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.
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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."
Organum (/ˈɔːrɡənəm/) is, in general, a plainchant melody with at least one added voice to enhance the harmony, developed in the Middle Ages. Depending on the mode and form of the chant, a supporting bass line (or bourdon) may be sung on the same text, the melody may be followed in parallel motion (parallel organum), or a combination of both of these techniques may be employed. As no real independent second voice exists, this is a form of heterophony. In its earliest stages, organum involved two musical voices: a Gregorian chant melody, and the same melody transposed by a consonant interval, usually a perfect fifth or fourth. In these cases the composition often began and ended on a unison, the added voice keeping to the initial tone until the first part has reached a fifth or fourth, from where both voices proceeded in parallel harmony, with the reverse process at the end. Organum was originally improvised; while one singer performed a notated melody (the vox principalis), another singer—singing "by ear"—provided the unnotated second melody (the vox organalis). Over time, composers began to write added parts that were not just simple transpositions, thus creating true polyphony.
In music, imitation is the repetition of a melody in a polyphonic texture shortly after its first appearance in a different voice. The melody may vary through transposition, inversion, or otherwise, but retain its original character. The intervals and rhythms of an imitation may be exact or modified; imitation occurs at varying distances relative to the first occurrence, and phrases may begin with voices in imitation before they freely go their own ways.
Imitation helps provide unity to a composition and is used in forms such as the fugue and canon.
A transposing instrument is a musical instrument for which music notation is not written at concert pitch (concert pitch is the pitch on a non-transposing instrument such as the piano). For example, playing a written middle C on a transposing instrument produces a pitch other than middle C; that sounding pitch identifies the interval of transposition when describing the instrument. Playing a written C on clarinet or soprano saxophone produces a concert B♭ (i.e. B♭ at concert pitch), so these are referred to as B♭ instruments. Providing transposed music for these instruments is a convention of musical notation. The instruments do not transpose the music; rather, their music is written at a transposed pitch. Where chords are indicated for improvisation they are also written in the appropriate transposed form.
For some instruments, a written C sounds as a C but is in a different octave; these instruments are said to transpose "at the octave". Pitches on the double bass sound an octave lower than written, while those on the piccolo and celesta sound an octave higher, and those on the glockenspiel sound two octaves higher.
A transposing piano is a special piano with a mechanism (operated by a pedal or lever) that changes the keyboard position relative to the action (see Development of the modern pianofor details). This transposes (changes the key of) any particular keyboard fingering.
A transposing piano enables a person who knows a composition's fingerings in a certain key but who cannot transpose that composition from one key to another to continue playing in the latter key using the fingerings of the familiar key. More generally, a person who learns keyboard fingerings on the basis of relative pitch with respect to the tonic of any given composition can use a transposing piano to play along with a choir and/or orchestra performing in any key. A correlative disadvantage is that individuals with absolute pitch may have difficulty playing on such a piano because the pitches they actually hear do not match the notes they are playing on the keyboard when its correspondence between nominally played note and generated pitch is altered.
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 are "limited". They were compiled by the French composer Olivier Messiaen, and published in his book La technique de mon langage musical ("The Technique of my Musical Language").
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.
Pitch shifting is a sound recording technique in which the original pitch of a sound is raised or lowered. Effects units that raise or lower pitch by a pre-designated musical interval (transposition) are known as pitch shifters.