Chapter 8: 20th- and 21st-Century Techniques
- Page ID
- 232619
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 8.1: Twentieth-Century Rhythmic Techniques
- This page discusses contemporary musical techniques such as polymeter, metric modulation, timeline notation, feathered notes, and ostinato. Polymeter involves multiple simultaneous meters, highlighted in the works of composers like Bartók and Ravel. Metric modulation enables smooth tempo changes, while timeline notation uses seconds in place of traditional measures. Feathered notes illustrate gradual speed changes, and ostinato denotes repeated musical ideas, exemplified in Holst’s “Mars.
- 8.2: Pitch and Pitch Class
- This page explains pitch and pitch class in set theory, defining pitches as distinct tones without octave equivalence and pitch classes as groups of pitches related by octave and enharmonic equivalence. It uses integer notation for representation and emphasizes the need for flexibility in analyzing post-tonal music due to varying composer approaches. Additional resources and assignments for further practice are also provided.
- 8.3: Intervals in Integer Notation
- This page analyzes atonal music by focusing on interval measurements in semitones, categorizing them into four types: ordered pitch intervals, unordered pitch intervals, ordered pitch class intervals, and interval classes. Ordered intervals indicate specific pitches and direction, while interval classes gauge the smallest distance between pitch classes, highlighting atonality's lack of tonal context that dictates consonance and dissonance in tonal music.
- 8.4: Pitch-Class Sets, Normal Order, and Transformations
- This page explains pitch-class sets (pc sets), highlighting concepts like normal order, transposition (Tn), and inversion (In). It discusses methods for analyzing inversionally related sets of integers, including pairing sets in reverse order and calculating index numbers with mod 12 adjustments. The use of a clock face for visualizing transpositions and inversions is introduced.
- 8.5: Set Class and Prime Form
- This page explains set classes in music theory, which are groups of pitch-class sets connected through transposition or inversion. It details naming conventions using prime form, differentiates between pitch and pitch class, and clarifies intervals versus interval classes. Additionally, it outlines the method for determining prime form and points to set class tables and compositional examples.
- 8.6: Interval-Class Vectors
- This page explains interval class vectors, which are six-digit numbers representing the overall sound of a music set class by counting pitch class intervals. It details a calculation method with examples like the C major triad, illustrating how these vectors enhance musical analysis and reveal relationships between sets based on interval distributions.
- 8.7: Analyzing with Set Theory (or not!)
- This page examines the challenges of applying set theory in music analysis, focusing on segmentation and pitch-class set relationships. It argues that while set theory offers flexibility, it can lead to misleading analyses without proper context. The author advocates for careful segmentation and meaningful set relations while noting set theory's limitations in ignoring non-pitch elements and historical contexts, promoting a more holistic approach to music analysis.
- 8.8: Diatonic Modes
- This page explores the historical and contemporary significance of church modes, originating from the medieval era and evolving through the 20th and 21st centuries. It contrasts these modes with the major-minor system and notes their presence in global musical cultures, like Indian ragas and Arabic maqam.
- 8.9: Collections
- This page examines pitch interval patterns and collections such as diatonic, pentatonic, whole-tone, octatonic, and hexatonic, highlighting their importance in 20th-century music. It focuses on Olivier Messiaen’s "modes of limited transposition" and Béla Bartók's distance model, exploring their modal properties, limited transposition capabilities, and triadic structures.
- 8.10: Analyzing with Modes, Scales, and Collections
- This page analyzes musical modes in 20th-century music, offering guidance on practical analysis from theoretical concepts. It discusses key aspects for identifying modes, such as pitch collections and melodic contours, and explores their emotional implications and relationships within compositions. Examples from Bartók show these ideas in action.