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Transcript of 14th Century Polyphony
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MOTET
Musicians at Nôtre-Dame created this
new genre in the
early thirteenth century
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MOTET
Motets originally consisted of newly written Latin words
added to the upper voices of discant clausulae.The earliest texts were often a textual trope of the clausula.
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MOTET
The French word for “word” MOT
inspired the name for the genre.
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MOTET
The Thirteenth-Century Motet is a
polyphonic works withone or more texted voices added to a pre-existing tenor,
which is set in a modal rhythm.
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MOTET
Motets are identified by a
compound title
comprising the first words of each voice fromhighest to lowest.
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MOTET
Motets are identified by a
compound title
comprising the first words of each voice fromhighest to lowest.
Factume est salutare / Dominus
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MOTET
The motet became the leading polyphonic
genre for both
sacred and secular music.
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MOTET
The Early Motet (to ca. 1250)
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MOTET
Based on the discant clausula
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MOTET
Based on the discant clausulaThe new text tropes the original chant text
Phrasing of original clausulashapes phrases of added text
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MOTET
Sung during the Mass or as independent entertainment
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MOTET
Factum est salutare / Dominus
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MOTET
These existing motets were reworked
New texts added to duplum in Latin or French
no longer linked to liturgical context
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MOTET
These existing motets were reworked
New texts added to duplum in Latin or French
no longer linked to liturgical context
Other voices (triplum) added
with texts of their own
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MOTET
Early Motets (to ca. 1250)
Double Motet: a motet with two addedtexts above the tenor(Double motet = three voices)
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MOTET
Early Motets (to ca. 1250)
Triple motet: a motet with three addedtexts above the tenor (Triple motet = four voices)
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MOTET
The “Additive” Motet
Original duplum discarded andanother one (or more) composed.
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MOTET
“Original” Motets composed “from scratch”
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MOTET
“Original” Motets composed “from scratch”
Chant tenor from clausula set in modal rhythm
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MOTET
“Original” Motets composed “from scratch”
Chant tenor from clausula set in modal rhythmDuplum / Triplum added above tenor
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MOTET
on “Dominus” of
“Viderunt omnes”
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MOTET
melisma
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MOTET
“Factum est salutare / Dominus”
∨“Fole acostumance / Dominus”
same tenor (2x)
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MOTET
“Factum est salutare / Dominus”
∨“Fole acostumance / Dominus”
same tenor (2x)
new duplum…
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MOTET
“Factum est salutare / Dominus”
∨“Fole acostumance / Dominus”
same tenor (2x)
new duplum…with secular text...
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MOTET
“Factum est salutare / Dominus”
∨“Fole acostumance / Dominus”
same tenor (2x)
new duplum…with secular text...in French
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MOTET
“Super te / Sed fulsit / Dominus”Tenor “Dominus” (first half 2x)
Duplum / Triplum with texts from Latin poem
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MOTET
“Super te / Sed fulsit / Primus Tenor / Dominus”
based on“Super te / Sed fulsit / Dominus”
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MOTET
“Super te / Sed fulsit / Primus Tenor / Dominus”
based on“Super te / Sed fulsit / Dominus”
with added untexted “primus tenor”
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MOTET
Motets in later thirteenth century
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MOTET
Motets in later thirteenth centuryBy 1250 three voices are typical
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MOTET
Motets in later thirteenth centuryBy 1250 three voices are typicalUpper voices with texts in Latin
or French, or French & Latin
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MOTET
By 1270 the tenor is now called the
CANTUS FIRMUS
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MOTET
By 1270 the TENOR is now called the
CANTUS FIRMUS=
A pre-existing melody
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MOTET
By 1270 the TENOR is now called the
CANTUS FIRMUS=A pre-existing melody
Melody predominantly CHANT
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FRANCONIAN NOTATION
Franco of Cologne Ars Cantus Mensurabilis (c. 1280)Innovations in notating RHYTHM
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FRANCONIAN NOTATION
Noteshape signifies relative duration
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FRANCONIAN NOTATION
Noteshapes are:
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FRANCONIAN NOTATION
Noteshapes are:
+ Double long
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FRANCONIAN NOTATION
The tempus (pl. tempora) is the basic unit
Long = 2 or 3 tempora Breve = 2 or 3 tempora
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FRANCONIAN NOTATION
The tempus (pl. tempora) is the basic unit
Long = 2 or 3 tempora Breve = 2 or 3 temporaFranconian system included signs for rests
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FRANCONIAN NOTATION
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FRANCONIAN NOTATION
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FRANCONIAN NOTATION
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FRANCONIAN NOTATION
With Franconian notationscore notation not needed
voices written in parts rather than score format
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FRANCONIAN NOTATION
DUPLUM
TRIPLUM
TENOR
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FRANCONIAN MOTETS
Motets written in Franconian Notation
Written in style made possible by Franconian Notation
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FRANCONIAN MOTETS
Motets written in Franconian Notation
Written in style made possible by Franconian NotationEach voice has distinctive rhythm
Rhythm no longer shaped by Modal Rhythm
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FRANCONIAN MOTETS
Adam DE LA HALLE
(c. 1240-1288?)
De ma dame vient / Dieus comment porroie /
Omnes
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FRANCONIAN MOTETS
Tenor “Omnes” > Gradual Viderunt Omnes
(4) x 3
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FRANCONIAN MOTETS
Tenor “Omnes” > Gradual Viderunt Omnes
(4) x 3Duplum (Motetus) > Dieux, comment porroie
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FRANCONIAN MOTETS
Tenor “Omnes” > Gradual Viderunt Omnes
(4) x 3Duplum (Motetus) > Dieux, comment porroie
Triplum > newly composedwith quotes from songs
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FRANCONIAN MOTETS
Each voice has its own paceDuplum = woman’s point of view
Triplum = man’s point of viewParts are independent
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FRANCONIAN MOTETS
Harmony allows thirds and other dissonances
P 4 now being treated like a dissonanceCadences still demand “perfect” consonances
Cadence patterns developing
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ROTA
English culture was tied to that of France after
the Norman Conquest in 1066
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ROTA
English culture was tied to that of France after
the Norman Conquest in 1066 Although they adopted French culture,
English musicians created a distinct musical style
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ROTA
Prominent “imperfect consonances” Improvised partsinging in close harmony
documented as early as 1200
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ROTA
Prominent “imperfect consonances” Improvised partsinging in close harmony
documented as early as 1200Emphasis on
harmonic thirds and triads
including the final sonority
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ROTA
Voice-exchange evolved into elaborate
techniques
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ROTA
Voice-exchange evolved into elaborate
techniquesThe RONDELLIUS
two or three phrases are heard simultaneously,
with each voicesinging each one in turn
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ROTA
Rondellus
Triplum: a b cDuplum: c a b
Tenor: b c a
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ROTA
A ROTA is a perpetual canon
or round at the unison
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ROTA
Sumer is icumen in
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ROTA
Sumer is icumen in
Two voices sing a voice-exchange pes (Latin for “foot” or “ground”).
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ROTA
Sumer is icumen in
Two voices sing a voice-exchange pes (Latin for “foot” or “ground”).Four upper voices in canon
producing alternating triadic sonorities of F–A–C and G–B-flat–D
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POLYPHONY
By 1300, “composition” meant creating
polyphony, not monophony.
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POLYPHONY
Writing down music of multiple parts in coordinating vertical sonorities to create a
sense of direction that would be a hallmark of Western tradition and set it apart from almost all other
musical traditions.
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FOURTEENTH CENTURY
Difficult conditions in Europe
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FOURTEENTH CENTURY
Difficult conditions in Europe
“Mini Ice Age”Floods
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FOURTEENTH CENTURY
Difficult conditions in Europe
“Mini Ice Age”Floods
The BLACK DEATH
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FOURTEENTH CENTURY
Difficult conditions in Europe
“Mini Ice Age”Floods
The BLACK DEATH
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FOURTEENTH CENTURY
BUBONIC PLAGUE
killed one third of the Europe’s population1347-1350
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FOURTEENTH CENTURY
BUBONIC PLAGUE
killed one third of the Europe’s population1347-1350
Victims died within daysSurvivors fled urban areas
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FOURTEENTH CENTURY
GREAT SCHISM
1378-1417 King Philip IV of France
French Pope in Avignon Corrupt clergy bureaucracy
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FOURTEENTH CENTURY
SCIENCE & SECULARISM
William of Ockham (c.1285-1349)Knowledge from experience and the senses
Eyeglasses, Mechanical clocks, Magnetic compass
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FOURTEENTH CENTURY
compassWilliam of Ockham
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FOURTEENTH CENTURY
VISUAL ARTS
The Florentine painter GIOTTO achieved morenaturalistic representation
and a sense of depth and symmetryPERSPECTIVE
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FOURTEENTH CENTURY
VISUAL ARTS
Giotto, Arena Chapel, Padua
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FOURTEENTH CENTURY
LITERATUREIncreased literacy led to
more literature in the vernacular. Dante Alighieri and Giovanni Boccacio in Italian
Geoffrey Chaucer in English
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FOURTEENTH CENTURY
MUSICIncreased attention to secular song,
though much sacred music continuedto be composed.
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FOURTEENTH CENTURY
ROMAN de FAUVEL
F latterie (Flattery) Avarice (Greed)
V illanie (Villany)
V ariété (Fickleness)
E nvie (Envy) Lâcheté (Cowardice)
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FOURTEENTH CENTURY
ROMAN de FAUVEL
F latterie (Flattery) Avarice (Greed)
V illanie (Villany)
V ariété (Fickleness)
E nvie (Envy) Lâcheté (Cowardice)
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ROMAN de FAUVEL
F latterie (Flattery)
Avarice (Greed)
V illanie (Villany)
V ariété (Fickleness)
E nvie (Envy)
Lâcheté (Cowardice)Fond Français 146, Paris, Bibliothèque Nationale
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ARS NOVA
Philippe de Vitry (1291-1361)
Ars Nova (c. 1320)“This completes the ars nova of Magister
Philippe de Vitry”
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ARS NOVA
Philippe de Vitry (1291-1361)
Ars Nova (c. 1320)“This completes the ars nova of Magister
Philippe de Vitry”Vitry compositions among the 169 pieces of
music in Fauvel
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ARS NOVA
MENSURATION SIGNS
MODE = Division of the LongTIME = Division of the Breve PROLATION= Division of the Semibreve
Major / Minor
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ARS NOVA
Shifting emphasis to duple meters was criticized
by Jacque de Liège
“Perfection is brought low, and imperfection
exalted.”
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ISORHYTHM
Motets of Philippe de Vitry some of the earliest
uses of ISORHYTHM
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ISORHYTHM
Motets of Philippe de Vitry some of the earliest
uses of ISORHYTHM
Rhythmic structure of the tenor of motet
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ISORHYTHM
TALEA
“cuttings” (pl. taleae) Rhythmic pattern
COLOR“color” (pl. colores)
The melodic notes of the tenor
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ISORHYTHM
TALEA
“cuttings” (pl. taleae) Rhythmic pattern
The tenor is laid out in segments of identical
rhythm.
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ISORHYTHM
TALEA
“cuttings” (pl. taleae) Rhythmic pattern
Taleae in tenors in 1200s = short patterns Taleae in tenors in 1300s = longer patterns
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ISORHYTHM
TALEA
“cuttings” (pl. taleae) Rhythmic pattern
The slow pace of the tenor makes it less a
melody and more of a foundational structure.
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ISORHYTHM COLOR
“color” (pl. colores)
The melodic notes of the tenor
The color and may repeat,
but not necessarily with the rhythm.
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ISORHYTHM
“In arboris / Tuba sacre fidei / Virgo sum”
attributed to Vitry
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ISORHYTHM
“In arboris / Tuba sacre fidei / Virgo sum”
attributed to Vitry
Tenor refers to the Virgin MaryDuplum ( Motetus) and Triplum refer to Mary
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ISORHYTHM
“In arboris / Tuba sacre fidei / Virgo sum”
attributed to VitryThe tenor includes
two statements of the color 6 repetitions of the talea
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ISORHYTHM
“In arboris / Tuba sacre fidei / Virgo sum”
attributed to Vitry Coloration indicates changes from duple to triple
Introitus
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HOCKET
“Hiccup”
Two voices alternating in rapid succession, each resting while the other sings
The device was developed in the thirteenthcentury
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ARS NOVA HARMONIC PRACTICES
Greater prominence of imperfect consonancesCadences required perfect consonances,but their resolution could be sustained
Parallel octaves and fifths continued to be used
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GUILLAUME de MACHAUT
(c. 1300-1377)
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GUILLAUME de MACHAUT
(c. 1300-1377)The leading composer of the French Ars Nova
Born in northeastern France, middle-class family
Educated as a cleric and took Holy Orders
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GUILLAUME de MACHAUT
(c. 1300-1377)1323–1340, worked as secretary for John
of Luxembourg, King of Bohemia,
Resided in Reims after 1340Royal patrons supported him, including the
kings of Navarre and France
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GUILLAUME de MACHAUT
(c. 1300-1377)First composer to compile his complete works
and to discuss his working method
He wrote his poems first, then the music
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GUILLAUME de MACHAUT
(c. 1300-1377)First composer to compile his complete works
and to discuss his working method
He wrote his poems first, then the musicLiked music “sweet and pleasing”
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GUILLAUME de MACHAUT
(c. 1300-1377)He paid for the preparation of several
illuminated manuscripts of his works
He composed many major musical works andnumerous narrative poems
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GUILLAUME de MACHAUT
(c. 1300-1377)23 motets, most from early in his career
20 are isorhythmic, 3 which usesecular songs as tenors.Often include hockets
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GUILLAUME de MACHAUT
(c. 1300-1377) Messe de Nostre Dame
“Mass of Our Lady”
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GUILLAUME de MACHAUT
(c. 1300-1377)Probably the earliest polyphonic setting of the
Mass Ordinary to be composed by a single
composer and conceived as a unitKyrie, Gloria, Credo, Santus, Agnus Dei
&
Ite missa est
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GUILLAUME de MACHAUT
(c. 1300-1377)In the fourteenth century, anonymous
composers in France, England, and Italyset individual movements polyphonically.A few mass “cycles” were assembled from
individual movements
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GUILLAUME de MACHAUT
(c. 1300-1377)Composed for the cathedral in Reims
Performed at a Mass for the Virgin Marycelebrated every Saturday
After Machaut’s death, an oration for
Machaut’s soul was added to the service,and performed until fifteenth century
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GUILLAUME de MACHAUT
(c. 1300-1377) UNIFYING DEVICES
Recurring motivesTonal focus on D in the first three
movements and on F in the last three
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GUILLAUME de MACHAUT
(c. 1300-1377) UNIFYING DEVICES
All six movements are for four voices, including a contratenor (“against the tenor”)
that moves in the same range as the tenor.
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GUILLAUME de MACHAUT
(c. 1300-1377) UNIFYING DEVICES
Kyrie, Sanctus, Agnus Dei, and Ite, missa est are isorhythmic.
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GUILLAUME de MACHAUT
(c. 1300-1377) KYRIE
Chant Kyrie Cunctipotens Genitor
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GUILLAUME de MACHAUT
(c. 1300-1377) KYRIE
TENOR: 28 notes of chant, 4-note talea x 7
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GUILLAUME de MACHAUT
(c. 1300-1377) KYRIE
TENOR: 28 notes of chant, 4-note talea x 7 Contratenor also isorhythmic
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GUILLAUME de MACHAUT
(c. 1300-1377) KYRIE
TENOR: 28 notes of chant, 4-note talea x 7 Contratenor also isorhythmic
Upper voices partially isorhythmic
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GUILLAUME de MACHAUT
(c. 1300-1377) Kyrie I: Polyphony, Chant, Polyphony
Christe: Chant, Polyphony, ChantKyrie II: Polyphony, Chant
Kyrie III: Polyphony
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GUILLAUME de MACHAUT
(c. 1300-1377)Polyphonic songs (chansons, “songs”)
in the formes fixes
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GUILLAUME de MACHAUT
(c. 1300-1377)“Treble-dominated” songs major
innovation of the Ars Nova
The treble or cantus carries the text
Slower untexted tenor supports the cantus.A contratenor may be added,
Triplum in same range as cantus
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GUILLAUME de MACHAUT
(c. 1300-1377) RONDEAUX
Two musical phrases ( A and B) Text includes a “refrain” (AB)
Form: ABaAabAB
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GUILLAUME de MACHAUT
(c. 1300-1377) RONDEAUX
“Rose, liz, printemps, verdure”
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A Rose, liz, printemps, verdure,Fleur, baume et tres douce odour, B Bele, passés en douçour, a Et tous les biens de Nature, Avez dont je vous aour.
A Rose, liz, printemps, verdure,Fleur, baume et tres douce oudour.
a Et quant toute creature Seurmonte vostre valour,
b Bien puis dire et par honnour: A Rose, liz, printemps, verdure,
Fleur, baume et tres douce oudour,B Bele, passés en douçour.
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ARS NOVA … ARS SUBTILIORComposers at the court of the Avignon pope
across southern France and northern Italy cultivated complex secular music.
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ARS NOVA … ARS SUBTILIOR
ARS SUBTILIOR a continuation of Ars Nova
in
secular polyphonic songs in the formes fixesand
developing the complexities of Ars Nova notation
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ARS NOVA … ARS SUBTILIOR
Love songs intended for an elite audience
Pieces notated in fanciful shapes
Rhythmically complex
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“Belle, bonne, sage”Baude Cordier
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“Tout par compas”Baude Cordier
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Performing Fourteenth-Century Music
There was no uniform way to perform
polyphonic music.Pictorial and literary sources indicate vocal,
instrumental, and mixed groups.All vocal performance was most common.
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INSTRUMENTS
Instruments separated into 2 categories:
HAUT and BAS
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INSTRUMENTS
HAUT (“high”) instruments were loud,
for outdoors and dancing. Cornetts TrumpetsShawmsSackbuts
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INSTRUMENTS
BAS (“low”) instruments were soft in volume
and were played indoors Stringed instruments: harps, lutes, and vielles
Portative organsTransverse Flutes
Recorders
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INSTRUMENTS
Percussion instruments were common in all
kinds of ensembles
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“FALSE MUSIC”
MUSICA FICTA, or Chromatic Alterations
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“FALSE MUSIC”
Raising or lowering a note by a half-step
to avoid the tritonePitches altered to make a smoother melodic line,
especially at cadences.
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“FALSE MUSIC”
Raising or lowering a note by a half-step
to avoid the tritonePitches altered to make a smoother melodic line,
especially at cadences.The resulting pitches lay “outside the gamut” andwere thus “false”, or ficta
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“FALSE MUSIC”
Raising or lowering a note by a half-step
to avoid the tritonePitches altered to make a smoother melodic line.The resulting pitches lay “outside the gamut” and
were thus “false” or ficta
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“FALSE MUSIC”
Medieval singers were trained to recognize
situations in which a ficta were needed,so accidentals were rarely notated.
(Modern editions ficta accidentals above the staff,
to indicate editorial intervention)
WHITE NOTATION
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WHITE NOTATIONWhite Notation uses a five-line staff,
and three clefs—G, C, and F. Usually the only accidental notated as a ‘key’
signature is B-flat, though later composers
experimented with more
WHITE NOTATION
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MEASURES AND BARLINES
There are no barlines or measuresBut the length of the breve usually acted as a time unit
analogous to the modern concept of a measure
WHITE NOTATION
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WHITE NOTATIONNOTE VALUES and RESTS
WHITE NOTATION
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WHITE NOTATIONMENSURATION
Mensuration deals with the
division of the Breve (called Tempus or “time”) and the Semibreve (Prolationis Species or
“prolation”)
WHITE NOTATION
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WHITE NOTATIONMENSURATION
Breve divisions (Tempus) are either
“perfect” (division into 3s) or “imperfect (divisioninto 2s).
Semibreve divisions (Prolation) are either
“major” (3) or “minor” (2)
WHITE NOTATION
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WHITE NOTATIONMENSURATION
A line through the mensuation symbol indicates
that all note values are cut in half (alla breve).
WHITE NOTATION
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WHITE NOTATIONCOLORATION
The value of a note in a mensuration can be
changed by coloring in the white space of breve,
semibreve, or minim and by dotting. In determining a note’s value, coloring is
calculated before dotting.
WHITE NOTATION
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In Perfect Time
—where a breve has the value of 3 semibreves—
coloring a breve will subtract a 1/3 or its value
and imperfects its value and makes a breve equalto 2 semibreves (a duplet)
WHITE NOTATION
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In Imperfect Time
—where a breve has the value of 2 semibreves—
coloring 3 consecutive semibreves creates a triplet
and perfects their value, momentarily making 3semibreves equal the value of 1 breve
WHITE NOTATION
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Josquin uses coloration for all the notes in his
lament on the death of Ockeghem, Nymphes des Bois
to create “eye music”where the blackened notes indicate mourning.
WHITE NOTATION
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Josquin uses coloration for all the notes in his
lament on the death of Ockeghem, Nymphes des Bois
to create “eye music”where the blackened notes indicate mourning. In doing so, Josquin limits himself to longs,
breves, semibreves, and minims, since semiminimand fusa values are already “black
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WHITE NOTATION
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WHITE NOTATIONLIGATURES
White Notation is complicated by several factors,
one of them being the continued use of theLIGATURES (multiple-note units)
and the conventions associated with their use
carried over from neumes.
WHITE NOTATION
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WHITE NOTATION“BREVE” ligatures
At the tempus level, each two-note ligatures has
the value of a breve followed by a long (indicated
by the downward tail).
WHITE NOTATION
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WHITE NOTATION“BREVE” ligatures
WHITE NOTATION
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WHITE NOTATION“BREVE” ligatures
WHITE NOTATION
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WHITE NOTATION“SEMIBREVE” ligatures
The two-note ligatures that begin with an upward tail are semibreves,
and each two-note pes or clivis has the value of
two semibreves,both the square or oblique forms.
WHITE NOTATION
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WHITE NOTATION“SEMIBREVE” ligatures
WHITE NOTATION
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WHITE NOTATION
CANONS
WHITE NOTATION
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WHITE NOTATIONIn his
Missa ‘L’homme armè’
Dufay writes “Cancer eat plenus et redeat medius”
(Let the crab proceed full, and let it return by half )
in the tenor part of the third section of the
“Agnus Dei.”
WHITE NOTATION
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WHITE NOTATION
WHITE NOTATION
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WHITE NOTATION
This indicates that the singers perform this part retrograde
(crabs where thought of as walking “backwards”)with full rhythmic value,and then forward (or “returning” for the crab)
with the notes at half value.
WHITE NOTATION
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WHITE NOTATION
Dufay composes his motet “Nuper rosarum flores”
as an isorhythmic motet, built on two tenors
WHITE NOTATION
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WHITE NOTATION
Dufay composes his motet “Nuper rosarum flores”
as an isorhythmic motet, built on two tenors
WHITE NOTATION
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WHITE NOTATIONDufay notates each tenor part with
four mensuration signs and a repeat, indicating that each performer plays their tenor
line four times, each time with a differentmensuration
WHITE NOTATION
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Dufay notates each tenor part with
four mensuration signs and a repeat, indicating that each performer plays their tenor
line four times, each time with a differentmensuration
WHITE NOTATION
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The numerical value of the breve changes from
6 : 4 : 2 : 3
WHITE NOTATION
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The numerical value of the breve changes from
6 : 4 : 2 : 3
WHY?
WHITE NOTATION
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Dufay wrote this motet for the consecration of the
Duomo in Florence.
WHITE NOTATION
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WHITE NOTATION
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Filippo Brunelleschi
(1377-1446)S. Maria del Fiore, begun 1296
Dome (1420-1436)consecrated by Pope Eugenius IV on
March 25, 1436
WHITE NOTATION
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WHITE NOTATION
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WHITE NOTATION
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WHITE NOTATION
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The numbers refer to the dimensions of
Solomon’s temple described in the Third Book of
Kings, 6:1-20(reduced to their lowest common denominators).
WHITE NOTATION
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2 And the house, which king Solomon built to the
Lord, was threescore (60) cubits in length, and
twenty cubits in breadth, and thirty cubits in
height…16 And he built up twenty cubits with boards of
cedar at the hinder part of the temple, from the
floor to the top: and made the inner house of the
oracle to be the holy of holies.
WHITE NOTATION
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2 And the house, which king Solomon built to the
Lord, was threescore (60) cubits in length, and
twenty cubits in breadth, and thirty cubits in
height…16 And he built up twenty cubits with boards of
cedar at the hinder part of the temple, from the
floor to the top: and made the inner house of the
oracle to be the holy of holies.
WHITE NOTATION
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2 And the house, which king Solomon built to the
Lord, was threescore (60) cubits in length, and
twenty cubits in breadth, and thirty cubits in
height…16 And he built up twenty cubits with boards of
cedar at the hinder part of the temple, from the
floor to the top: and made the inner house of the
oracle to be the holy of holies.
WHITE NOTATION
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6 : 4 : 2 : 3
6 (the Temple’s total length) 4 (the length of the nave)
2 (the length of the sanctuary and width of the
building)
3 (the height of the building)
WHITE NOTATION
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6 : 4 : 2 : 3
6 (the Temple’s total length) 4
WHITE NOTATION
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6 : 4 : 2 : 3
6 (the Temple’s total length) 4 (the length of the nave)
2 (the length of the sanctuary and width of the
building)
3 (the height of the building)