“Interval class”的意思、由来-开放百科全书

词条

Interval class

释义

Use of interval classes
Notation of interval classes
Table of interval class equivalencies
See also
Sources
Further reading
External links

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'" ({{harvnb|Rahn|1980|loc=29}}; {{harvnb|Whittall|2008|loc=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.

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: {{Audio|Octatonic_ic7.ogg|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 (a, b) may be defined as

where i <a, b> is an ordered pitch-class interval {{harv|Rahn|1980|loc=28}}.

While notating unordered intervals with parentheses, as in the example directly above, is perhaps the standard, some theorists, including Robert {{harvtxt|Morris|1991}}, prefer to use braces, as in i {a,b}. 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

Sources

{{wikicite|ref={{harvid|Morris|1991}}|reference=Morris, Robert (1991). Class Notes for Atonal Music Theory. Hanover, NH: Frog Peak Music.}}
{{wikicite|ref={{harvid|Rahn|1980}}|reference=Rahn, John (1980). Basic Atonal Theory. {{ISBN|0-02-873160-3}}.}}
{{wikicite|ref={{harvid|Whittall|2008}}|reference=Whittall, Arnold (2008). The Cambridge Introduction to Serialism. New York: Cambridge University Press. {{ISBN|978-0-521-68200-8}} (pbk).}}

External links

Solomon's Set Theory Primer

1 : Musical set theory

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Use of interval classes

Notation of interval classes

Table of interval class equivalencies

See also

Sources

Further reading

External links