|
In post-tonal music theory, identity is similar to identity in universal algebra. An identity function is a permutation or transformation which transforms a pitch or pitch class set into itself. For instance, inverting an augmented triad or C4 interval cycle, 048, produces itself, 084. Performing a retrograde operation upon the pitch class set 01210 produces 01210. In addition to being a property of a specific set, identity is, by extension, the "family" of sets or set forms which satisfy a possible identity. George Perle provides the following example:〔Perle, George (1995). ''The Right Notes: Twenty-Three Selected Essays by George Perle on Twentieth-Century Music'', p.237-238. ISBN 0-945193-37-8.〕 :"C-E, D-F, E-G, are different instances of the same interval ()...() other kind of identity...has to do with axes of symmetry. C-E belongs to a family () of symmetrically related dyads as follows:" C=0, so in mod12: Thus, in addition to being part of the interval-4 family, C-E is also a part of the sum-4 family. ==See also== *Klumpenhouwer network 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Identity (music)」の詳細全文を読む スポンサード リンク
|