Версия от 16:18, 26 марта 2024; EducationBot(обсуждение | вклад)(Новая страница: «{{Английская Википедия/Панель перехода}} {{Short description|Distance between unordered pitch classes}} thumb|275px|right|Interval class {{audio|Interval class.mid|Play}}. In musical set theory, an '''interval class''' (often abbreviated: '''ic'''), also known as '''unordered pitch-class interval''', '''interval distance''', '''undirected interval''', or "(even completely i...»)
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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'" (Шаблон:Harvnb; Шаблон:Harvnb), 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.
(To hear a MIDI realization, click the following: Шаблон:Audio
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 intervali(a, b) may be defined as
<math>i (a,b) =\text{ the smaller of }i \langle a,b\rangle\text{ and }i \langle b,a\rangle,</math>
While notating unordered intervals with parentheses, as in the example directly above, is perhaps the standard, some theorists, including Robert Morris,[1] prefer to use braces, as in i{a, b}. Both notations are considered acceptable.