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Intervals may be labelled according their pitch ratios, as is commonly used in just intonation. Intervals may also be labelled according to their diatonic functionality, as is commonly done for tonal music, and according to the number of notes they span in a diatonic scale. The interval of a note from its tonic is its scale degree, thus the fifth degree of a scale is a fifth from its tonic. For atonal music, such as that written using the twelve tone technique or serialism, integer notation is often used, such as in musical set theory. Finally, it is also possible to label intervals using the logarithmic measure of centss, as is used to compare other intervals with those of twelve tone equal temperament.
Intervals may also be described as narrow and wide or small and large, consonant and dissonant or stable and unstable, simple interval and compound interval, and, if melodic, as steps or skips. Simple intervals are those which lie within an octave and compound are those which are larger than a single octave. Thus a tenth is known as a compound third. Finally, intervals may be labelled with or modified by the addition of perfect, major, minor, augmented, and diminished before the number of notes apart (for instance, augmented fourth). Perfect intervals are never major or minor and major and minor intervals are never perfect. Major and minor intervals are one semitone above, or below, their minor and major counterparts, respectively (see minor second below). Augmented and diminished intervals are raised or lowered a step and any interval may be augmented or diminished and may even be double augmented or diminished.
It is important to note that while intervals named by their harmonic functions, for instance, a major second, may be described by a ratio, cent, or integer, not every interval described by these more general terms may be described with the harmonic function name. For instance, all major seconds (in twelve tone equal temperament) are 200 cents, but not every interval of 200 cents is a major second. See: enharmonic.
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2 Ordered and unordered pitch and pitch class intervals 3 Non-equal temperament intervals |
In atonal or musical set theory there are numerous types of intervals, the first being ordered pitch interval, the distance between two pitches upward or downward. For instance, the interval from C to G upward is 7, but the interval from G to C downward is -7. Using integer notation and modulo 12, ordered pitch interval, ip, may be defined, for any two pitches x and y, as:
One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, similar to the interval of tonal theory. This may be defined as:
For unordered pitch class interval see interval class.
Simple diatonic intervals
Below are listed the most commonly used harmonic function, ratio, integer, cents, and relative consonance or dissonance of common diatonic simple intervals. There are other intervals and ratios, some of which follow.Common simple intervals
Augmented and diminished intervals
Along with all seconds and sevenths, all augmented and diminished intervals are considered dissonant. However, in twelve tone equal temperament, most intervals, when augmented or diminished, are enharmonically equivalent to another interval. For example, a diminished minor second is a unison and thus only the fourth and fifth are commonly altered.
Ordered and unordered pitch and pitch class intervals
and:
the other way.
The interval between pitch classes may be measured with ordered and unordered pitch class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. Thus the ordered pitch class interval, i<x,y>, may be defined as:
mod 12, of course.Non-equal temperament intervals
There are also a number of intervals not found in the chromatic scale which have names of their own. These intervals describe small discrepancies between notes tuned according to the tuning systems used. Most of the following intervals may be described as microtones.
For the mathematical use of the word "interval", see interval (mathematics).\n