Information about transposition (music)

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.

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-B♭4. 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.

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.

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.

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.

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.

Using integer notation and modulo 12, to transpose a pitch x by n semitones:

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For pitch class transposition by a pitch class interval:

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(Rahn 1980)

Source

Rahn, John (1980). Basic Atonal Theory. ISBN 0-02-873160-3.

External links

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Pitch is the perceived fundamental frequency of a sound. While the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones, or partials, in the sound.
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In music theory, the term interval describes the difference in pitch between two notes. Although frequently used in connection with intervals, the term "distance" does not adequately describe the physics and subjective effects of two interacting frequencies.
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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. Although the key of a piece may be named in the title (e.g.
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In music, a tone row or note row (German: Tonreihe) refers to a non-repetitive ordering of the twelve notes (pitch-classes in musical set theory) of the chromatic scale.
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chord (from Greek χορδή: gut, string) is three or more different notes that sound simultaneously. Most often, in European-influenced music, chords are tertian sonorities that can be constructed as stacks of thirds relative to some underlying scale.
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A transposing instrument is a musical instrument whose music is written at a pitch different from concert pitch. Concert pitch is the pitch as notated for piano (or any other non-transposing instrument) - e.g., the note "C" on piano is a concert C.
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In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest.
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In music, a scale is a collection of musical notes that provides material for part or all of a musical work. Scales are ordered in pitch or pitch class, with their ordering providing a measure of musical distance.
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In music, the term tessitura (Italian: texture) generally describes the most musically acceptable and comfortable timbre for a given voice or, less frequently, musical instrument.
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In musical notation, the staff is a set of five horizontal lines and four spaces, on which note symbols are placed to indicate their relative pitch. The lines and spaces are numbered from bottom to top; the bottom line is the first line and the top line is the
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note has two primary meanings: 1) a sign used in music to represent the relative duration and pitch of a sound; and 2) a pitched sound itself. Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis
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scale degree is the name of a particular note of a scale in relation to the tonic (the note of the scale that is considered the most important). The degrees of the traditional major and minor scales may be identified several ways:

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In modern music, an enharmonic is a note (or key signature) which is the equivalent of some other note (or key signature), but spelled differently. For example, in twelve-tone equal temperament (the modern system of musical tuning in the west), the notes C♯ (C sharp) and
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Perfect octave
Inverse unison
Name
Other names -
Abbreviation P8
Size
Semitones 12
Interval class 0
Just interval 2:1
Cents
Equal temperament 1200
Just intonation 1200 In music, an octave
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In music, musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson in connection with tonal music, and then mostly developed in connection with atonal music; the concepts of
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In integer notation, or the integer model of pitch, all pitch classes and intervals between pitch classes are designated using the numbers 0 through 11. It is not used to notate music for performance, but is a common analytical and compositional tool when working with chromatic
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Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value — the modulus.
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In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g. the pitch class C consists of the Cs in all octaves. Thus, using scientific pitch notation the pitch class "C" is the infinite set