Modes of limited transposition are musical modes or scales that fulfill specific criteria relating to their symmetry and the repetition of their interval groups. 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").
Based on our present chromatic system, a tempered system of 12 sounds, these modes are formed of several symmetrical groups, the last note of each group always being common with the first of the following group. At the end of a certain number of chromatic transpositions which varies with each mode, they are no longer transposable, giving exactly the same notes as the first.
There are two complementary ways to view the modes: considering their possible transpositions, and considering the different modes contained within them.
Transposing the diatonic major scale up in semitones results in a different set of notes being used each time. For example, C major consists of C, D, E, F, G, A, B, and the scale a semitone higher (D♭ major) consists of D♭, E♭, F, G♭, A♭, B♭, C. By transposing D♭ major up another semitone, another new set of notes (D major) is produced, and so on, giving 12 different diatonic scales in total. When transposing a mode of limited transposition this is not the case. For example, the mode of limited transposition that Messiaen labelled "Mode 1", which is the whole tone scale, contains the notes C, D, E, F♯, G♯, A♯; transposing this mode up a semitone produces C♯, D♯, F, G, A, B. Transposing this up another semitone produces D, E, F♯, G♯, A♯, C, which is the same set of notes as the original scale. Since transposing the mode up a whole tone produces the same set of notes, mode 1 has only 2 transpositions.
Any scale having 12 different transpositions is not a mode of limited transposition.
Consider the intervals of the major scale: tone, tone, semitone, tone, tone, tone, semitone. Starting the scale on a different degree will always create a new mode with individual interval layouts—for example starting on the second degree of a major scale gives the "Dorian mode"—tone, semitone, tone, tone, tone, semitone, tone. This is not so of the modes of limited transposition, which can be modally shifted only a limited number of times. For example, mode 1, the whole tone scale, contains the intervals tone, tone, tone, tone, tone, tone. Starting on any degree of the mode gives the same sequence of intervals, and therefore the whole tone scale has only 1 mode. Messiaen's mode 2, or the diminished scale, consists of semitone, tone, semitone, tone, semitone, tone, semitone, tone, which can be arranged only 2 ways, starting with either a tone or a semitone. Therefore mode 2 has two modes.
Any scale having the same number of modes as notes is not a mode of limited transposition.
Messiaen's first mode, also called the whole-tone scale, is divided into six groups of two notes each. The intervals it contains are tone, tone, tone, tone, tone, tone – it has two transpositions and one mode.
The second mode, also called octatonic/diminished/semitone-tone/tone-semitone, may be divided into four groups of three notes each. It contains the intervals semitone, tone, semitone, tone, semitone, tone, semitone, tone – it has three transpositions, like the diminished 7th chord, and two modes:
The third mode is divided into three groups of four notes each. It contains the intervals tone, semitone, semitone, tone, semitone, semitone, tone, semitone, semitone – it has four transpositions, like the augmented triad, and three modes.
The fourth mode contains the intervals semitone, semitone, minor third, semitone, semitone, semitone, minor third, semitone – it has six transpositions, like the tritone, and four modes.
The fifth mode contains the intervals semitone, major third, semitone, semitone, major third, semitone – it has six transpositions, like the tritone, and three modes.
The sixth mode has the intervals tone, tone, semitone, semitone, tone, tone, semitone, semitone – it has six transpositions, like the tritone, and four modes.
The seventh mode contains the intervals semitone, semitone, semitone, tone, semitone, semitone, semitone, semitone, tone, semitone – it has six transpositions, like the tritone, and five modes.
Messiaen wrote, "Their series is closed, it is mathematically impossible to find others, at least in our tempered system of 12 semitones."More modes can be found that fit the criteria, but they are truncations of the original seven modes.
Truncation involves the removal of notes from one of the modes to leave a new truncated mode. Both the notes removed and the notes remaining must preserve the symmetry of the parent mode, and must therefore fulfil the conditions for limited transposition. For example, consider mode 1.
Removing alternate notes creates a new truncated mode of limited transposition.
Removing two notes for every one kept creates a new truncated mode of limited transposition.
Keeping two notes for every one removed creates another truncated mode of limited transposition.
Only Messiaen's mode 7 and mode 3 are not truncated modes: the other modes may be constructed from them or from one or more of their modes. Mode 7 contains modes 1, 2, 4 and 6. Mode 6 contains modes 1 and 5. Mode 4 contains mode 5. Mode 3 contains mode 1.
Messiaen found ways of employing all of the modes of limited transposition harmonically, melodically, and sometimes polyphonically. The whole-tone and octatonic scales have enjoyed quite widespread use since the turn of the 20th century, particularly by Debussy (the whole-tone scale) and Stravinsky (the octatonic scale).
The symmetry inherent in these modes (which means no note can be perceived as the tonic), together with certain rhythmic devices, Messiaen described as containing "the charm of impossibilities".
The composer Tōru Takemitsu made frequent use of Messiaen's modes, particularly the third mode.
There are no modes of limited transposition in any prime equal division of the octave, such as 19 equal temperament or 31 equal temperament.
Composite divisions, such as 15 equal temperament or 22 equal temperament, have them. The 12-note chromatic scale can itself be considered such a mode when viewed as a subset of a larger system that contains it, such as quarter tones or 72 equal temperament.
In music theory, a diatonic scale is a heptatonic scale that includes five whole steps and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other.
In music theory, the term minor scale refers to three scale patterns – the natural minor scale, the harmonic minor scale, and the melodic minor scale – rather than just one as with the major scale.
In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Some scales contain different pitches when ascending than when descending, for example, the melodic minor scale.
In music theory, an interval is the difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is also commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B and B–F. In twelve-equal temperament, the tritone divides the octave exactly in half.
This is an alphabetical index of articles related to music.
In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or hexatonic scales:
An octatonic scale is any eight-note musical scale. However, the term most often refers to the symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory, this scale is commonly called the octatonic scale, although there are a total of 42 non-enharmonically equivalent, non-transpositionally equivalent eight-note sets.
A jazz scale is any musical scale used in jazz. Many "jazz scales" are common scales drawn from Western European classical music, including the diatonic, whole-tone, octatonic, and the modes of the ascending melodic minor. All of these scales were commonly used by late nineteenth and early twentieth-century composers such as Rimsky-Korsakov, Debussy, Ravel and Stravinsky, often in ways that directly anticipate jazz practice. Some jazz scales, such as the bebop scales, add additional chromatic passing tones to the familiar diatonic scales.
A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor seventh. However, a variety of sevenths may be added to a variety of triads, resulting in many different types of seventh chords.
In music, the mystic chord or Prometheus chord is a six-note synthetic chord and its associated scale, or pitch collection; which loosely serves as the harmonic and melodic basis for some of the later pieces by Russian composer Alexander Scriabin. Scriabin, however, did not use the chord directly but rather derived material from its transpositions.
In Western music, the adjectives major and minor may describe an interval, chord, scale, or key. As such, a composition, movement, section, or phrase may be referred to by its key, including whether that key is major or minor.
The chromatic circle is a geometrical space that shows relationships among the 12 equal-tempered pitch classes making up the familiar chromatic scale on a circle.
In classical music from Western culture, an augmented second is an interval that, in equal temperament, is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone. For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to D♯ is an augmented second, spanning three semitones.
In music theory, the harmonic major scale is a musical scale found in some music from the common practice era and now used occasionally, most often in jazz. It was named by Rimsky-Korsakov. In George Russell's Lydian Chromatic Concept it is the fifth mode (V) of the Lydian Diminished scale.
Jazz chords refer to chords, chord voicings and chord symbols that jazz musicians commonly use in composition, improvisation, and harmony. In jazz chords and theory, most triads that appear in lead sheets or fake books can have sevenths added to them, using the performer's discretion and ear. For example, if a tune is in the key of C, if there is a G chord, the chord-playing performer usually voices this chord as G7. While the notes of a G7 chord are G–B–D–F, jazz often omits the fifth of the chord—and even the root if playing in a group. However, not all jazz pianists leave out the root when they play voicings: Bud Powell, one of the best-known of the bebop pianists, and Horace Silver, whose quintet included many of jazz's biggest names from the 1950s to the 1970s, included the root note in their voicings.
In diatonic set theory, Rothenberg propriety is an important concept, lack of contradiction and ambiguity, in the general theory of musical scales which was introduced by David Rothenberg in a seminal series of papers in 1978. The concept was independently discovered in a more restricted context by Gerald Balzano, who termed it coherence.
Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.
In music, a symmetric scale is a music scale which equally divides the octave. The concept and term appears to have been introduced by Joseph Schillinger and further developed by Nicolas Slonimsky as part of his famous "Thesaurus of Scales and Melodic Patterns". In twelve-tone equal temperament, the octave can only be equally divided into two, three, four, six, or twelve parts, which consequently may be filled in by adding the same exact interval or sequence of intervals to each resulting note.
Musicology commonly classifies scales as either hemitonic or anhemitonic. Hemitonic scales contain one or more semitones, while anhemitonic scales do not contain semitones. For example, in traditional Japanese music, the anhemitonic yo scale is contrasted with the hemitonic in scale. The simplest and most commonly used scale in the world is the atritonic anhemitonic "major" pentatonic scale. The whole tone scale is also anhemitonic.