Diminution


In Western music and music theory, diminution has four distinct meanings. Diminution may be a form of embellishment in which a long note is divided into a series of shorter, usually melodic, values. Diminution may also be the compositional device where a melody, theme or motif is presented in shorter note-values than were previously used. Diminution is also the term for the proportional shortening of the value of individual note-shapes in mensural notation, either by coloration or by a sign of proportion. A minor or perfect interval that is narrowed by a chromatic semitone is a diminished interval, and the process may be referred to as diminution.

Diminution as embellishment

Diminution is a form of embellishment or melodic :wikt:variation|variation in which a long note or a series of long notes is divided into shorter, usually melodic, values, as in the similar practices of breaking or division in England, passaggio in Italy, double in France and glosas or diferencias in Spain. Thoroughly documented in written sources of the 16th, 17th and early 18th centuries, with a remarkable flowering in Venice from about 1580–1620, diminution is an integral aspect of modern performance practice. Donington describes the consequences of failing to add "necessary figuration" as "disastrous".

Italian literature of the 16th and early 17th century

*
For Heinrich Schenker, "all foreground is diminution". "All diminution must be secured firmly to the total work by means which are precisely demonstrable and organically verified by the inner necessities of the voice-leading". This conception has been essential to Schenker's theory from some of his earliest writings. In Schenkerian analysis a diminution is an elaboration by which an event formed of notes of longer value is expressed in notes of smaller value. See nonchord tone.

Diminution in composition

A melody or series of notes is diminished if the lengths of the notes are shortened; diminution is thus the opposite of augmentation, where the notes are lengthened. A melody originally consisting of four crotchets for example, is diminished if it later appears with four quavers instead. In the following theme from Beethoven’s Leonora no. 3 Overture, the melodic ideas in bars 3 and 5 recur at twice the speed in bars 7-8: This technique is often used in contrapuntal music, as in the "canon by diminution", in which the notes in the following voice or voices are shorter than those in the leading voice, usually half the length. ''. Observe the lower voice of the canon in halved note values. In jazz, Thelonious Monk’s composition “Brilliant Corners” consists of a that is repeated at twice the speed, an effect known as “double time.”

Diminution of note values

In mensural notation, diminution of the duration of note shapes is the most common function of coloration. Diminution is most often by one-third of the note-value, so that three colored notes fit into the time of two uncolored notes of the same shape; it is thus often found in notation of triplet or hemiola figures.
Diminution may also be achieved by a sign of proportion. Thus a sign such as is in proportional notation not a modern time signature, but a proportional signature indicating diminutio sesquialtera, that is, that after the sign each three notes of the basic note value integer valor occupy the time of two such notes elsewhere in the piece, either previously in the same voice, or simultaneously in another voice.

Diminution of intervals

An interval is diminished if a minor or perfect interval is narrowed by a chromatic semitone; the process may occasionally be referred to as diminution. A diminished fifth interval is a chromatic semitone narrower than the perfect fifth, and a diminished seventh interval is a chromatic semitone narrower than the minor seventh.
The standard abbreviations for diminished intervals are dX, such that a diminished third = d3.

Diminished chords

A diminished triad consists of two superposed minor thirds, and thus contains a diminished fifth. In classical repertoire the usual symbol is the degree, °, as in vii°. In lead sheets and popular music books it is usually written Cdim or C°.
A diminished seventh chord consists of three superposed minor thirds, and thus has all successive notes a minor third apart; it contains two diminished fifths. In jazz theory, a diminished seventh chord has four available tensions, each a major ninth above the chord tones, and thus forming a diminished seventh chord a whole tone above the root chord. Because any chord tone of the diminished seventh can be heard as the root, the tensions are not numbered as ninth, eleventh and so on. The usual notation is Cdim7 or C°7, but some lead sheets or popular music books may omit the 7.
on C.
A diminished triad with a minor seventh is a half-diminished chord, usually notated either Cm7 or Cø7.

Diminished scales

Several scales may be referred to as diminished. One of the more common is the Octatonic scale constructed from C°7 and its tensions, which has alternating tone and semitone intervals.
on C.