Interval region
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.
Concrete regions vs abstract categories
An interval region usually implies it is concrete, defined by concrete boundaries of interval sizes. The boundaries are usually fuzzy to allow some vagueness, in line with how we perceive them. Which region an interval falls into solely depends on the interval's size.
An interval category is usually meant to be abstract. It uses some mapping to determine which category an interval falls into, short-circuiting the question of where exactly to place the boundaries. It also takes account of an interval's prime components, allowing us to find a composite interval's category through interval arithmetic.
The diatonic interval category system commonly used to categorize JI intervals consists of a quality and a diatonic scale degree.
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.
Latitude
When describing interval regions in terms of size relative to a (possibly tempered) fifth, it leads to the system of latitude and medial intervals.
Schulter system
Margo Schulter describes her system for categorizing intervals in Regions of the Interval Spectrum, which begins:
- In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature.
Schulter proposes the following categories and gives a tentative range of cents values for intervals that fall within those categories. In Regions, she points out, "A main caution is that the borders are inevitably 'fuzzy,' so that one region shades into another and suggested values in cents are more illustrative than definitive."
| Interval Category | Approx. Cents Ranges | sub-category | |
|---|---|---|---|
| Pure Unison (1:1) | 0 | ||
| Commas | 0-30 | ||
| Dieses | 30-60 | ||
| Minor Seconds | 60-125 | small | 60-80 |
| middle | 80-100 | ||
| large | 100-125 | ||
| Neutral Seconds | 125-170 | small | 125-135 |
| middle | 135-160 | ||
| large | 160-170 | ||
| Equable Heptatonic | 160-182 | ||
| Major Seconds | 180-240 | small | 180-200 |
| middle | 200-220 | ||
| large | 220-240 | ||
| Interseptimal (Maj2-min3) | 240-260 | ||
| Minor Thirds | 260-330 | small | 260-280 |
| middle | 280-300 | ||
| large | 300-330 | ||
| Neutral Thirds | 330-372 | small | 330-342 |
| middle | 342-360 | ||
| large | 360-372 | ||
| Major Thirds | 372-440 | small | 372-400 |
| middle | 400-423 | ||
| large | 423-440 | ||
| Interseptimal (Maj3-4) | 440-468 | ||
| Perfect Fourths | 468-528 | small | 468-491 |
| middle | 491-505 | ||
| large | 505-528 | ||
| Superfourths | 528-560 | ||
| Tritonic Region | 560-640 | small | 560-577 |
| middle | 577-623 | ||
| large | 623-640 | ||
| Subfifths | 640-672 | ||
| Perfect Fifths | 672-732 | small | 672-695 |
| middle | 695-709 | ||
| large | 709-732 | ||
| Interseptimal (5-min6) | 732-760 | ||
| Minor Sixths | 760-828 | small | 760-777 |
| middle | 777-800 | ||
| large | 800-828 | ||
| Neutral Sixths | 828-870 | small | 828-840 |
| middle | 840-858 | ||
| large | 858-870 | ||
| Major Sixths | 870-940 | small | 870-900 |
| middle | 900-920 | ||
| large | 920-940 | ||
| Interseptimal (Maj6-min7) | 940-960 | ||
| Minor Sevenths | 960-1025 | small | 960-987 |
| middle | 987-1000 | ||
| large | 1000-1025 | ||
| Equable Heptatonic | 1018-1040 | ||
| Neutral Sevenths | 1030-1075 | small | 1030-1043 |
| middle | 1043-1065 | ||
| large | 1065-1075 | ||
| Major Sevenths | 1075-1140 | small | 1075-1100 |
| middle | 1100-1120 | ||
| large | 1120-1140 | ||
| Octave less diesis | 1140-1170 | ||
| Octave less comma | 1170-1200 | ||
| Pure Octave (2:1) | 1200 | ||
See also
- Interval region naming schemes
- Mike Sheiman's Alternative Interval Categorizations
- SKULO interval names
- Walker brightness notation
- 5L 2s/Interval categories
- Other related concepts
- Supermajor and subminor
- Interval size measure
- Table of MOSes
- Gallery of just intervals
- Universal solfege - solfege based on the Schulter system