Transcript Piano Study in Mixed Accents

piano study in mixed accents
Music 150x
UCSC
Winter, 2011
Polansky
1/27/12
Tenney/Crawford Seeger Pitch Profiles
Pitch profiles of Ruth Crawford Seeger’s Piano Study in Mixed Accents (1 minute 17 seconds
long, spans about 6 octaves), and Tenney’s Seegersong #2 (12 minutes long, spans about 3
octaves). Horizontal axis is time in seconds, vertical axis is pitch (MIDI semitones). The gray
region shows the time-dependent pitch range used in each piece
the thirteen possible ternary contours
the 14 impossible ternary contours
How many melodies are there?
The number of combinatorial (ternary) contours can be expressed by Sterling numbers of the second kind:
where S(L,h) is a Stirling number of the second
morphological metrics
three four elements
morphologies and their
combinatorial direction
half-matrices
Morphological mutations
(in the spectral domain, from Soundhack)
analysis/resynthesis by multidimensional distance functions
(The Casten Variation)
The Casten Variation
(for solo piano or ensemble)
Sarah Cahill, piano
On the CD Change, Artifact
dissonant counterpoint algorithm
melodic dissonant counterpoint
“Carl Ruggles has developed a process for himself in writing melodies for
polyphonic purposes which embodies a new principle and is more purely
contrapuntal than a consideration of harmonic intervals. He finds that if the
same note is repeated in a melody before enough notes have intervened to
remove the impression of the original note, there is a sense of tautology,
because the melody should have proceeded to a fresh note instead of to a note
already in the consciousness of the listener. Therefore Ruggles writes at least
seven or eight different notes in a melody before allowing himself to repeat the
same note, even in the octave.”
Henry Cowell, NMR, pp. 41-42
“Avoid repetition of any tone until at least six progressions have been made.”
Seeger, Manual of Dissonant Counterpoint.” p. 174.
Tenney on the evolution of Carl Ruggles’ melodic style
“I believe that what he was primarily concerned with was freshness — newness,
maximal variety of pitch-content — and the sustaining of a high degree of atonal or
atonical (but nevertheless harmonic) tension.”
James Tenney, 1997. “The Chronological Evolution of Carl Ruggles’ Melodic Style”
Statistical Feedback
(Charles Ames)
“Along with backtracking, statistical feedback is probably the most pervasive
technique used by my composing programs. As contrasted with random
procedures which seek to create unpredictability or lack of pattern, statistical
feedback actively seeks to bring a population of elements into conformity with a
prescribed distribution. The basic trick is to maintain statistics describing how
much each option has been used in the past and to bias the decisions in favor of
those options which currently fall farthest short of their ideal representation”
Charles Ames “Tutorial on Automated Composition.”
CA in the CR
uh-oh!
H T H H H H H T T T
• limited frame size
• probability vs. statistics
• colored local distributions
• “odd” strings
• method, not result
Tenney, dissonant counterpoint (melody) algorithm
(incorporating statistical feedback)
simplest version
1. Take N elements and associated probabilities pn
2. Using a pseudo-random number generator, pick an element
3. Set the selected element’s probability to zero (or some very
low value)
4. Increment all other probabilities by some uniform or weighted
amount
5. Pick again
Tenney algorithm
probability progressions (1)
Tenney algorithm
probability progressions (2)
Thanks to Kimo Johnson for his collaboration on these graphs
exponentially decreasing weights
Tenney dissonation algorithm
histograms of simple version of the
function
Tenney mode example
Mathematica Demo of DC alorithm
By Mike Winter