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Diminution
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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").
Diminution as embellishment
[edit]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
[edit]- Silvestro Ganassi Opera Intitulata Fontegara (Venice, 1535)
- Diego Ortiz, Nel qual si tratta delle Glose (1553)
- Giovanni Maffei, Delle lettere del Sr. Gio. Camillo Maffei da Solofra (1562)
- Girolamo Dalla Casa, Il vero modo di diminuir (1584)
- Giovanni Bassano, Ricercate, Passaggi et Cadentie (1585)
- Giovanni Luca Conforti, Breve et facile maniera d'essercitarsi a far passaggi (1593)
- Riccardo Rogniono, Passaggi per potersi essercitare nel diminuire terminatamente (1594)
- Giovanni Battista Bovicelli, Regole, passaggi di musica (1594)
- Aurelio Virgiliano, Il Dolcimelo (ms, c. 1600; first publication 1979)
- Francesco Rognoni Taeggio, Selve de varii passaggi (1620 )
- Giovanni Battista Spadi, Libro de passaggi ascendenti et descendenti (1624)
Spanish literature
[edit]English literature
[edit]- Christopher Simpson, The Division-Violist (1659)
- The Division-Violin (Playford, 1684)
- The Division Flute (Walsh, c. 1706)
German literature
[edit]- Adrianus Petit Coclico, Compendium Musices (Nuremberg, 1552)
- Michael Praetorius, Syntagma Musicum, book 3 (1618)
- Johann Andreas Herbst, Musica practica (1642)
Dutch literature
[edit]- Jacob van Eyck, Der Fluyten Lust-hof (Amsterdam, 1646) is a huge collection of diminutions.[3]: 3
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
[edit]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:
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]
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
[edit]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
[edit]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 second | Diminished third | Diminished fourth | Diminished fifth | Diminished sixth | Diminished seventh | Diminished octave |
|---|---|---|---|---|---|---|
|
|
|
|
|
|
|
| ⓘ | ⓘ | ⓘ | ⓘ | ⓘ | ⓘ | ⓘ |
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
[edit]
A diminished triad consists of two superposed minor thirds, and thus contains a diminished fifth. In classical repertoire the usual symbol o resembles the degree symbol, as in viio. In lead sheets and popular music books it is usually written Cdim or Co.
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 Co7, but some lead sheets or popular music books may omit the 7.
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
, C♯ E G B♭, and D F A♭ C♭, as all other diminished 7th chords are inversions of one of those three.
Diminished scales
[edit]
Several scales may be referred to as diminished. One of the more common is the Octatonic scale constructed from Co7 and its tensions (transposed into the same octave), which has alternating tone and semitone intervals.
See also
[edit]References
[edit]- ^ Greer Garden, Robert Donington (2001). Diminution. Grove Music Online. Oxford Music Online. Accessed August 2011. doi:10.1093/gmo/9781561592630.article.42071. (subscription required).
- ^ Robert Donington (1989). The Interpretation of Early Music (new revised edition). London: Faber and Faber. pp. 152–188. ISBN 0571150403.
- ^ 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.
- ^ Schenker, Heinrich (1979). Free Composition. Translated by Ernst Oster. New York, London: Longman. pp. 96, § 252.
- ^ Schenker, Heinrich (1979). Free Composition. Translated by Ernst Oster. New York, London: Longman. pp. 98, § 253.
- ^ Schenker, Heinrich (1908) [1904]. Ein Beitrag zur Ornamentik als Einführung zu Ph. Em. Bach's Klavierwerken. Wien, Leipzig: Universal Edition.
- ^ 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.
- ^ a b Roger Bowers (2001). Proportional notation. Grove Music Online. Oxford Music Online. Accessed August 2011. doi:10.1093/gmo/9781561592630.article.22424. (subscription required).
- ^ Robert Donington, Peter Wright (2001). Coloration. Grove Music Online. Oxford Music Online. Accessed August 2011. doi:10.1093/gmo/9781561592630.article.06153. (subscription required).
- ^ a b Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0.
- ^ Arthur Foote, Walter Raymond Spalding (1905). Modern Harmony in its Theory and Practice, p.5. Arthur P. Schmidt.
- ^ Renold, Maria (2004). Intervals, scales, tones and the concert pitch, p.15. ISBN 1-902636-46-5.
- ^ Benward & Saker (2003), p.92. Benward & Saker (2009). Music: In Theory and Practice, Vol. II, p.36. ISBN 978-0-07-310188-0.
Diminution
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Diminution is a fundamental technique in Western music theory and composition, involving the subdivision of longer note values into a series of shorter ones to elaborate on a melody, add rhythmic complexity, and enhance expressiveness.[1][2] This process, the opposite of augmentation, typically halves or further reduces durations, such as transforming a quarter note into two eighth notes or more intricate patterns, while preserving the original melodic contour.[3]
The concept traces its theoretical origins to the 14th century, with the earliest known discussion appearing in Johannes de Muris's Ars practica mensurabilis cantus (also known as the Libellus cantus mensurabilis), where it was defined in the context of mensural notation and proportional changes in rhythm.[4] By the 15th century, theorists expanded on Muris's ideas, distinguishing types such as proportional diminution (altering the value of the semibreve relative to the minim), mensural diminution (shifting the tactus), and acceleratio mensurae (gradual speeding up), influencing the interpretation of notation in medieval and Renaissance polyphony.[4] In the 16th century, diminution evolved into a performative practice, where musicians improvised embellishments by adding divisions to written lines, as seen in treatises on ornamentation for both vocal and instrumental music.[5]
Throughout later periods, diminution remained a key tool for variation and development, prominently featured in Baroque music for creating excitement and personalization in performances, and continuing in modern composition to build tension or urgency by accelerating rhythmic motion.[2][1] In counterpoint and analysis, it serves to elaborate motives without altering their harmonic structure, ensuring coherence in phrasing and texture.[6]
G (semibreve, held for two tactus beats) Diminished (semiquaver passaggi):
G-F-E-D-C-D-E-F-G (ascending return for resolution, each note light and equal in the tactus) This division maintains the melodic contour while adding florid motion, as notated in full rather than shorthand to guide performers.[17] Similarly, Conforti's exercises divide a unison on C into eighth notes with a groppo: C-B-C (trill) resolving to D, emphasizing stepwise elegance over virtuosic display.[16] These examples underscore diminution's role in bridging madrigal polyphony—where upper voices might receive passaggi for textual accent—and the monodic style of emerging opera.[17]
This pattern divides the original note value into seven shorter ones, creating stepwise motion around F while resolving the cadence, a technique typical for reducing polyphonic lines to gamba solos.[21][25]
This embellishment subdivides the melody into faster values, adding chromatic inflections for expressive tension release, a hallmark of Dowland's style in lute ayres and pavans.)
Such divisions, notated in Ammerbach's letter tablature, allowed organists to improvise variations during services.)
Under diminution (e.g., slashed signs like Ç), these values halved, with the breve often equaling the undiminished semibreve's duration, effectively doubling the tempo across the hierarchy.[10][44]
General Concepts
Definition and Etymology
In music theory, diminution refers to the process of subdividing longer note values into shorter ones, often to create embellishments, introduce rhythmic variation, or alter structural proportions while preserving the original melodic contour. This technique can involve proportional reduction, where all note durations are systematically halved or otherwise shortened, or more elaborate divisions that add ornamental figures such as runs or passaggi.[7][8] The term "diminution" derives from the Latin diminutio (nominative diminutio), meaning "a lessening" or "reduction," which entered musical discourse through medieval and Renaissance treatises on mensural notation, where it described the shortening of note values via symbols like a vertical line through the staff or specific proportion signs.[9][10] In this context, it contrasts with augmentation, the opposite process of lengthening note values by doubling or tripling durations to expand a melody's temporal scale.[3] Mensural notation, the rhythmic system prevalent from the 13th to 16th centuries, underpins these concepts, employing a hierarchy of note values—such as the long (longa), breve (brevis), semibreve (semibrevis), and minim (minima)—whose proportions could be adjusted through diminution to achieve precise rhythmic complexity.[10] Diminution first appears systematically in the 14th-century ars subtilior style, a sophisticated French and Italian repertory known for its intricate notational innovations and rhythmic experimentation, where composers like Philippe de Caserta employed it to halve note values or introduce irregular subdivisions for expressive effect.[11][12] This early application laid the groundwork for later embellishment practices, though without delving into national traditions.Historical Overview
Diminution emerged as a theoretical concept in the 14th century, with the earliest known discussion appearing in Johannes de Muris's Ars practica mensurabilis cantus, which served as the foundational text on the practice for over a century.[4] This period coincided with the ars subtilior style, flourishing in late 14th- and early 15th-century France and Italy, where diminution involved reducing note values to produce intricate rhythmic patterns in secular polyphonic compositions, enhancing expressiveness through notational innovation.[11] In this context, diminution played a role in counterpoint by allowing performers to realize ambiguous notations, contributing to the era's emphasis on rhythmic complexity and ornamental elaboration. By the Renaissance (c. 1450–1600), diminution gained prominence in polyphonic music, where it became integral to interpreting mensural notation and structuring contrapuntal lines. Theorists like Johannes Tinctoris (1435–1511) categorized diminution into types such as proportional reduction of note durations and acceleratio mensurae, influencing the rationalization of rhythmic practices in ensemble performance.[13] In the 16th century, performers routinely added diminutions as embellishments to written polyphony, with some composers notating them explicitly, while treatises began codifying techniques for melodic division and ornamentation.[5] The invention of music printing around 1500, exemplified by Ottaviano Petrucci's publications, facilitated the widespread dissemination of such treatises and scores, broadening access to diminution practices across Europe and supporting their integration into contrapuntal and ornamental frameworks.[14] During the Baroque era (1600–1750), diminution shifted toward improvisation, with performers elaborating melodies through on-the-spot divisions and figurations, as seen in the works of composers like J.S. Bach and Antonio Vivaldi.[5] This transition from primarily notated embellishments in the Renaissance to spontaneous additions reflected evolving performance conventions, where diminution enhanced affective expression in solo and ensemble contexts. The practice persisted into the Classical period, notably in C.P.E. Bach's improvisational preludes, where diminution involved varied figural elaborations of harmonies to create dynamic fantasies and modulate keys fluidly.[15] Through the Romantic era, such improvisatory techniques continued to influence keyboard and vocal ornamentation, underscoring diminution's enduring role in musical elaboration.Diminution as Embellishment
Italian Literature of the Sixteenth and Early Seventeenth Century
In the late sixteenth century, Italian music theory increasingly emphasized diminution as a vital embellishment technique for both vocal and instrumental performance, particularly in the context of the Renaissance's shift toward expressive individualism. Girolamo Diruta's Il Transilvano (1593), a dialogue on organ and keyboard playing published in Venice, provides one of the earliest systematic treatments of keyboard diminutions, advocating for melodic elaborations using shorter note values to compensate for the limited sustain of quilled instruments and to heighten emotional expression. Diruta describes techniques such as groppi—short diatonic turns or runs ascending and descending, often with accidentals at cadences—and tremoli, shakes that occupy half the value of the principal note, starting from the main pitch and incorporating an upper auxiliary. These diminutions, executed in crotchets, quavers, or semiquavers, are integrated into toccatas and variations (partite), with Diruta recommending a deliberate tempo (pigliare il tempo largo) to ensure clarity and avoid rushing, distinguishing them from more rapid shakes. For instance, a groppo might conclude a trill at a cadence, transforming a minim into a sequence of quavers for graceful resolution. Concurrently, Giovanni Luca Conforti's Breve et facile maniera d'essercitarsi a far passaggi (1593), aimed at singers, focuses on vocal embellishments through structured exercises that divide long notes into shorter, melodic segments to enhance agility and textual interpretation.[16] Conforti presents passaggi—diatonic runs or divisions—as the core method for ornamenting intervals from unisons to octaves, starting with simple eighth-note patterns and progressing to more complex variants, including groppi (trills) and trilli (tremolos) that double note values at cadences for dramatic emphasis.[16] His approach, adaptable across seven clefs to suit any vocal range, encourages performers to vary embellishment length based on proficiency, with a regimen to master basics in nine days and full technique in under two months.[16] These techniques draw from the seconda prattica, prioritizing word-painting over strict counterpoint, and are exemplified in Conforti's later Salmi passaggiati (1601–1603), where psalm verses like "Nisi Dominus" feature passaggi on unisons and fifths to convey spiritual depth.[16] Such practices were deeply influenced by the Venetian school, centered at St. Mark's Basilica, where composers like Girolamo Dalla Casa integrated passaggi into wind and vocal lines, dividing semibreves into quavers, semiquavers, or even 32nd notes while maintaining the steady tactus beat for rhythmic integrity.[17] This ornamental style facilitated the transition to early Baroque opera, as seen in Claudio Monteverdi's L'Orfeo (1607), where diminution enhances monody and arias, such as the famed "Possente spirto," with passaggi filling the melodic body to evoke pathos, though cadences remain relatively plain to spotlight effetti like trills for emotional climaxes.[18] Monteverdi provided both unadorned and embellished versions of select arias, reflecting the improvisatory ethos of Venetian polyphony evolving into dramatic solo expression.[18] Period notation often juxtaposed plain melodies against diminished variants to illustrate division. For example, in Dalla Casa's treatise, a descending semibreve on G might appear as: Original:G (semibreve, held for two tactus beats) Diminished (semiquaver passaggi):
G-F-E-D-C-D-E-F-G (ascending return for resolution, each note light and equal in the tactus) This division maintains the melodic contour while adding florid motion, as notated in full rather than shorthand to guide performers.[17] Similarly, Conforti's exercises divide a unison on C into eighth notes with a groppo: C-B-C (trill) resolving to D, emphasizing stepwise elegance over virtuosic display.[16] These examples underscore diminution's role in bridging madrigal polyphony—where upper voices might receive passaggi for textual accent—and the monodic style of emerging opera.[17]
Spanish Literature
In Spanish musical theory during the Renaissance, diminution manifested prominently through the practice of glosas, or divisions, which involved elaborating simple melodic lines into intricate ornamental passages, particularly for plucked and bowed string instruments. Luis de Milán's El maestro (1536), the first printed collection of vihuela music, exemplifies this approach by providing tablature examples where basic tenor lines are diminished into flowing sequences of shorter notes, often grouped in patterns of four quavers (e.g., short-short-short-long for a showy effect).)[19] These glosas integrated seamlessly with vihuela tablature, allowing performers to reduce polyphonic vocal models to solo instrumental lines while preserving contrapuntal essence through rhythmic subdivision.[20] Diego Ortiz's Tratado de glosas (1553) advanced these techniques for the viola da gamba, offering systematic examples of ornamenting cadences and grounds in two books: the first on embellishing plainchants and tenors, and the second on composing recercadas over polyphonic themes.) Ortiz categorized glosas into perfect (returning to the original note), licensed (with consonant deviations), and free (improvised, used sparingly), emphasizing their role in polyphonic reduction for instrumental performance accompanied by harpsichord.[21] This work built briefly on Italian precursors like passaggi but adapted them to Spanish instrumental idioms, focusing on bowed string embellishments.[22] During the Spanish Golden Age, these diminution practices influenced contrapuntal applications in both courtly and ecclesiastical settings, with vihuela and gamba glosas facilitating expressive elaboration in fantasias and variations. The dissemination of such treatises to the New World via Seville trade routes and missionary activities introduced vihuela techniques to colonial Latin America by the late 16th century, where they informed early music education in viceregal centers like Mexico City and Lima.[23][24] A practical example from Ortiz's Tratado de glosas illustrates a simple glosa on the cadence "Clausulas en F fa ut," transforming a single quarter-note F into a divided sequence:Original: F (quarter note)
Glosa: F - E - F - G - A - G - F (semiminims)
Original: F (quarter note)
Glosa: F - E - F - G - A - G - F (semiminims)
English Literature
In English musical literature of the Elizabethan era, diminution—often termed "divisions"—emerged as a key technique for embellishing melodies, particularly in lute and consort settings, where performers subdivided longer notes into faster, more intricate patterns to demonstrate virtuosity. Thomas Morley's A Plaine and Easie Introduction to Practicall Musicke (1597) provides one of the earliest systematic discussions, framing divisions within the practice of descant, or improvising counterpoint over a fixed plainsong or ground bass. In its second part, Morley instructs readers on "singing a descant" by breaking plain notes into semibreves, minims, or smaller values, emphasizing rhythmic variety while preserving the original harmony; he illustrates this with examples over simple cantus firmi, advising moderation to avoid "jangling" or excess.[26] This pedagogical approach reflected the growing emphasis on practical improvisation in English music education, adapting continental ideas of melodic ornamentation to vocal and instrumental contexts.[27] John Dowland's influence further solidified divisions in lute music, as seen in his contributions to Varietie of Lute-Lessons (1610), compiled by his son Robert, which includes pavans, galliards, and fantasies featuring written-out repeats with added divisions. Dowland favored "breaking divisions," where performers fragmented semibreves or breves into chains of semiminims or fusae, often incorporating descending "falling" figures to evoke pathos in ayres—strophic songs for voice and lute—or the free-form fantasies for solo lute. These techniques allowed lutenists to vary repeats dynamically, transforming a plain strain into a florid display while maintaining the piece's harmonic structure; for instance, in consort ayres, the lute might underpin vocal lines with broken divisions, echoing the voice's melody in ornamental echoes.) English practices shared roots with Italian and Spanish traditions of passaggi and diferencias, imported via traveling musicians, but adapted for the lute's polyphonic capabilities in secular genres.[27] Within the English virginal school, diminution played a central role in keyboard compositions, influenced by lute precedents and continental imports like Italian intabulations. William Byrd's works from the 1590s, such as those in My Ladye Nevells Booke (c. 1591), exemplify this through variation sets where initial plain statements of a theme yield to increasingly elaborate diminutions, often in the treble voice over a sustained bass. Byrd's pavans and grounds feature breaking divisions that accelerate rhythmic motion—semiminims evolving into hemious—creating textural contrast and emotional depth, as in his variations on popular airs; surviving manuscripts show variants with added ornaments, highlighting performers' improvisatory freedom.[28] This integration of lute-derived divisions into virginal music underscored the era's blend of instrumental agility and contrapuntal rigor, influencing consort fantasies where mixed ensembles applied similar embellishments.[29] A representative example appears in Dowland's Pavana Lachrymae (c. 1590s, included in Varietie of Lute-Lessons), where the opening strain in G minor presents a somber theme in long notes, repeated with breaking divisions:Original strain (simplified notation):
G4 - F4 - E4 - D4 - C4 (semibreves, descending)
Diminished repeat:
G4 - F#8 E8 - F8 E8 D8 - C#8 D8 C8 B8 - A8 G8 (semiminims, with passing notes and falling appoggiaturas)
Original strain (simplified notation):
G4 - F4 - E4 - D4 - C4 (semibreves, descending)
Diminished repeat:
G4 - F#8 E8 - F8 E8 D8 - C#8 D8 C8 B8 - A8 G8 (semiminims, with passing notes and falling appoggiaturas)
German Literature
In German theoretical literature of the late Renaissance, diminution emerged as a vital technique for embellishing organ and polyphonic music, particularly within the Lutheran tradition of sacred composition. Elias Nikolaus Ammerbach's Orgel oder Instrument Tabulatur (1571), the first printed collection of German keyboard music in tablature notation, exemplifies this approach through its intabulations of chorale melodies, where plainchant-like lines are subdivided into faster note values to add expressive ornamentation while preserving harmonic structure. Ammerbach's work, drawing from broader Renaissance practices of melodic division, provided organists with practical models for improvisatory embellishment in church settings.[30] Complementing Ammerbach, Seth Calvisius's Exercitationes musicae duae (1600) addressed contrapuntal divisions, advocating for the systematic breaking down of melodic lines in polyphonic textures to enhance rhythmic vitality and imitate rhetorical eloquence.[31] Calvisius emphasized divisions as a means to balance simplicity in sacred music with artistic elaboration, influencing pedagogical texts on counterpoint. These treatises reflect the integration of diminution with Lutheran chorale practices, where intabulation methods transformed vocal hymn melodies into keyboard pieces by fragmenting long notes into sequences of shorter ones, often in the pedal or manual lines, to support congregational singing.[32] Diminution techniques in this era focused on rhythmic subdivision, such as converting semibreves into minims or semiminims, to create flowing passages that maintained the chorale's modal integrity while allowing for idiomatic organ registration. In Lutheran church music, these methods were applied to intabulate chorales like Nun komm, der Heiden Heiland, breaking the cantus firmus into embellished phrases that alternated between literal statements and ornate divisions, fostering a dialogue between tradition and improvisation.[33] The influence of Michael Praetorius and Samuel Scheidt extended these ideas into the early seventeenth century; Praetorius's Syntagma musicum (1614–1620) documented organ techniques including diminutive variations on chorales, while Scheidt's Tabulatura nova (1624) incorporated rhythmic diminutions in chorale fantasias, bridging Renaissance intabulation with Baroque elaboration. For completeness, diminution appeared in German motets after 1550, as seen in works by composers like Johann Walter, where polyphonic lines featured subdivided rhythms to heighten textual expression in settings of psalm or hymn texts. A representative example from Ammerbach's tablature is the chorale prelude on Christ ist erstanden, where the original melody's long notes undergo rhythmic diminution: the opening phrase's semibreve on the tonic is divided into two minims, followed by semiminims in the consequent, creating a cascading effect in the right hand over a sustained bass. This can be illustrated as follows:Original (simplified): Diminution (rhythmic breakdown):
Semibreve ([whole note](/page/Whole_note)) Minim + Minim (two half notes)
Semiminim + Semiminim + ... (four quarter notes)
Original (simplified): Diminution (rhythmic breakdown):
Semibreve ([whole note](/page/Whole_note)) Minim + Minim (two half notes)
Semiminim + Semiminim + ... (four quarter notes)
Dutch Literature
In the early 17th century, Dutch musicians and scholars advanced diminution practices—known as divisions or embellishments through note subdivision—primarily in instrumental and pedagogical settings, reflecting the Dutch Golden Age's emphasis on chamber music and private performance. This period saw the dissemination of musical ideas via trade networks, which facilitated the exchange of Italian and French techniques across Europe, filling gaps in formal vocal traditions by prioritizing intimate, embellished ensemble playing.[34] Constantijn Huygens (1596–1687), a prominent statesman, poet, and lutenist, contributed significantly through his extensive correspondence and compositions, which documented diminution as an essential skill for expressive lute playing. In letters to figures like Marin Mersenne, Huygens discussed acquiring superior Italian lutes from Bologna for their resonance in embellished passages and emphasized "swier" (verve) in divisions, advocating nimble, even execution of cadences to enhance melodic flow.[34][35] His over 800 lute pieces, including those in the Pathodia Sacra et Profana (1647), often incorporated continuo and demonstrated diminution for string instruments like the viola da gamba, promoting its use in diplomatic and household chamber settings.[34] Huygens's pedagogical approach involved structured daily lessons for his sons, critiquing repetitive practice while integrating graces and holds, as seen in manuscripts like the Ghent University Library's Hs.3898 with examples of double appoggiaturas and trills.[34] Jan Pieterszoon Sweelinck (1562–1621), the era's leading organist and composer, influenced diminution through his keyboard variations, which his pupils adapted into treatises around 1620 emphasizing divisions on wind and string instruments. Works like his polyphonic psalm settings (1606–1621) and variations, such as on "Mein junges Leben hat ein End," feature progressive note division: the initial theme in long values yields to later variations with semiquavers and intricate figurations, serving as models for improvisational embellishment in chamber contexts.[36] Pupils' treatises, drawing from Sweelinck's English-influenced style, focused on pedagogical exercises for organ and lute divisions, adapting techniques like those in Nicolas Vallet's psalm embellishments for practical home use.[34] Adriaan Valerius's Neder-lants Gedenc-cloecke (1626) exemplifies these approaches in a collection of 76 songs with lute and cittern tablatures, where diminution appears in upper voices through semiquavers and added accidentals for expressive contrafacta.[34] Tailored for amateur string players, it promoted embellished accompaniments in early Baroque chamber music, often using French D minor tuning for wind-like fluidity on lute. These works, influenced briefly by neighboring German organ traditions via Sweelinck's students, underscored diminution's role in elevating private Dutch musical life amid trade-driven cultural exchange.[34][36]Compositional Techniques
Diminution in Melody and Structure
Diminution serves as a core compositional technique in music, distinct from ornamentation, which involves performer-added embellishments to enhance expressivity; instead, diminution is embedded within the score as a method of subdividing longer melodic notes into shorter ones to drive structural and thematic evolution. This integral approach allows composers to generate rhythmic vitality and motivic variation directly in the fabric of the piece, fostering development without relying on external improvisation.[5][37] In melodic applications, particularly within variation forms such as those built on a ground bass, diminution creates interest by dividing sustained notes of the theme into rapid subdivisions, thereby elaborating the upper voices while preserving the underlying harmonic framework. For instance, in Baroque ground bass compositions, this note division transforms static melodic lines into dynamic passages, heightening tension and release over repetitions of the bass pattern. A prominent example appears in Johann Sebastian Bach's Goldberg Variations (1741), where variations on the aria's sarabande-like theme employ diminution to intensify melodic contours, such as in Variation 7, which subdivides the original's quarter notes into eighths and sixteenths for heightened ornament-like energy within the composed structure.[38][3] Structurally, diminution facilitates motivic development in forms like fugues and sonatas by compressing rhythmic values to propel thematic transformation and create contrast. In fugues, it often halves or quarters note durations in subsequent entries or episodes, accelerating the pace and building intensity; Bach's The Art of Fugue (c. 1740s) exemplifies this in canons where diminution combines with inversion to unify disparate sections. In sonata form, diminution aids the development section by shortening motifs to facilitate fragmentation and recombination, providing balance when paired with augmentation, which elongates durations for grandeur and repose. This rhythmic opposition—diminution for urgency versus augmentation for expansiveness—establishes formal equilibrium and narrative progression.[39][3][40] Among specific techniques, sequential diminution applies progressive rhythmic compression across repeated melodic segments transposed to new pitches, expanding thematic material while maintaining coherence. In 20th-century serialism, Arnold Schoenberg incorporated diminution to rhythmically alter twelve-tone rows, deriving variants that enhance textural density without disrupting pitch ordering; this approach, seen in works like Schoenberg's Suite for Piano, Op. 25 (1921), integrates diminution as a structural tool for atonal development.[41][42]Rhythmic Diminution of Note Values
Rhythmic diminution involves the systematic reduction of note durations in musical notation, effectively accelerating the tempo while preserving proportional relationships among notes. In mensural notation, prevalent from the late 13th to the early 17th century, this process often entailed converting larger note values—such as breves into semibreves—through specific signs that halved or otherwise shortened durations relative to an established mensuration. For instance, a vertical stroke through the mensuration sign, like a slashed circle (O), indicated that the perfect breve of the undiminished sign (o) was to be performed as two perfect breves, thereby doubling the speed of the passage.[10] Proportional relationships were central, with tempus perfectum dividing a breve into three semibreves (3:1 ratio) and tempus imperfectum into two (2:1 ratio), allowing diminution to alter these divisions without disrupting the underlying pulse.[10][7] The history of rhythmic diminution in notation traces from medieval practices, such as isorhythm in motets around 1300–1450, where repeating rhythmic patterns (talea) underwent strict or free diminution to compress durations, often reducing values to one-third through successive levels. This evolved into the white mensural notation of the Renaissance, where numerical ciphers (e.g., "o 2" for proportio dupla) specified exact proportional shortenings, such as replacing three imperfect semibreves with three imperfect breves to halve the overall tempo. By the Baroque era, these techniques influenced proportional notation and early forms of metric modulation, where note values were halved—equivalent in modern terms to transforming whole notes into half notes or quarters into eighths—to facilitate smooth transitions between sections or voices.[10][7] In performance, rhythmic diminution required precise tempo adjustments to maintain the intended pulse, as the notated values no longer aligned directly with the original mensuration; for example, a diminished section might double the speed, demanding conductors and performers to recalibrate based on the proportional sign. This added interpretive depth, particularly in polyphonic works where voices might enter under different diminutions. In the 20th century, Igor Stravinsky extended these principles into heightened rhythmic complexity, employing diminution on ostinati—such as progressively shortening melodic rhythmic values in works like The Rite of Spring—to create layered, accelerating textures that evoke tension and forward momentum without explicit mensural signs.[10][43] Specific rules for note value hierarchies in mensural notation varied by tempus and prolatio (the semibreve-minim division, perfect at 3:1 or imperfect at 2:1). The following table outlines key relationships in undiminished mensurations, where the longa typically equaled two breves in imperfect time or a variable in perfect time:| Mensuration Sign | Tempus | Prolatio | Breve Division | Semibreve Division | Longa Relation to Breve |
|---|---|---|---|---|---|
| c (imperfect/imperfect) | Imperfect | Imperfect | 2 semibreves | 2 minims | 2 breves [] |
| o (perfect/imperfect) | Perfect | Imperfect | 3 semibreves | 2 minims | 2 breves [] |
| ç (imperfect/perfect) | Imperfect | Perfect | 2 semibreves | 3 minims | 2 breves [] |
| ø (perfect/perfect) | Perfect | Perfect | 3 semibreves | 3 minims | 2 breves [] |
Harmonic Applications
In harmonic contexts, diminution primarily serves to elaborate melodic lines or rhythmic elements without disrupting the underlying harmonic progression, allowing composers and performers to add complexity while preserving structural coherence. For instance, in counterpoint, diminutions fill in motives with shorter notes that pass through non-chord tones, ensuring the essential harmonies—such as root-position triads or seventh chords—remain intact and the voice leading stays smooth.[3] This technique contrasts with direct harmonic alterations, focusing instead on rhythmic subdivision to enhance expressiveness over a stable bass or cantus firmus.[6] Diminution can also apply to harmonic rhythm, the rate at which chords change, by progressively shortening the duration of each harmonic unit to accelerate the pace and build tension. In Baroque and Classical music, this creates drive toward cadences; for example, a sequence might begin with chords lasting full measures and then diminish to half or quarter notes, intensifying the forward motion without altering chord qualities. Such applications heighten urgency, as seen in developmental sections where rhythmic compression propels the harmony toward resolution.[1]References
- https://en.wikisource.org/wiki/A_Dictionary_of_Music_and_Musicians/Ground_Bass