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In music transposition refers to the process of moving a collection of notes (pitches) up or down in pitch by a constant interval. For example, one 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. See also Transposing instrument and modulation. For other uses, see Music (disambiguation). ...
Pitch is the perceived fundamental frequency of a sound. ...
Pitch is the perceived fundamental frequency of a sound. ...
In music theory, the term interval describes the difference in pitch between two notes. ...
In music theory, the key identifies the tonic triad, the chord, major or minor, which represents the final point of rest for a piece, or the focal point of a section. ...
In music, a tone row or note row is a permutation, an arrangement or ordering, of the twelve notes of the chromatic scale. ...
Typical fingering for a second inversion C major chord on a guitar. ...
A transposing instrument is a musical instrument whose music is written at a pitch different from concert pitch. ...
In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. ...
Two different types of transposition
There are two different kinds of transposition, depending on whether one is measuring intervals according to the chromatic scale or some other scale. In chromatic transposition one shifts every pitch in a collection of notes by a fixed number of semitones. For instance, if one transposes the pitches C4-E4-G4 upwards by four semitones, one obtains the pitches E4-G#4-B4. In scalar transposition one shifts every pitch in a collection by a fixed number of scale steps relative to some scale. For example, if one transposes the pitches C4-E4-G4 up by two steps relative to the familiar C major scale, one obtains the pitches E4-G4-B4. If one transposes the same pitches up by two steps relative to the F major scale, one obtains instead E4-G4-Bb4. Scalar transposition is sometimes called diatonic transposition, but this term can be misleading, as it suggests transposition with respect to a diatonic scale. However, scalar transposition can occur with respect to any type of scale, not just the diatonic. In music, a scale is a collection of musical notes that provides material for part or all of a musical work. ...
Sight transposition Although transpositions are usually written out, musicians are occasionally asked to transpose music "at sight", that is, to read the music in one key while playing in another. Musicians who play transposing instruments sometimes have to do this (for example when encountering an unusual transposition, such as clarinet in C), as well as singers' accompanists, since singers sometimes request a different key than the one printed in the music to better fit their tessitura. A transposing instrument is a musical instrument whose music is written at a pitch different from concert pitch. ...
In music, tessitura (Italian: texture) is a range of pitches compared to the instrument for which it was intended to be used. ...
There are three basic techniques for teaching sight transposition: interval, clef, and numbers.
Interval First one determines the interval between the written key and the target key. Then one imagines the notes up (or down) by the corresponding interval. A performer using this method may calculate each note individually, or group notes together (e.g. "a descending chromatic passage starting on F" might become a "descending chromatic passage starting on A" in the target key).
Clef Clef transposition is routinely taught in Belgium and France. One imagines a different clef than the one printed so that the lines and spaces correspond to different notes. Seven clefs are used for this: treble, bass, baritone, and C-clefs on the four lowest lines; these allow any given staff position to correspond to each of the seven note names A through G. The octave may also have to be adjusted, but this is a trivial matter for most musicians. In musical notation, the staff or stave is a set of five horizontal lines on which note symbols are placed to indicate pitch and rhythm. ...
Numbers Transposing by numbers means, one determines the scale degree of the written note (e.g. first, fourth, fifth, etc.) in the given key. The performer then plays the corresponding scale degree of the target key. In music theory, a scale degree is the name of a particular note of a scale in relation to the tonic (the first note in the scale). ...
Transpositional equivalency Two musical objects are transpositionally equivalent if one can be transformed into another by transposition. It is similar to enharmonic equivalence and octave equivalence. In many musical contexts, transpositionally equivalent chords are thought to be similar. Transpositional equivalence is a feature of musical set theory. In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ...
In music, an octave (sometimes abbreviated 8ve) is the interval between one musical note and another with half or double its frequency. ...
Musical set theory is an atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ...
Using integer notation and modulo 12, to transpose a pitch x by n semitones: Music notation is a system of writing for music. ...
Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic because of its use in the 24-hour clock system) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value — the modulus. ...
 or  For pitch class transposition by a pitch class interval: In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ...
 (Rahn 1980)
Source - Rahn, John (1980). Basic Atonal Theory. ISBN 0-02-873160-3.
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