diminution

In Western music and music theory, diminution (from Medieval Latin diminutio, alteration of Latin deminutio, decrease) 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 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] 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".^[2]

The substantial Italian literature of the 16th and early 17th century begins with the Fontegara of Silvestro Ganassi (1535) and includes the treatises and compositions of Diego Ortiz, Giovanni Maffei, Girolamo Dalla Casa, Giovanni Bassano, Riccardo Rogniono, Giovanni Battista Bovicelli, Aurelio Virgiliano and Francesco Rognoni Taeggio.^[3] Notable English works include The Division-Violist of Christopher Simpson (1659), The Division-Violin (Playford, 1684) and The Division Flute (Walsh, c.1706). Der Fluyten Lust-hof of Jacob van Eyck (Amsterdam, 1646) is a huge collection of diminutions.

In Schenkerian analysis a diminution is a division, rather than a diminishing is a prolongation or expansion, "the process by which an interval formed by notes of longer value is expressed in notes of smaller value," see nonchord tone.^{[clarification needed]}

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 (quarter-notes) for example, is diminished if it later appears with four quavers (eighth-notes) instead. This technique is often used in contrapuntal music, as in the "canon by diminution" ("per diminutionem"), in which the notes in the following voice or voices are shorter than those in the leading voice, usually half the length.^[4]

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.^[5][6]

Diminution may also be achieved by a sign of proportion. Thus a sign such as ^{3 2} 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.^[5]

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. Diminished intervals are often used in jazz, art and Heavy Metal music, but not as often in pop music.^{[citation needed]}

Diminished intervals on C

Diminished second	Diminished third	Diminished fourth	Diminished fifth	Diminished sixth	Diminished seventh	Diminished octave
Play (help·info)	Play (help·info)	Play (help·info)	Play (help·info)	Play (help·info)	Play (help·info)	Play (help·info)

a diminished unison is unthinkable, and the diminished 2d and 9th are of no practical use:...

—Foote^[7]

Augmented octave and diminished unison.^{[8][9][10][11]} Note how the diminished unison is essentially equivalent to the augmented unison.  Play (help·info) ( simultaneously (help·info))

In the theory of harmony it is known that a diminished interval needs to be resolved inwards, and an augmented interval outwards.

—Maria Renold (2004), p.15.^[12]

Augmented intervals have a rather over-tense quality, while diminished intervals are experienced as rather cramped. Therefore, one may call the former luciferic in tendency and the latter ahrimanic.

—Renold (2004), p.16^{[clarification needed]}

If a perfect or major interval is made one-half step larger (without changing its interval number) it becomes augmented. If a perfect or minor interval is made one-half step smaller (without changing its interval number) it becomes diminished.

—Benward & Saker (2003), p.54.^[13]

Most nonharmonic tones are dissonant and create intervals of a second, fourth, or seventh. Diminished or augmented intervals are also considered dissonant.

—Benward & Saker (2003), p.92.^[14]

The standard abbreviations for diminished intervals are dX, such that a diminished third = d3.^[13]

Diminished chords

Diminished triad on C  play (help·info).

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°.

Diminished seventh chord on C  Play (help·info).

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 (or major ninth) 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.

Half-diminished seventh chord on C ( Play (help·info)).

A diminished triad with a minor seventh is a half-diminished chord, usually notated either Cm7(♭5) or Cø7.

Diminished scales

Octatonic scales on C  Play (help·info).

Several scales may be referred to as diminished. 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.

Half diminished scale on C  Play (help·info).

See also

• Augmentation (music)

Sources

1. ^ Garden, Greer, and Robert Donington.. "Diminution". Grove Music Online. Oxford Music Online. http://www.oxfordmusiconline.com/subscriber/article/grove/music/42071. Retrieved August 2011.  (subscription needed)
2. ^ Donington, Robert (1989). The Interpretation of Early Music (New revised ed.). London: Faber and Faber. pp. 152–188. ISBN 0571150403. 
3. ^ Conforto, Giovanni Luca (1986). Giancarlo Rostirolla. ed (in Italian). Breve et facile maniera d'essercitarsi a far passaggi, Roma 1593. Roma: Società Italiana dl Flauto Dolco. p. 3. 
4. ^ Jeppesen, Knud. Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century. trans. Glen Haydon. New York: Dover Publications. 1992. p. 235 . ISBN 978-0-486-27036-4. 
5. ^ ^{a b} Bowers, Roger. "Proportional notation". Grove Music Online. Oxford Music Online. http://www.oxfordmusiconline.com/subscriber/article/grove/music/22424. Retrieved August 2011.  (subscription needed)
6. ^ Donington, Robert, and Peter Wright. "Coloration". Grove Music Online. Oxford Music Online. http://www.oxfordmusiconline.com/subscriber/article/grove/music/06153. Retrieved August 2011.  (subscription needed)
7. ^ Arthur Foote, Walter Raymond Spalding (1905). Modern Harmony in its Theory and Practice, p.5. Arthur P. Schmidt.
8. ^ Sembos (2006). Principles of Music Theory, p.51. ISBN 1430309555. online.
9. ^ Porter, Steven (1986). Music, A Comprehensive Introduction, p.66. ISBN 9780935016819.
10. ^ Burrows, Terry (1999). How To Read Music, p.62. ISBN 9780312241599.
11. ^ Middleton, Robert (1967). Harmony in Modern Counterpoint, p.20. Allyn and Bacon.
12. ^ Renold, Maria (2004). Intervals, scales, tones and the concert pitch, p.15. ISBN 1902636465.
13. ^ ^{a b} Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0.
14. ^ Benward & Saker (2003), p.92. Benward & Saker (2009). Music: In Theory and Practice, Vol. II, p.36. ISBN 978-0-07-310188-0.