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three excellent ideas
polansky
Seattle, March 2009
1.Tempo Melody
(Cowell/Beyer)
Cowell: tempo melody
“If we wish to use tempo as melody, we have but to establish the
tempo value of various tones, and change them as the piece
progresses…
This use of consecutive changes of tempo is of course no new thing; it
is the mathematical ratio between tempi that has not been
systematized. It can be observed in current practice that when the
relations between successive tempi do not follow a simple ratio, but
are accidental and arbitrary, the result is felt to be rhythmically rough.
Conversely, I am convinced that further investigation would confirm my
own experiments, which show that when successive tempi…. Give an
impression of smoothness, [the] ratio … is demonstrably simple.”
NMR, p. 92
Beyer, first clarinet suite, 4th movement, (excerpt)
first 8 phrases
Frog Peak edition, edited by Daniel Goode and Dennis Bathory-Kitsz
Beyer, second clarinet suite, 4th movement, (excerpt)
first 6 phrases
Frog Peak edition, edited by Marguerite Boland
Examples of Beyer’s use of tempo melodies
Clarinet Suites 1 and 1b, 4th mvmts.
Performed by Daniel Goode (1)
Craig Hill (1b)
From Johanna Beyer: Sticky Melodies, New World Records
Tempo ratios, per line, in Johanna Beyer’s two clarinet suites, 4th movement
Line
1
2
3
4
5
6
7
8
9
10
11
12
Suite I ratios
1:1
2:3
2:5
5:2
4:3
2:3
2:3
4:2
2:5
2:3
2:3
2:3
Suite I tempi
132
88
35
88
117
78
52
104
42
28
19
12
Suite Ib ratios
1:1
3:2
3:2
2:6
3:2
3:2
3:2
4:2
3:4
4:2
3:2
4:2
Suite Ib tempi
56
84
126
42
63
95
142
284
213
425
638
1276
Tempi, Beyer Clarinet Suites
1400
1200
Tempo
1000
800
Suite I tempo
Suite Ib tempo
600
400
200
0
1
3
5
7
Line #
9
11
4th Movement, 2nd clarinet suite (Beyer)
Note names
Line
Tempo Scalar
Tempo Ratio
Note Name
1
2
3
4
5
6
7
8
9
10
11
12
1/1
3/2
3/2
1/3
3/2
3/2
3/2
2/1
3/4
2/1
3/2
2/1
--3/2
9/4
3/4
9/8
27/16
81/32
81/16
243/64
243/32
729/64
729/32
C
G
D
G
D
A
E
E
B
B
F#
F#
(cycle of 5ths, “mixolydian” mode)
4th Movement, 2nd clarinet suite (Beyer)
Interval sequence
Line
Tempo Scalar
1
2
3
4
5
6
7
8
9
1/1
3/2
3/2
1/3
3/2
3/2
3/2
2/1
3/4
Interval Name
Pitch (octave reduced)
P5th
P5th
P5th (down)
P5th
P5th
P5th
Octave
P4th (down)
C
G
D
G
D
A
E
E
B
References (tempo melodies/Beyer)
Boland, Marguerite. 2007. “Experimentation and Process in the Music of Johanna Beyer.” VivaVoce No. 86,
Journal of the Internationaler Arbeitskreis Frau and Musik (in German). www.archiv-frau-musik.de. (English
version on Polansky, website)
— 2007a. (ed.) Suite for Clarinet Ib. Annotated performance edition. Frog Peak/Johanna Beyer Project #17.
Series editor: Polansky, Larry. Hanover: Frog Peak Music (A Composers’ Collective)
Cowell, Henry. 1930. New Musical Resources. Republished by Something Else Press, 1969.
Goode, Daniel. 2007. Suite for Clarinet I . Annotated performance edition. Frog Peak/Johanna Beyer Project #16.
Kitsz, Dennis, copyist and co-editor.
Kennedy, J. and Polansky, L. 1996. “’Total Eclipse’: The Music of Johanna Magdalena Beyer: An Introduction and
Preliminary Annotated Checklist.” Musical Quarterly. 80/4.
Polansky, Larry. 2008. “’Sticky Melodies’”: The Choral and Chamber Music of Johanna Magdalena Beyer.” Liner
notes to Sticky Melodies, New World CD 80678.
— “Johanna Magdalena beyer: miscellaneous materials”:
http://eamusic.dartmouth.edu/~larry/misc_writings/talks/beyer.index.html
1930. Seeger, Charles. Tradition and Experiment in the New Music, in Studies in Musicology II, (ed.) Ann
Pescatello, University of California Press. Berkeley, CA. 1994.
Thanks to Marguerite Boland and Amy Beal for help with these ideas
2. Dissonant counterpoint and statistical
feedback
(Cowell/Seeger/Tenney/Ames)
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”
Tenney: Chronological graphs of ALSD, ALSC
in Ruggles’ works
(average length of different pitch classes; average length of consonant pitch strings)
“Consider for a moment what is meant
by the incredibly high values for ALSD
reached in Sun Treader, the
Evocations, and Organum. It is, in
each case, almost 9, which means
that at every moment in the process of
composing these melodic lines there
were only four pitch-classes remaining
to chose from for the next tone — and
not even all of these four would
necessarily satisfy certain other
conditions, such as the desire for
dissonant relations in close proximity.
Very severe constraints indeed, for a
music which sounds so free!” (Tenney)
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.”
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
Tenney dissonation algorithm
histograms of simple version of the
function
different probability increment functions
Tenney dissonation algorithm
autocorrelation over n trials
Original, linear function (no
curvature)
Strong positive curvature
Linear function with MAX =1
Very strong positive curvature
Thanks to Mike Winter and Alexander Barnett for collaboration in this work.
Tenney mode example
Example of Tenney’s use of the melodic algorithm
Seegersong #2
solo flute
Performed by Margaret Lancaster
Forthcoming on her solo CD, Have Faith!, New World Records
Selected References: Melodic dissonant counterpoint/statistical feedback
Charles Ames
1996. “Thresholds of Confidence: An Analysis of Statistical Methods for Composition: Part 2: Applications,”
Leonardo Music Journal 6.
1995. Thresholds of Confidence: An Analysis of Statistical Methods for Composition, Part 1: Theory.”
Leonardo Music Journal 5.
1993. “How to Level a Driver Sequence,” Leonardo Music Journal 3.
1992. “Catalog of Sequence Generators,” Leonardo Music Journal 2.
1991. “Catalog of Statistical Distributions: Techniques for Transforming Random, Determinate and Chaotic
Sequences,” Leonardo Music Journal 1.
1990. “Statistics and Compositional Balance,” Perspectives of New Music, 28/1.
1987a. “Automated Composition in Retrospect,” Leonardo, 20/2.
1987b. “Tutorial on Automated Composition,” Proceedings of the ICMC. International Computer Music
Association. Urbana, Illinois.
1986. “Two Pieces for Amplified Guitar,”Interface: Journal of New Music Research, 15/1.
James Tenney
1977. “The Chronological Development of Carl Ruggles' Melodic Style,” Perspectives of New Music, 16/1.
Larry Polansky, Mike Winter (with Alexander Barnett).
In progress. “A Few More Words About James Tenney: Dissonant Counterpoint and Statistical Feedback.”
Paper given NYC (2007) and Phoenix (2006)
Michael Casey
1992. “HS: A Symbolic Programming Language for Computer Assisted Composition.” M.A Thesis,
Dartmouth College.
3. Freestyle tuning and paratactical
intonation
(Harrison)
“scales” in Arion’s Leap
Metal Strung Harp
E
E
F
F
F#
Ab
A
Bb
Bb
B
B
C#
C#
D
D#
D#
0
20
22
112
182
337
498
520
610
680
729
858
884
996
1040
1108
1/1
2048/
2025
40/
39
16/
15
10/9
243
/200
4/3
27/
20
64/
45
40/
27
32/
21
64
/339
5/3
16/
9
640
/351
256/135
Ya chengs
3-part chord with the intervals 7/6 and 4/3, tuned as A-C-D (4/3, 14/9, 16/9), transposed up 25 /24,
16/15, 6/5, down 25/24.
Troubadour Harp
Adds Eb (50/27), Bb (25/18), G (32/27) to the total fabric
tyvarb (B’rey’sheet) (in the beginning ... )
(Cantillation Study #1)
(1985; revised 1987, 1989)
for voice and live computer
Jody Diamond, voice
Larry Polansky and Phil Burk, live computer systems
from The Theory of Impossible Melody
New World Records, 2009
(reissue of Artifact CD, #4, 1991)
References: freestyle tuning, paratactical intonation
Lou Harrison
1971. Music Primer. New York, C.F. Peters
1974. A Phrase for Arion’s Leap. Score published in Ear (West) #1. Recording on Tellus #14: Just
Intonation (1986).
Leta Miller and Fredric Lieberman
1998. Lou Harrison: Composing a World. Oxford University Press.
Larry Polansky
1987. “Item: Lou Harrison as a Speculative Theorist.” In A Lou Harrison Reader. Santa Fe:
Soundings Press, edited by Peter Garland.
1987. “Paratactical Tuning: An Agenda for the Future Use of Computers in Experimental
Intonation,” Computer Music Journal, 11(1).
1987. “HMSL Intonation Environment,” 1/1: The Journal of the Just Intonation Nework, 3:1.
Ezra Sims
1987. “Letter to CMJ”, Computer Music Journal, 11/4
James Tenney
1987. “About ‘Changes: Sixty-four Studies for Six Harps’,” Perspectives of New Music, 25:1/2
Harold Wagge
1985. “The Intelligent Keyboard,” 1/1: The Journal of the Just Intonation Nework, 1:4.