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In this chromatic transposition, the melody on the first line is in the key of D, while the melody on the second line is identical except that it is a major third lower, in the key of B ♭. In music, transposition refers to the process or operation of moving a collection of notes (pitches or pitch classes) up or down in pitch by a constant ...
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 .
In diatonic set theory the common tone theorem explains that scales possessing the deep scale property share a different number of common tones, not counting enharmonic equivalents (for example, C ♯ and C ♭ have no common tones with C major), for every different transposition of the scale.
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.
A set class (an abbreviation of pitch-class-set class) in music theory is an ascending collection of pitch classes, transposed to begin at zero. For a list of ordered collections, see: list of tone rows and series. Sets are listed with links to their complements. The prime form of unsymmetrical sets is marked "A".
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 .
Music theory is the study of theoretical frameworks for understanding the practices and possibilities ... Such transposition raises or lowers the overall pitch range ...