Diminution

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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. Trattado p.5.JPG
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 Trattado p.5 bottom.png
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

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 (also called "coloration"; Ger. Kolorieren). 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 (this, too, was sometimes referred to as "coloration").

Contents

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] 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". [2] : 152 

Italian literature of the sixteenth and early seventeenth century

Spanish literature

English literature

German literature

Dutch literature

For Heinrich Schenker, "all foreground is diminution". [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". [5] This conception has been essential to Schenker's theory from some of his earliest writings. [6] 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 (quarter-notes) for example, is diminished if it later appears with four quavers (eighth-notes) 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:

Beethoven, Leonora no. 3 overture, bars 69–76
Leonora no 3 Leonora no 3.png
Leonora no 3

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. [7]

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. Art de la fugue exemple04.png
Contrapuntus VII from Bach's Art of Fugue . Observe the lower voice of the canon in halved (i.e. diminished) note values.

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."

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. [8] [9]

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. [8]

Diminution of intervals

A diminished interval is an interval obtained from a minor interval or perfect interval by narrowing it by a chromatic semitone, meaning that the interval is narrowed by a semitone, but the staff positions are not changed (only an accidental is changed); the process may occasionally be referred to as diminution For example, a diminished sixth is a chromatic semitone narrower than the minor sixth: starting with the interval from B to G, which is a minor sixth, eight semitones wide, the interval from B to G♭ is a diminished sixth, spanning seven semitones, but the same staff lines. By contrast, the interval from B to F♯ is not a diminished sixth (it is a perfect fifth): even though it is seven semitones wide, it spans five staff positions, and is thus a fifth, not a sixth; it is a diatonic semitone narrower than a minor sixth. The standard abbreviations for diminished intervals are dX, such that a diminished third = d3. [10] The diminished fifth (d5) is the only diminished interval that appears in diatonic scales (in D♭ major it occurs between C and G♭).

Diminished intervals on C
Diminished second Diminished third Diminished fourth Diminished fifth Diminished sixth Diminished seventh Diminished octave
Diminished second on C.png Diminished third on C.png Diminished fourth on C.png Diminished fifth on C.png Diminished sixth on C.png Diminished seventh on C.png Diminished octave on C.png
Play ⓘ Play ⓘ Play ⓘ Play ⓘ Play ⓘ Play ⓘ Play ⓘ

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

— Foote [11]

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. [10]

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. [13]

Diminished chords

Diminished triad on C play. Diminished triad on C.png
Diminished triad on C play .

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. Diminished seventh chord on C.png
Diminished seventh chord on C Play .

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). Half-diminished seventh chord on C.png
Half-diminished seventh chord on C ( Play ).

A diminished triad with a minor seventh is a half-diminished chord, usually notated either Cm7(♭5) or Cø7. A diminished triad played over a root a major third away creates a Dominant 7th chord, notated C7, with a C Major triad on the bottom, and an E° from the chord third of C (C E G B♭). A minor third below would give a fully diminished 7th chord which is made entirely of minor thirds that evenly divide an octave. This even division of the octave leaves us with only three unique diminished 7th chords: C E♭ G♭ B Doubleflat.svg , C♯ E G B♭, and D F A♭ C♭, as all other diminished 7th chords are inversions of one of those three.

Diminished chords with sheet music and tab. Diminishedchords.png
Diminished chords with sheet music and tab.

Diminished scales

Octatonic scales on C Play. Octatonic scales on C.png
Octatonic scales on C Play .

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. Half diminished scale C.png
Half diminished scale on C Play .

See also

Related Research Articles

<span class="mw-page-title-main">Major scale</span> Musical scale made of seven notes

The major scale is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double its frequency so that it is called a higher octave of the same note.

In western classical music theory, the minor scale refers to three scale patterns – the natural minor scale, the harmonic minor scale, and the melodic minor scale.

In music theory, a leading-tone is a note or pitch which resolves or "leads" to a note one semitone higher or lower, being a lower and upper leading-tone, respectively. Typically, the leading tone refers to the seventh scale degree of a major scale, a major seventh above the tonic. In the movable do solfège system, the leading-tone is sung as ti.

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.

<span class="mw-page-title-main">Chord (music)</span> Harmonic set of two or more notes

In music, a chord is a group of two or more notes played simultaneously, typically consisting of a root note, a third, and a fifth. Chords are the building blocks of harmony and form the harmonic foundation of a piece of music. They can be major, minor, diminished, augmented, or extended, depending on the intervals between the notes and their arrangement. Chords provide the harmonic support and coloration that accompany melodies and contribute to the overall sound and mood of a musical composition. For many practical and theoretical purposes, arpeggios and other types of broken chords may also be considered as chords in the right musical context.

A secondary chord is an analytical label for a specific harmonic device that is prevalent in the tonal idiom of Western music beginning in the common practice period: the use of diatonic functions for tonicization.

<span class="mw-page-title-main">Augmented fifth</span> Musical interval

In Western classical music, an augmented fifth is an interval produced by widening a perfect fifth by a chromatic semitone. For instance, the interval from C to G is a perfect fifth, seven semitones wide, and both the intervals from C♭ to G, and from C to G♯ are augmented fifths, spanning eight semitones. Being augmented, it is considered a dissonant interval.

In music theory, a diminished triad is a triad consisting of two minor thirds above the root. It is a minor triad with a lowered (flattened) fifth. When using chord symbols, it may be indicated by the symbols "dim", "o", "m♭5", or "MI(♭5)". However, in most popular-music chord books, the symbol "dim" and "o" represents a diminished seventh chord, which in some modern jazz books and music theory books is represented by the "dim7" or "o7" symbols.

In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, was further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.

In music theory, a ninth chord is a chord that encompasses the interval of a ninth when arranged in close position with the root in the bass.

The ninth chord and its inversions exist today, or at least they can exist. The pupil will easily find examples in the literature [such as Schoenberg's Verklärte Nacht and Strauss's opera Salome]. It is not necessary to set up special laws for its treatment. If one wants to be careful, one will be able to use the laws that pertain to the seventh chords: that is, dissonances resolve by step downward, the root leaps a fourth upward.

Chromaticism is a compositional technique interspersing the primary diatonic pitches and chords with other pitches of the chromatic scale. In simple terms, within each octave, diatonic music uses only seven different notes, rather than the twelve available on a standard piano keyboard. Music is chromatic when it uses more than just these seven notes.

In music theory, a dominant seventh chord, or major minor seventh chord, is a seventh chord, composed of a root, major third, perfect fifth, and minor seventh. Thus it is a major triad together with a minor seventh, denoted by the letter name of the chord root and a superscript "7". In most cases, dominant seventh chord are built on the fifth degree of the major scale. An example is the dominant seventh chord built on G, written as G7, having pitches G–B–D–F:

In Classical music theory, a Neapolitan chord is a major chord built on the lowered (flattened) second (supertonic) scale degree. In Schenkerian analysis, it is known as a Phrygian II, since in minor scales the chord is built on the notes of the corresponding Phrygian mode.

The diminished seventh chord is a four-note chord composed of a root note, together with a minor third, a diminished fifth, and a diminished seventh above the root:. For example, the diminished seventh chord built on B, commonly written as Bo7, has pitches B-D-F-A♭:

<span class="mw-page-title-main">Augmented sixth</span> Musical interval

In music, an augmented sixth is an interval produced by widening a major sixth by a chromatic semitone. For instance, the interval from C to A is a major sixth, nine semitones wide, and both the intervals from C♭ to A, and from C to A♯ are augmented sixths, spanning ten semitones. Being augmented, it is considered a dissonant interval.

In Western music and music theory, augmentation is the lengthening of a note or the widening of an interval.

<span class="mw-page-title-main">Diminished seventh</span> Musical interval

In classical music from Western culture, a diminished seventh is an interval produced by narrowing a minor seventh by a chromatic semitone, and its inversion is the augmented second. For instance, the interval from A to G is a minor seventh, ten semitones wide, and both the intervals from A♯ to G, and from A to G♭ are diminished sevenths, spanning nine semitones. Being diminished, it is considered a dissonant interval.

<span class="mw-page-title-main">Diminished third</span> Musical interval

In classical music from Western culture, a diminished third is the musical interval produced by narrowing a minor third by a chromatic semitone. For instance, the interval from A to C is a minor third, three semitones wide, and both the intervals from A♯ to C, and from A to C♭ are diminished thirds, two semitones wide. Being diminished, it is considered a dissonant interval.

<span class="mw-page-title-main">Diatonic and chromatic</span> Terms in music theory to characterize scales

Diatonic and chromatic are terms in music theory that are used to characterize scales. The terms 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.

Musicians use various kinds of chord names and symbols in different contexts to represent musical chords. In most genres of popular music, including jazz, pop, and rock, a chord name and its corresponding symbol typically indicate one or more of the following:

  1. the root note,
  2. the chord quality,
  3. whether the chord is a triad, seventh chord, or an extended chord,
  4. any altered notes,
  5. any added tones, and
  6. the bass note if it is not the root.

References

  1. ↑ Greer Garden, Robert Donington (2001). Diminution. Grove Music Online. Oxford Music Online. Accessed August 2011. doi:10.1093/gmo/9781561592630.article.42071. (subscription required).
  2. ↑ Robert Donington (1989). The Interpretation of Early Music (new revised edition). London: Faber and Faber. pp. 152–188. ISBN   0571150403.
  3. ↑ Giovanni Luca Conforto, Giancarlo Rostirolla (editor) (1986). Breve et facile maniera d'essercitarsi a far passaggi, Roma 1593 (in Italian). Roma: Società Italiana del Flauto Dolce.
  4. ↑ Schenker, Heinrich (1979). Free Composition. Translated by Ernst Oster. New York, London: Longman. pp. 96, § 252.
  5. ↑ Schenker, Heinrich (1979). Free Composition. Translated by Ernst Oster. New York, London: Longman. pp. 98, § 253.
  6. ↑ Schenker, Heinrich (1908) [1904]. Ein Beitrag zur Ornamentik als Einführung zu Ph. Em. Bach's Klavierwerken. Wien, Leipzig: Universal Edition.
  7. ↑ Jeppesen, Knud. Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century. trans. Glen Haydon. New York: Dover Publications. 1992. p. 235 Jeppesen, Knud (January 1992). Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century . Courier Corporation. ISBN   978-0-486-27036-4.
  8. 1 2 Roger Bowers (2001). Proportional notation. Grove Music Online. Oxford Music Online. Accessed August 2011. doi:10.1093/gmo/9781561592630.article.22424. (subscription required).
  9. ↑ Robert Donington, Peter Wright (2001). Coloration. Grove Music Online. Oxford Music Online. Accessed August 2011. doi:10.1093/gmo/9781561592630.article.06153. (subscription required).
  10. 1 2 Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN   978-0-07-294262-0.
  11. ↑ Arthur Foote, Walter Raymond Spalding (1905). Modern Harmony in its Theory and Practice, p.5. Arthur P. Schmidt.
  12. ↑ Renold, Maria (2004). Intervals, scales, tones and the concert pitch, p.15. ISBN   1-902636-46-5.
  13. ↑ Benward & Saker (2003), p.92. Benward & Saker (2009). Music: In Theory and Practice, Vol. II, p.36. ISBN   978-0-07-310188-0.
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