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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