Santa Fe Institute

2 Talks

polansky

june, 2006

EXAMPLES (audio, quotes, charts)

(updated, 6/14/06)

Talk 1: Introduction; Form; Distance; Morphology; Non-contextual analysis

Intro

- 4 Examples of "music", in completely different musical "styles"
- Formosan millet chant
("Ritual song for millet sowing: "Passipot-pot". Men's Choir, Bounoun
tribe)

- Cecil Taylor, soloist, "Communications 8,"
by Michael Mantler, Jazz Composer's Orchestra, excerpt

- "Go
Down 'Ol Hannah," Iron Head, Clear Rock, et. al. 1933, Central
State Farm, Sugar Land, Tx.

- "The
Race is On," George Jones

- Quote from
Xenakis' Arts/Sciences: Alloys,
on math and music

- Two pages from The Sacred Harp, showing some
strange explanations of music and sound

- Tenney Meta + Hodos (Frog Peak Music), Tenney and Polansky "Hierarchical Temporal Gestalt Perception in Music: A Metric Space Model" (Journal of Music Theory)
- several pages of examples of HTGM
- Rock and Palmer (Scientific American): pictures of gestalt formation
- Tenney and Polansky (JMT), definition of a TG boundary
- simple examples of TG boundaries in Beethoven's Fifth
melody (Meta + Hodos)

- first page and cover of Varése Density 21.5
- TG segmentation of Density
(JMT)

- First page of Ruggles' Portals
(Polansky paper on Ruggles)

- TG segmentation of Portals
- Comparison of computer analysis with Thomas Peterson's
"hand"
analysis of Portals (from
Peterson's early PhD Dissertation on Ruggles' music).

- Sound and analysis examples: Varese Density
21.5, recording and charts; Ruggles' Portals
(recording).

- Shapes and ordered values, contour, examples
- Adams: "Melodic contour typology..."
- Seeger: "moods" (Kolinski not shown)

- Number of possible contours (Polansky and Bassein, JMT)

- Possible and impossible contour descriptors (numerical)

- Thirteen possible ternary contours

- Fourteen impossible ternary contours
- Equation for number of
possible contours

- Teitelbaum's Similarity Index
(early example of an L2 norm in music)

- Several morphological metrics examples

- Melodic transformation by mathematically defineable functions ("Eighth of January")
- OCD, UCD, OCM (from draft of metrics article)
- Two-dimensional metric space of melodies (melodies not
shown)

- Morphing examples

- General morphing equation
- Some pictures of spectral morphs (from Erbe, Polansky, Computer Music Journal article)

- Example of distance, statistics, use of multi-dimensional scaling: The Casten Variation (Polansky)
- Ruth Crawford Seeger: Piano
Study in Mixed Accents

- First page
- Time series analysis
- Some other example analyses:
- The Casten Variation for solo piano
- MDS
plots, metrics

- Recording
(from Artifact CD entitled Change).

- Score

- McKay, some
features used in style analysis

- Maneris et al,

- Selected features
- Zipf's law

- graph of note durations (vis a vis Zipf's Law)
- "beauty"

- Recent work with Dan Rockmore and Danny Shapira (at
Dartmouth College)

- Pareto graphs of PCR and PNR 3 single piano pieces, Mozart, Bach, Bartok
- Bartok: Allegro Barbaro (1911), Bach: Well-tempered Clavier, Book II, (ca. 1738-42), Prelude in C major; Piano Sonata no. 13 in B-flat major, KV 333 (E 315c) (1778) 3. Allegretto grazioso
- averages, PNR, PCR. Linear and log scales
- slopes and R2 values, 6 composers, 75 pieces
- a simple example of slope- and R2-finding (Bach, WTC)

- means of three composers, 75 pieces, over four features
- means of six composers, 75 pieces, over four features
- mean and SD of 6 composers, four features
- scatter plots, 2D, of composers by feature (R2, slope: PNR, PCR)

Talk 2: Experimental Intonation, Optimal Well-temperament

Introduction to Tuning Theory

- Harmony primer
- A few basic principles: cents, ratios, the concept of pitch
vs.
frequency, just scales

- The fundamentals: the historical tuning problem
- Harmonic complexity and distance: Tenney, Euler (two
different measures)

- Example of complex intonational experiment/usage: Colluricincla Harmonica by Ron
Nagorcka (samplers, bird sounds, fretless electric guitar). Recording
(off his book/cd: Rhythms of the
Tarkine)

- Problem of slendro as a tuning system: recording of
Lokananta CD of Ld. Pankgkur,
Laras slendro ("key") pathet manyura ("mode").

- OWT primer
- Quotes about WTC,
Werckmeister
III

- The concept of error: John Chalmers, Rudolf Rasch
- Lou Harrison diagrams
of tuning well-temperaments, other pages from Rasch

- Examples of Bach in two different tunings.

- WTC Book 1, C Major Prelude (score)

- Harpsichord, Huguette Dreyfus, W3
- Piano, Rosalyn Tureck, ET
- WTC Book 1, Bb
Minor Prelude (score)

- Piano, Glen Gould, ET

- Harpsichord, W2
(?)

- JAVA code to solve the problem as a genetic algorithm (with Douglas Repetto)
- Dan Rockmore's explanation
of the deterministic solution to the problem

- Matlab functions for a deterministic solution (with Kimo Johnson)
- example scales (data)

- A
simple 3-tone scale

- Equal-temperament example (don't care about weights!)
- just for laughs, a 17-tone
just scale repeating at the octave + p5th

- Examination of one set of ideal weights, intervals, for a
just scale approximating well-temperament

- Fixing ideal intervals, let weights roam ("hill-climbing"
algorithm)

- Find W3 (statistics)
- Find slendro (statistics)
- bad scales, mathematical questions