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In many musical contexts, transpositionally equivalent chords are thought to be similar. Transpositional equivalence is a feature of musical set theory. The terms transposition and transposition equivalence allow the concept to be discussed as both an operation and relation, an activity and a state of being.
Modes of limited transposition are musical modes or scales that fulfill specific criteria relating to their symmetry and the repetition of their interval groups. These scales may be transposed to all twelve notes of the chromatic scale , but at least two of these transpositions must result in the same pitch classes , thus their transpositions ...
Although musical set theory is often thought to involve the application of mathematical set theory to music, there are numerous differences between the methods and terminology of the two. For example, musicians use the terms transposition and inversion where mathematicians would use translation and reflection.
Transformations include multiplication, rotation, permutation (i.e. transposition, inversion, and retrograde), prolation (augmentation, diminution) and combinations thereof. Transformations may also be applied to simpler or more complex variables such as interval and spectrum or timbre .
Common tones between G major and C major and between C major and F ♯ major, 6 and 1 common tones respectively.. A common tone is a pitch class that is a member of, or common to, a musical scale and a transposition of that scale, as in modulation. [1]
Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo , chord progression , form , and meter . The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory , abstract algebra and number theory .
Thematic transformation (also known as thematic metamorphosis or thematic development) is a musical technique in which a leitmotif, or theme, is developed by changing the theme by using permutation (transposition or modulation, inversion, and retrograde), augmentation, diminution, and fragmentation.
A variety of musical terms are encountered in printed scores, music reviews, and program notes. Most of the terms are Italian, in accordance with the Italian origins of many European musical conventions. Sometimes, the special musical meanings of these phrases differ from the original or current Italian meanings.