Set (music) in the context of "Igor Stravinsky"

Free dance is a 20th-century dance form that preceded modern dance. Rebelling against the rigid constraints of classical ballet, Loie Fuller, Isadora Duncan and Ruth St. Denis (with her work in theater) developed their own styles of free dance and laid the foundations of American modern dance with their choreography and teaching. In Europe, Rudolf Laban, Emile Jaques-Dalcroze and François Delsarte developed their own theories of human movement and methods of instruction that led to the development of European modern and Expressionist dance.

Free dance was prolific in Central and Eastern Europe, where national schools were created, such as the School of Musical Movement (Heptachor), in Russia, and the Orkesztika School, in Hungary.

In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Important to musical set theory, a pitch class is "all pitches related to each other by octave, enharmonic equivalence, or both." Thus, using scientific pitch notation, the pitch class "C" is the set

Although there is no formal upper or lower limit to this sequence, only a few of these pitches are audible to humans. Pitch class is important because human pitch-perception is periodic: pitches belonging to the same pitch class are perceived as having a similar quality or color, a property called "octave equivalence".

In music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though some of his contemporaries were also working to establish serialism as a form of post-tonal thinking. Twelve-tone technique orders the twelve notes of the chromatic scale, forming a row or series and providing a unifying basis for a composition's melody, harmony, structural progressions, and variations. Other types of serialism also work with sets, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called "parameters"), such as duration, dynamics, and timbre.

The idea of serialism is also applied in various ways in the visual arts, design, and architecture, and the musical concept has also been adapted in literature.

In music, a common tone is a pitch class that is a member of, or common to (shared by) two or more chords or sets. Typically, it refers to a note shared between two chords in a chord progression. According to H.E. Woodruff:

The example below shows the seven diatonic triads of C major. The common tones between the tonic triad and the other six triads are highlighted in blue. As Woodruff describes, the tonic triad shares no common tones with either II and VII (consecutive to I), one common tone with IV and V (four and five degrees from I) each, and two common tones with III and VI (three and six degrees from I) each.

In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates (all twelve tones). Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively."

Combinatoriality is a side effect of derived rows, where the initial segment or set may be combined with its transformations (T,R,I,RI) to create an entire row. "Derivation refers to a process whereby, for instance, the initial trichord of a row can be used to arrive at a new, 'derived' row by employing the standard twelve-tone operations of transposition, inversion, retrograde, and retrograde-inversion."

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music, drawing on the twelve-tone theory of Milton Babbitt. The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that.

One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, melodic inversion, and complementation. Some theorists apply the methods of musical set theory to the analysis of rhythm as well.

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 interval.

For example, a music transposer might transpose an entire piece of music into another key. Similarly, one might transpose a tone row or an unordered collection of pitches such as a chord so that it begins on another pitch.