Download 1. Infinite, continuous spectrum (line)

1. Infinite, continuous spectrum (line)
Thursday, May 14, 15
1. Infinite, continuous spectrum (line)
2. Bounded, uniformly punctuated line-segment
3. uniformly punctuated cycle
4. Orientation and associated semantic values
Thursday, May 14, 15
STAGE 1
Thursday, May 14, 15
STAGE 1
1. Continuous Infinite Spectrum
Thursday, May 14, 15
STAGE 1
1. Continuous Infinite Spectrum
Acoustic Frequency
Thursday, May 14, 15
Time
STAGE 1
1. Continuous Infinite Spectrum
Acoustic Frequency
Thursday, May 14, 15
Time
2. Continuous Bounded Spectrum
Thursday, May 14, 15
2. Continuous Bounded Spectrum
Audible Frequency
Thursday, May 14, 15
“Piece” time
2. Continuous Bounded Spectrum
Audible Frequency
Thursday, May 14, 15
“Piece” time
3. Segmented Bounded Spectrum
Thursday, May 14, 15
3. Segmented Bounded Spectrum
bands of pitch space durational spans
Thursday, May 14, 15
3. Segmented Bounded Spectrum
bands of pitch space durational spans
Thursday, May 14, 15
4. Quantization of segments to Points
Thursday, May 14, 15
4. Quantization of segments to Points
Pitches
Thursday, May 14, 15
Time Points
5. Punctuated Bounded Spectrum
Pitches
Thursday, May 14, 15
Time Points
6. (Notionally) Uniform Unit Intervals
Thursday, May 14, 15
6. (Notionally) Uniform Unit Intervals
semitone
Thursday, May 14, 15
6. (Notionally) Uniform Unit Intervals
semitone
Thursday, May 14, 15
semiquaver, etc.
Thursday, May 14, 15
STAGE 2
Thursday, May 14, 15
STAGE 2
7. Uniformly spaced selection (equivalence operator)
Thursday, May 14, 15
STAGE 2
7. Uniformly spaced selection (equivalence operator)
Thursday, May 14, 15
STAGE 2
7. Uniformly spaced selection (equivalence operator)
octave
Thursday, May 14, 15
measure
STAGE 2
7. Uniformly spaced selection (equivalence operator)
octave
pitch class
Thursday, May 14, 15
measure
beat class
Thursday, May 14, 15
Thursday, May 14, 15
Thursday, May 14, 15
8. Punctuated Cycle
Thursday, May 14, 15
8. Punctuated Cycle
chromatic universe
Thursday, May 14, 15
beat-class universe
STAGE 3
c = 12
Thursday, May 14, 15
c=8
STAGE 3
9. Maximally Even Selection
c = 12
Thursday, May 14, 15
c=8
STAGE 3
9. Maximally Even Selection
c = 12
Thursday, May 14, 15
c=8
STAGE 3
9. Maximally Even Selection
c = 12
Thursday, May 14, 15
c=8
STAGE 3
9. Maximally Even Selection
c = 12
diatonic scale
Thursday, May 14, 15
c=8
“on” beats
STAGE 3
9. Iteration
c = 12
Thursday, May 14, 15
c=8
STAGE 3
9. Iteration
c = 12
Thursday, May 14, 15
c=8
STAGE 3
9. Iteration
c = 12
Thursday, May 14, 15
c=8
STAGE 3
9. Iteration
c = 12
Consonant triad
Thursday, May 14, 15
c=8
strong beats
STAGE 3
9. Iteration
c = 12
Consonant triad
Thursday, May 14, 15
c=8
strong beats
STAGE 3
9. Iteration
c = 12
Consonant triad
Thursday, May 14, 15
c=8
strong beats
STAGE 3
10. Orientation
c = 12
Consonant triad
Thursday, May 14, 15
c=8
strong beats
STAGE 4
10. Orientation
c = 12
Consonant triad
Thursday, May 14, 15
c=8
strong beats
11. Telos
c = 12
Consonant triad
Thursday, May 14, 15
c=8
strong beats
STAGE 4
11. Telos
c = 12
Consonant triad
Thursday, May 14, 15
c=8
strong beats
11. Telos
c = 12
Thursday, May 14, 15
c=8
11. Telos
c = 12
Thursday, May 14, 15
c=8
11. Telos
c = 12
“goes to”
Thursday, May 14, 15
c=8
11. Telos
c = 12
“goes to”
attraction magnetism
summoning energy
leading
desire
Thursday, May 14, 15
c=8
11. Telos
c = 12
“goes to”
attraction magnetism
summoning energy
leading
desire
Thursday, May 14, 15
c=8
11. Telos
c = 12
“goes to”
attraction magnetism
summoning energy
leading
desire
Thursday, May 14, 15
c=8
“goes to”
11. Telos
c = 12
“goes to”
attraction magnetism
summoning energy
leading
desire
discharge
Thursday, May 14, 15
c=8
“goes to”
attraction magnetism
energy
leading
discharge
60
55
50
45
40
35
30
25
20
15
10
5
5
Thursday, May 14, 15
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
Thursday, May 14, 15
Thursday, May 14, 15
q=
Thursday, May 14, 15
60
q=
60
e=
60
Thursday, May 14, 15
q=
60
e=
60
q=
180
Thursday, May 14, 15
Thursday, May 14, 15
"Meter provides the framework that organizes groups of beats and rhythms
into larger patterns of accented and unaccented beats. "
Lester
Thursday, May 14, 15
"Meter provides the framework that organizes groups of beats and rhythms
into larger patterns of accented and unaccented beats. "
Lester
"Beats are almost always grouped into a regular repeating pattern of strong and weak.
This pattern is the meter. "
Laitz
Thursday, May 14, 15
"Meter provides the framework that organizes groups of beats and rhythms
into larger patterns of accented and unaccented beats. "
Lester
"Beats are almost always grouped into a regular repeating pattern of strong and weak.
This pattern is the meter. "
Laitz
"The pattern of stressed and unstressed beats results in a sense of metrical grouping or meter "
Gauldin
Thursday, May 14, 15
"Meter provides the framework that organizes groups of beats and rhythms
into larger patterns of accented and unaccented beats. "
Lester
"Beats are almost always grouped into a regular repeating pattern of strong and weak.
This pattern is the meter. "
Laitz
"The pattern of stressed and unstressed beats results in a sense of metrical grouping or meter "
Gauldin
"A repetitive pattern that combines accented and unaccented beats.”
Aldwell & Schachter
Thursday, May 14, 15
"Meter provides the framework that organizes groups of beats and rhythms
into larger patterns of accented and unaccented beats. "
Lester
"Beats are almost always grouped into a regular repeating pattern of strong and weak.
This pattern is the meter. "
Laitz
"The pattern of stressed and unstressed beats results in a sense of metrical grouping or meter "
Gauldin
"A repetitive pattern that combines accented and unaccented beats.”
Aldwell & Schachter
Thursday, May 14, 15
"Meter provides the framework that organizes groups of beats and rhythms
into larger patterns of accented and unaccented beats. "
Lester
"Beats are almost always grouped into a regular repeating pattern of strong and weak.
This pattern is the meter. "
Laitz
"The pattern of stressed and unstressed beats results in a sense of metrical grouping or meter "
Gauldin
"A repetitive pattern that combines accented and unaccented beats.”
Aldwell & Schachter
Thursday, May 14, 15
"Meter provides the framework that organizes groups of beats and rhythms
into larger patterns of accented and unaccented beats. "
Lester
"Beats are almost always grouped into a regular repeating pattern of strong and weak.
This pattern is the meter. "
Laitz
"The pattern of stressed and unstressed beats results in a sense of metrical grouping or meter "
Gauldin
"A repetitive pattern that combines accented and unaccented beats.”
Aldwell & Schachter
Thursday, May 14, 15
"Meter provides the framework that organizes groups of beats and rhythms
into larger patterns of accented and unaccented beats. "
Lester
"Beats are almost always grouped into a regular repeating pattern of strong and weak.
This pattern is the meter. "
Laitz
"The pattern of stressed and unstressed beats results in a sense of metrical grouping or meter "
Gauldin
"A repetitive pattern that combines accented and unaccented beats.”
Aldwell & Schachter
Thursday, May 14, 15
Thursday, May 14, 15
"When we hear a series of beats (Schlage), we divide them regularly (taktmässige), and
arrange these regular divisions into segments (in Glieder ordnen)...We place an accent on
the first beat of each segment (den ersten Schlag eines jedes Gliedes einen Accent legen).”
Kirnberger
Thursday, May 14, 15
"When we hear a series of beats (Schlage), we divide them regularly (taktmässige), and
arrange these regular divisions into segments (in Glieder ordnen)...We place an accent on
the first beat of each segment (den ersten Schlag eines jedes Gliedes einen Accent legen).”
Kirnberger
Thursday, May 14, 15
Thursday, May 14, 15
q = 60
SIMPLE DUPLE
e = 60
COMPOUND DUPLE
q = 180
SIMPLE TRIPLE
Thursday, May 14, 15
MUSIC 101: Basics of Meter
Welcome to your ,irst-­‐semester of music theory study! Week 1. Entrainment and Projection
Week 2. Pulse and Tactus
Week 3. Minimal meters: Duple and Triple Meter
Week 4. The Metric Hierarchy
Week 5. Notational matters: meter signatures and bar lines
Week 6. Tactus and the Idea of the Primary Level. Conducting Patterns.
Week 7. Classi,ications of Meter
Week 8. Representing Meter: Dot Notations and Ski-­‐Hill Graphs
Week 9. Key signature, scale, and chord. The 26 Kinds of Tonality
Week 10. Kinds of Phenomenal Accent
Week 11. Metric Induction
Week 12. Consonance and Dissonance
Week 13. Second Species Counterpoint (controlling two levels of pulse)
Week 14. Third-­‐species counterpoint (controlling three levels of pulse)
Thursday, May 14, 15
MUSIC 101: Basics of Meter
Welcome to your ,irst-­‐semester of music theory study! Week 1. Entrainment and Projection
Week 2. Pulse and Tactus
Week 3. Minimal meters: Duple and Triple Meter
Week 4. The Metric Hierarchy
Week 5. Notational matters: meter signatures and bar lines
Week 6. Tactus and the Idea of the Primary Level. Conducting Patterns.
Week 7. Classi,ications of Meter
Week 8. Representing Meter: Dot Notations and Ski-­‐Hill Graphs
Week 9. Key signature, scale, and chord. The 26 Kinds of Tonality
Week 10. Kinds of Phenomenal Accent
Week 11. Metric Induction
Week 12. Consonance and Dissonance
Week 13. Second Species Counterpoint (controlling two levels of pulse)
Week 14. Third-­‐species counterpoint (controlling three levels of pulse)
Thursday, May 14, 15
MUSIC 101: Basics of Meter
Welcome to your ,irst-­‐semester of music theory study! Week 1. Entrainment and Projection
Week 2. Pulse and Tactus
Week 3. Minimal meters: Duple and Triple Meter
Week 4. The Metric Hierarchy
Week 5. Notational matters: meter signatures and bar lines
Week 6. Tactus and the Idea of the Primary Level. Conducting Patterns.
Week 7. Classi,ications of Meter
Week 8. Representing Meter: Dot Notations and Ski-­‐Hill Graphs
Week 9. Key signature, scale, and chord. The 26 Kinds of Tonality
Week 10. Kinds of Phenomenal Accent
Week 11. Metric Induction
Week 12. Consonance and Dissonance
Week 13. Second Species Counterpoint (controlling two levels of pulse)
Week 14. Third-­‐species counterpoint (controlling three levels of pulse)
Thursday, May 14, 15
MUSIC 102: Metric Ambiguity and Conflict; Meter in Classical Music
Welcome to your second-­‐semester of music theory study! Week 1. Meter and phrase structure
Week 2. Metric malleability and ambiguity
Week 3. Fourth-­‐species counterpoint (displacement con,licts)
Week 4. Metric con,lict 1: Syncopation
Week 5. Metric Modes in the 18th century 1: Tempo giusto
Week 6. Metric Modes in the 18th century 2: Meter, affect, and Dance
Week 7. Representing Meter: Dot Notations and Ski-­‐Hill Graphs
Week 8 Cadential Harmonic Progressions
Week 9. Metric con,lict 2: Baroque Hemiola and 3-­‐against-­‐2
Week 10. Overlapping Hemiola
Week 11. 3-­‐against-­‐2 direct con,licts
Week 12. Metric Modulation
Week 13. Hypermeter Week 14. Hypermetric Transitions
Thursday, May 14, 15
MUSIC 102: Metric Ambiguity and Conflict; Meter in Classical Music
Welcome to your second-­‐semester of music theory study! Week 1. Meter and phrase structure
Week 2. Metric malleability and ambiguity
Week 3. Fourth-­‐species counterpoint (displacement con,licts)
Week 4. Metric con,lict 1: Syncopation
Week 5. Metric Modes in the 18th century 1: Tempo giusto
Week 6. Metric Modes in the 18th century 2: Meter, affect, and Dance
Week 7. Representing Meter: Dot Notations and Ski-­‐Hill Graphs
Week 8 Cadential Harmonic Progressions
Week 9. Metric con,lict 2: Baroque Hemiola and 3-­‐against-­‐2
Week 10. Overlapping Hemiola
Week 11. 3-­‐against-­‐2 direct con,licts
Week 12. Metric Modulation
Week 13. Hypermeter Week 14. Hypermetric Transitions
Thursday, May 14, 15
Thursday, May 14, 15
THEORY OF METER IS...
Thursday, May 14, 15
THEORY OF METER IS...
not useful/important?
Thursday, May 14, 15
THEORY OF METER IS...
not useful/important?
too elementary to warrant attention?
Thursday, May 14, 15
THEORY OF METER IS...
not useful/important?
too elementary to warrant attention?
as unfathomably complex as time itself?
Thursday, May 14, 15
THEORY OF METER IS...
not useful/important?
too elementary to warrant attention?
as unfathomably complex as time itself?
about bodily rather than mental knowledge?
Thursday, May 14, 15
THEORY OF METER IS...
not useful/important?
too elementary to warrant attention?
as unfathomably complex as time itself?
about bodily rather than mental knowledge?
about African rather than European knowledge?
Thursday, May 14, 15
THEORY OF METER IS...
not useful/important?
too elementary to warrant attention?
as unfathomably complex as time itself?
about bodily rather than mental knowledge?
about African rather than European knowledge?
not pertinent to the repertories that concern us?
Thursday, May 14, 15
THEORY OF METER IS...
not useful/important?
too elementary to warrant attention?
as unfathomably complex as time itself?
about bodily rather than mental knowledge?
about African rather than European knowledge?
not pertinent to the repertories that concern us?
too late, no space in curriculum, zero sum?
Thursday, May 14, 15
THEORY OF METER IS...
not useful/important?
too elementary to warrant attention?
as unfathomably complex as time itself?
about bodily rather than mental knowledge?
about African rather than European knowledge?
not pertinent to the repertories that concern us?
too late, no space in curriculum, zero sum?
not supported by teaching resources?
Thursday, May 14, 15
Thursday, May 14, 15
Artur Schnabel
Thursday, May 14, 15
Artur Schnabel
Thursday, May 14, 15
Artur Schnabel
1
Thursday, May 14, 15
2 3 4 5 6
7
X
Alfred Brendel
1
Thursday, May 14, 15
2 3 4 5 6
7
X
Alfred Brendel
Thursday, May 14, 15
Alfred Brendel
Thursday, May 14, 15
Alfred Brendel
1 2 3 4 5 ?
Thursday, May 14, 15
hyper-extended upbeat (mm. 12-17)
Thursday, May 14, 15
hyper-extended upbeat (mm. 12-17)
Thursday, May 14, 15
hyper-extended upbeat (mm. 12-17)
2
4
Thursday, May 14, 15
hyper-extended upbeat (mm. 12-17)
2
4
Thursday, May 14, 15
hyper-extended upbeat (mm. 12-17)
0 1
Thursday, May 14, 15
2
3 4
5
6
7
8 9 10
12 13 14 15
16 17
18 19 20 21 22 23
24
hyper-extended upbeat (mm. 12-17)
0 1
Thursday, May 14, 15
2
3 4
5
6
7
8 9 10
12 13 14 15
16 17
18 19 20 21 22 23
24
hyper-extended upbeat (mm. 12-17)
0 1
Thursday, May 14, 15
2
3 4
5
6
7
8 9 10
12 13 14 15
16 17
18 19 20 21 22 23
24
hyper-extended upbeat (mm. 12-17)
?
0 1
Thursday, May 14, 15
2
3 4
5
6
7
8 9 10
12 13 14 15
16 17
18 19 20 21 22 23
24
initial extended upbeat (mm. 0-2)
Thursday, May 14, 15
initial extended upbeat (mm. 0-2)
Thursday, May 14, 15
initial extended upbeat (mm. 0-2)
Thursday, May 14, 15
initial extended upbeat (mm. 0-2)
Thursday, May 14, 15