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Four Voice Canons #2-18 Larry Polansky

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Four Voice Canons #2-18 Larry Polansky Four Voice Canons #2-18 Notes and diagrams Larry Polansky revision, 7/22/03 http://music.dartmouth.edu/~larry Sample Four Element Permutation List (determines the order of events for a given voice, using the concept of 2-transposition to maintain “continuity” between permutations) (Four Voice Canons) CBAD BCAD BACD BADC BDAC DBAC DABC DACB DCAB CDAB CADB CABD ACBD ABCD ADCB ACDB BCDA BDCA DBCA DCBA ABDC ADBC CDBA CBDA (this list used in FVC #6) An example of a 2-transposition A B C D E E B C D A A Typical Mensuration Canon (time structure) (Four Voice Canons) Voice 1 (1:1) Voice 2 (3:2) Voice 3 (5:3:2) Voice 4 (8:5:3:2) (duration of voice 2 = 2/3 * duration of voice 1, etc.) The equation for the the starting point of a voice, based on its duration ratio, is: Sv = 1 - (b/a) • where Sv is the starting point in time for voice v; a/b is the duration ratio for voice v (a/b > 1); 1 is the duration of the piece. For example (above): S2 = 1/3; S3 = 3/5; S4 = 3/4 Tempo Ratios Used in the Canons (so far) #4, #5, #7, #11 (for instruments), whole number ratios are used, based on the Fibbonacci sequence (2, 3, 5, 8). #3, #6, and #8, one irrational ratio (the golden mean). #9 (“Anna Canon”), there are four versions, three with a different set of superparticular ratios (a: 4:5:6:7, b: 6:7:8:9, c: 8:9:10:11), one with the golden mean (d: f). #10 (“Four Boys Mannin’”), seven voices, with the superparticular ratios 6:7:8:9:10:11:12. #11 (“Parsons Canon” from Tetherball), 5 voices, with the ratios 4:5:6:8:12 #12 (“Doggerel” from 3 New Hampshire Songs), four voices, with the ratios 4:5:6:7. #7, #13, #14, #15, #17, #19 do not specify the tempo ratios for their realizations. On the Cold Blue CD set, #7 (gamelan) uses: 12:17:29:43; #14 (“Kid Canon”) uses 1: 6/5 : 7/5 : 5/3: 11/6 : 2/1 (or 30:36:42:50:55:60); #17 (“Guitar Canon”) uses 4:5:6:7:9:11; #18 (“Trio Canon”) uses 6:7:8:10. A word processor example of a mensuration canon row row row your boat gently down the stream row row row your boat gently down the stream row row row your boat gently down the stream row row row your boat gently down the stream !! Caution: Do not try this at home without strict parental supervision !! Four Voice Canon #1 (computer-controlled analog synthesizer) Date: 1975 Place: Electronic Music Studios, University of California Santa Cruz; assistance from Bob Hoover Instrumentation: Interdata Model 2 Computer, Moog Synthesizer, machine code Elements: various analog control data Comments: Unavailable Four Voice Canon #2 (computer-controlled analog synthesizer) Date: 1975 Place: Electronic Music Studios, University of California Santa Cruz: assistance from Bob Hoover Instrumentation: Interdata Model 2 Computer, Moog Synthesizer, machine code, 4-tr. tape recorder Elements: various analog control data (envelopes, sequencer control, and so on) Comments: On my website (http://music.dartmouth.edu/~larry). Four Voice Canon #3 (computer) Date: 1975 Place: CCRMA, Stanford University; assistance from Andy Moorer and Scott Kim Instrumentation: Digital synthesis system (PDP-10 computer), SAIL (Stanford Artificial Intelligence Language) Elements: pitch, spatial location (5 points in stereo space), duration, amplitude, several FM indices, envelope parameters (some 15-20 controls, in the case of timbres, varied very slightly) Comments: Used backtracking algorithm to compute list; true golden mean ratios for durations of voices. On Artifact CD, The Theory of Impossible Melody. Four Voice Canon #4 (marimba) Date: 1978/79 Place: Canadian National Composer/Choreographer Seminar, written for a dance by Andréa Smith, percussionist William Winant; revised, Mills College, 1980 Instrumentation: One marimba (full four octave), four parts Elements: pitch (each voice uses four higher pitches from the harmonic series), duration, accent (each four element permutation has an accent on first element, "out of synch" with grupetti) Comments: Later rewritten for Dean Drummond's harmonic series tuned Zoomoozophone; Fibbonacci approximations of golden mean ratios, in a kind of rhythmicana. On Artifact CD, The Theory of Impossible Melody. FVC #3–#6 released on The Theory of Impossible Melody, now out of print, but available as MP3s on my website. (4-6 also on Cold Blue Records release of complete Four Voice Canons) Four Voice Canon #5 (percussion) Date: 1983 Place: Mills College, for William Winant Instrumentation: Score calls for "organized percussion." Instruments used in recording (skin, metal, tambourine, wood): Voice 1: large bass drum, large brake drum (courtesy of Lou Harrison), large Egyptian tambourine (courtest of Peter Maund), lowest note of American Gamelan gambang (built by Lou Harrison/Bill Colvig) Voice 2: low roto-tom, amglocken, low tambourine, temple block Voice 3: middle-range roto-tom, salad bowl (wedding gift from Laura Daigen), "normal" tambourine, high temple block Voice 4: highest roto-tom, high amglocken, small tambourine, highest note of gambang Elements: instrument, duration, two types of accents. Comments: Orchestrated by LP and WW; 5/4 rhythmic pattern consisting of half-note, dotted-quarter, quarter, eighth. The Theory of Impossible Melody and Cold Blue CD. Four Voice Canon #6 (homebrew sampler) Date: 1986 Place: Mills College Center for Contemporary Music Instrumentation: 68000 single board S-100 computer, 2 MB of memory, A/D, D/A converters, 68000 assembly code, early version of HMSL. Generated and performed in real-time. Sounds: Mill College Frog Pond, Anthony Braxton (baritone sax), Jody Diamond (Central Javanese rebab), Kurzweil 250 sine wave. Each sound about 4 seconds long (2 MB), rising over its duration, with the exception of the frogs (who were not digitally controllable). Elements: Duration (in number of bytes), starting location in memory (stochastically selected by the computer, higher and higher for each voice) Comments: "Found sounds" from the Mills soundscape; intentionally raw sampling procedures (no zero-crossing, filtering, smoothing, etc.); reasonably close golden mean ratios. On The Theory of Impossible Melody and Cold Blue CD. Four Voice Canon #6 (stochastic start times in memory) (Sax lick, rising over about 4 seconds) voice 1 voice 2 voice 3 voice 4 Four Voice Canon #7 Date: 1990 Commisioned by Gamelan Son of Lion, New York City. Premiered May, 1990, NYC. Instrumentation: Gamelan. Elements: Duration, notes of a four-note seleh (cadence), to be chosen by the group, in any pathet, with accents, kenong and gong tones. Comments: Recorded, 2002, by Jody Diamond, (Miriam Kolar, engineer), instruments from Gamelan Lipur Sih (four gongs, four kenong pots, slentem, gendér, peking). Released on Cold Blue CD. Four Voice Canon #7, 2002 recording, gong structure Tempo ratios: 12:17:29:43. Seleh: 3 2 1 6 Four Voice Canon #8 Date: 1992 Co-composed with Ray Guillette. Based on Nick Didkovsky’s “nerve events” from the CD Beta 14 ok. Instrumentation: Tape. Software used: HMSL, Tom Erbe’s SoundHack, TurboSynth, Eric Smith’s Mutator. HMSL composed and “realized” the piece via MIDI on some commercial samplers and DSPs. Sounds: 36 samples: 12 original nerve events, the “chromatic scale”; 12 transformations each by Ray and I. Elements: Duration, selection of samples from a complex “virtual keyboard,” spatial location (a 2-dimensional grid of 16 locations), pitch inflection, loudness. Comments: Excerpted on Cuneiform CD, Transforms: The Nerve Events Project. Complete piece on Cold Blue CD. Four Voice Canon #9 (“Anna Canon”) a, b, c, φ Date: 1994. Place: Dartmouth. Sounds: Four short non-verbal samples of my daughter Anna’s voice at age 3. Instrumentation: Tape. Elements: Duration, stereo placement, loudness, pitch. Comments: Meant to be a kind of “public domain” music software canon, using Csound, HMSL, and Soundhack collaboratively. Grew out of efforts to teach large computer music classes outside of a studio, and an interest, at the time, in cheap or free pluralistic, but powerful, music software. HMSL wrote the piece (using the Knuth algorithm, and in the process, I developed a large “general” software library for four voice canons which, naturally, I’ve never used again), generating a score for Csound, which realized one voice using a simple soundfile playback orchestra. That voice was pitch/duration shifted by Soundhack to make the canon. There are four versions, each with their own superparticular pitch/tempo ratios: 9a: 4:5:6:7 9b: 6:7:8:9 9c: 8:9:10:11 9d: φ (golden mean). #9b is on the Bregman Electronic Music Studio CD-ROM, and is the only one that has been “performed.” This piece is also part of a set of tape works called the Three Anna Studies (each released independently, but all three on my Artifact CD, Change). #9b also released on Cold Blue CD. Four Voice Canon #10 (“Four Boys Mannin’”) Date: 1997. Place: Dartmouth. Sounds: One minute Chris Mann “collaboration” soundfile. Elements: No permutation list used. Comments: Part of the Frog Peak Collaboriations Project CD, a project I curated in which 60+ composers made pieces out of a one-minute soundfile of Chris Mann reading a text. My pieces on this CD were quickly produced, simple, conceptual works using software and ideas I had developed for other projects. #10 is the simplest, and uses Soundhack in a similar way to #9, except that here the seven versions of the one minute soundfile are simply varisped (6:…:12) and overlayed with an exponential crescendo on each, starting at nothing and going to maximum loudness. Four Boys Mannin’ #10 is on the Frog Peak Collaborations CD and on the Cold Blue CD.
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