval qualities]] to the usual set. While some systems preserve the fifth-based structure entirely, other systems define regions based on the proximity to the intervals associated with the diatonic intervals, which are then divided into finer subregions. | | Many interval naming systems extend the diatonic interval names by adding new [[interval qualities]] to the usual set. While some systems preserve the fifth-based structure entirely, other systems define regions based on the proximity to the intervals associated with the diatonic intervals, which are then divided into finer subregions. |
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| == Latitude ==
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| When describing interval regions in terms of size relative to a (possibly tempered) fifth, it leads to the system of [[Latitude|latitude and medial intervals]].
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| == Schulter system == | | == Schulter system == |
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| <pre>Pure unison (1:1) 0 cents
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| Commas 0-30 cents (Section 11)
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| Dieses 30-60 cents (Section 11)
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| Minor seconds 60-125 cents (Section 5)
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| small 60-80 cents
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| middle 80-100 cents
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| large 100-125 cents
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| Neutral seconds 125-170 cents (Section 6)
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| small 125-135 cents
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| middle 135-160 cents
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| large 160-170 cents
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| Equable heptatonic
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| (heartland range) 160-182 cents (Section 12)
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| Major seconds
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| (or tones) 180-240 cents (Section 4)
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| small 180-200 cents
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| middle 200-220 cents
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| large 220-240 cents
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| Interseptimal
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| (Maj2-min3) 240-260 cents (Section 9)
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| Minor thirds 260-330 cents (Section 2)
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| small 260-280 cents
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| middle 280-300 cents
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| large 300-330 cents
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| Neutral thirds 330-372 cents (Section 3)
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| small 330-342 cents
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| middle 342-360 cents
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| large 360-372 cents
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| Major thirds 372-440 cents (Section 2)
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| small 372-400 cents
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| middle 400-423 cents
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| large 423-440 cents
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| Interseptimal 440-468 cents (Section 9)
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| (Maj3-4)
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| Perfect fourths 468-528 cents (Section 7)
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| small 468-491 cents
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| middle 491-505 cents
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| large 505-523 cents
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| Superfourths 528-560 cents (Section 10)
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| Tritonic region 560-640 cents (Section 8)
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| small 560-577 cents
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| middle 577-623 cents
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| large 623-640 cents
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| Subfifths 640-672 cents (Section 10)
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| Perfect fifths 672-732 cents (Section 7)
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| small 672-695 cents
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| middle 695-709 cents
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| large 709-732 cents
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| Interseptimal 732-760 cents (Section 9)
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| (5-min6)
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| Minor sixths 760-828 cents (Section 2)
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| small 760-777 cents
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| middle 777-800 cents
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| large 800-828 cents
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| Neutral sixths 828-870 cents (Section 3)
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| small 828-840 cents
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| middle 840-858 cents
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| large 858-870 cents
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| Major sixths 870-940 cents (Section 2)
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| small 870-900 cents
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| middle 900-920 cents
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| large 920-940 cents
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| Interseptimal 940-960 cents (Section 9)
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| (Maj6-min7)
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| Minor sevenths 960-1025 cents (Section 4)
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| small 960-987 cents
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| middle 987-1000 cents
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| large 1000-1025 cents
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| Equable heptatonic 1018-1040 cents (Section 12)
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| (heartland range)
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| Neutral sevenths 1030-1075 cents (Section 6)
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| small 1030-1043 cents
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| middle 1043-1065 cents
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| large 1065-1075 cents
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| Major sevenths 1075-1140 cents (Section 5)
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| small 1075-1100 cents
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| middle 1100-1120 cents
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| large 1120-1140 cents
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| Octave less diesis 1140-1170 cents (Section 11)
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| Octave less comma 1170-1200 cents (Section 11)
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| Pure octave (2:1) 1200 cents</pre>
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| == See also == | | == See also == |
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| * [[Mike Sheiman's Alternative Interval Categorizations]] | | * [[Mike Sheiman's Alternative Interval Categorizations]] |
| * [[SKULO interval names]] | | * [[SKULO interval names]] |
| * [[User:VectorGraphics/Walker brightness notation]] | | * [[User:VectorGraphics/Walker brightness notation|Walker brightness notation]] |
| * [[5L 2s/Interval categories]] | | * [[5L 2s/Interval categories]] |
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| * [[Gallery of just intervals]] | | * [[Gallery of just intervals]] |
| * [[Universal solfege]] - [[solfege]] based on the Schulter system | | * [[Universal solfege]] - [[solfege]] based on the Schulter system |
| | * [[User:VectorGraphics/Latitude]] |
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| [[Category:Interval regions| ]] | | [[Category:Interval regions| ]] |