PowerPoint Presentation

piano study in mixed accentsMusic 150xUCSCWinter, 2011Polansky1/27/12

Tenney/Crawford Seeger Pitch Profiles

Pitch profiles of Ruth Crawford Seegers Piano Study in Mixed Accents (1 minute 17 seconds long, spans about 6 octaves), and Tenneys 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 elementsmorphologies and theircombinatorial directionhalf-matricesMorphological mutations(in the spectral domain, from Soundhack)

analysis/resynthesis by multi-dimensional distance functions (The Casten Variation)The Casten Variation (for solo piano or ensemble)Sarah Cahill, pianoOn the CD Change, Artifact

dissonant counterpoint algorithmmelodic dissonant counterpointCarl 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. 174.20Tenney on the evolution of Carl Ruggles melodic styleI 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

21Statistical 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.

22CA 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 result24Tenney, dissonant counterpoint (melody) algorithm (incorporating statistical feedback)

simplest version

1.Take N elements and associated probabilities pn2.Using a pseudo-random number generator, pick an element3.Set the selected elements probability to zero (or some very low value)4.Increment all other probabilities by some uniform or weighted amount5.Pick again

25Tenney algorithmprobability progressions (1)

26Tenney algorithmprobability progressions (2)

Thanks to Kimo Johnson for his collaboration on these graphs27exponentially decreasing weights

Tenney dissonation algorithmhistograms of simple version of the function

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Tenney mode example30

Mathematica Demo of DC alorithmBy Mike WinterThe Casten VariationLarry PolanskyC H A N G E, track 3/82002Unclassifiable217195.42eng - iTunNORM 0000034F 00000152 00004AC7 00004259 0001F32F 0001A814 00007FE9 000054D3 0000ABBC 00010CE0eng - iTunSMPB 00000000 00000210 000008A0 0000000000921A50 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000eng - iTunes_CDDB_IDs8+58E1CB32F65B26237368153273FC1EAA+2876526