Interval class


In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'" (Rahn 1980, 29; Whittall 2008, 273–74), is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 ≡ 7 (mod 12). See modular arithmetic for more on modulo 12. The largest interval class is 6 since any greater interval n may be reduced to 12 − n.

Contents

Use of interval classes


The concept of interval class accounts for octave, enharmonic, and inversional equivalency. Consider, for instance, the following passage:

(To hear a MIDI realization, click the following: 106 KB 

In the example above, all four labeled pitch-pairs, or dyads, share a common "intervallic color." In atonal theory, this similarity is denoted by interval class—ic 5, in this case. Tonal theory, however, classifies the four intervals differently: interval 1 as perfect fifth; 2, perfect twelfth; 3, diminished sixth; and 4, perfect fourth.

Notation of interval classes


The unordered pitch class interval i(ab) may be defined as

\({\displaystyle i(a,b)={\text{ the smaller of }}i\langle a,b\rangle {\text{ and }}i\langle b,a\rangle ,}\)

where iab⟩ is an ordered pitch-class interval (Rahn 1980, 28).

While notating unordered intervals with parentheses, as in the example directly above, is perhaps the standard, some theorists, including Robert Morris (1991), prefer to use braces, as in i{ab}. Both notations are considered acceptable.

Table of interval class equivalencies


Interval Class Table
ic included intervals tonal counterparts extended intervals
0 0 unison and octave diminished 2nd and augmented 7th
1 1 and 11 minor 2nd and major 7th augmented unison and diminished octave
2 2 and 10 major 2nd and minor 7th diminished 3rd and augmented 6th
3 3 and 9 minor 3rd and major 6th augmented 2nd and diminished 7th
4 4 and 8 major 3rd and minor 6th diminished 4th and augmented 5th
5 5 and 7 perfect 4th and perfect 5th augmented 3rd and diminished 6th
6 6 augmented 4th and diminished 5th

See also


Sources


Further reading









Categories: Musical set theory




Information as of: 12.06.2021 11:55:57 CEST

Source: Wikipedia (Authors [History])    License : CC-BY-SA-3.0

Changes: All pictures and most design elements which are related to those, were removed. Some Icons were replaced by FontAwesome-Icons. Some templates were removed (like “article needs expansion) or assigned (like “hatnotes”). CSS classes were either removed or harmonized.
Wikipedia specific links which do not lead to an article or category (like “Redlinks”, “links to the edit page”, “links to portals”) were removed. Every external link has an additional FontAwesome-Icon. Beside some small changes of design, media-container, maps, navigation-boxes, spoken versions and Geo-microformats were removed.

Please note: Because the given content is automatically taken from Wikipedia at the given point of time, a manual verification was and is not possible. Therefore LinkFang.org does not guarantee the accuracy and actuality of the acquired content. If there is an Information which is wrong at the moment or has an inaccurate display please feel free to contact us: email.
See also: Legal Notice & Privacy policy.