Diminution

Diminution may be a form of embellishment in which a long note is divided into a series of shorter, usually melodic, values (also called "coloration"; Ger.

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 a form of embellishment or melodic 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.

[1] It is thoroughly documented in written sources of the sixteenth, seventeenth and early eighteenth centuries, and enjoyed a remarkable flowering in Venice from about 1580–1620.

It is an integral aspect of modern performance practice; Donington describes the consequences of failing to add "necessary figuration" as "disastrous".

[4] "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".

[7] In jazz, Thelonious Monk's composition "Brilliant Corners" consists of a theme that is repeated at twice the speed, an effect known as "double time."

One of the more common is the Octatonic scale constructed from C°7 and its tensions (transposed into the same octave), which has alternating tone and semitone intervals.

Extract from Diego Ortiz 's El Primo Libro ... Nel qual si tratta delle Glose depicting rhythm and generic intervals. Observe the diminution (i.e. division) process suggested by the composer, in reference to the rhythmic figures in the upper and lower musical parts.
A realization of the bottom line of the above Diego Ortiz extract in modern notation, completed with an arbitrarily chosen clef and a time signature. Play
Beethoven, Leonora no. 3 overture, bars 69–76
Leonora no 3
Contrapunctus VII from Bach's Art of Fugue
Contrapuntus VII from Bach's Art of Fugue . Observe the lower voice of the canon in halved (i.e. diminished) note values.
Diminished triad on C play .
Diminished seventh chord on C Play .
Diminished chords with sheet music and tab.
Octatonic scales on C Play .