Rhythm Necklace & Hemiola: Hidden Meter in Radiohead and Björk
Stephen Taylor, University of Illinois at Urbana-Champaign Bellairs, Barbados, February 6-8, 2010
Monday, February 8, 2010 Rhythm ... is a closed, timelike loop.
Richard Powers, The Time of Our Singing (2003)
The beat is not in the signal; it is in your mind.
William Sethares, Rhythm and Transforms (2007)
Monday, February 8, 2010 Example 1. (from Demaine et al., 2007) Six African and Latin American rhythms arranged in a 4/4 circular lattice; 0 equals the downbeat, and the other strong beats fall on 4, 8, and 12. Intuitively the most even rhythm is (e), Bossa-Nova, a 3-3-4-3-3 beat cycle. In these examples, n =16, and k = 5.
Monday, February 8, 2010 Example 1. (from Demaine et al., 2007) Six African and Latin American rhythms arranged in a 4/4 circular lattice; 0 equals the downbeat, and the other strong beats fall on 4, 8, and 12. Intuitively the most even rhythm is (e), Bossa-Nova, a 3-3-4-3-3 beat cycle.
Monday, February 8, 2010 Example 1. (from Demaine et al., 2007) Six African and Latin American rhythms arranged in a 4/4 circular lattice; 0 equals the downbeat, and the other strong beats fall on 4, 8, and 12. Intuitively the most even rhythm is (e), Bossa-Nova, a 3-3-4-3-3 beat cycle.
Monday, February 8, 2010 Example 1. (from Demaine et al., 2007) Six African and Latin American rhythms arranged in a 4/4 circular lattice; 0 equals the downbeat, and the other strong beats fall on 4, 8, and 12. Intuitively the most even rhythm is (e), Bossa-Nova, a 3-3-4-3-3 beat cycle.
Monday, February 8, 2010 Example 1. (from Demaine et al., 2007) Six African and Latin American rhythms arranged in a 4/4 circular lattice; 0 equals the downbeat, and the other strong beats fall on 4, 8, and 12. Intuitively the most even rhythm is (e), Bossa-Nova, a 3-3-4-3-3 beat cycle.
Monday, February 8, 2010 Example 2. The “Erdös-deep” property of the diatonic mode
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Monday, February 8, 2010 i jumped in the river and what did I see? radiohead, black-eyed angels swimming with me pyramid song a moon full of stars and astral cars all the figures i used to see (from Amnesiac, 2001) all my lovers were there with me all my past and futures and we all went to heaven in a little row boat
there was nothing to fear and nothing to doubt
i jumped in the river black-eyed angels swimming with me a moon full of stars and astral cars all the figures i used to see all my lovers were there with me all my past and futures and we all went to heaven in a little row boat
there was nothing to fear and nothing to doubt there was nothing to fear and nothing to doubt there was nothing to fear and nothing to doubt there was nothing to fear and nothing to doubt
Monday, February 8, 2010 Example 3. Partial transcription of Radiohead’s “Pyramid Song.”
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Monday, February 8, 2010 rhythm necklace rotation
15 0 1 14 2 13 3
12 4
11 5 10 6 9 8 7 n = 16 k = 5
Monday, February 8, 2010 Example 4. Partial transcription of Radiohead’s “Pyramid Song.”
Monday, February 8, 2010 Example 3. Partial transcription of Radiohead’s “Pyramid Song.”
Monday, February 8, 2010 Ex. 5
16
Monday, February 8, 2010 rhythm necklace
15 0 1 14 2 13 3
12 4
11 5 10 6 9 8 7 n = 16 k = 5
p = 4
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Monday, February 8, 2010 rhythm necklace vs. hemiola
0 15 0 1 14 2 11 1 10 2 13 3
12 4 9 3
11 5 8 4 10 6 9 7 7 5 8 6 n = 16 n = 12 k = 5 k = 6
p = 4 p = 4
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Monday, February 8, 2010 It’s tricky when With a palm full of stars You feel someone I throw them like dice Has done something Repeatedly On your behalf I shake them like dice And throw them on the table It's slippery when Repeatedly Your sense of justice Repeatedly Murmurs underneath Until the desired constellation And is asking you: appears And I ask myself: How am I going to make it right? How am I going to make it right? And you hear How am I going to make it right?
Björk, Desired Constellation (from Medúlla, 2004)
Monday, February 8, 2010 Example 6. Partial transcription of “Desired Constellation” by Björk and Olivier Alary.
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Monday, February 8, 2010 g# - B (uncertain rhythm) Example 7. E 6x (quarter notes) ths “Desired Constellation,” g# 4x (4:3, dotted 8 ) first verse and chorus. The E 3x (with inner voice appoggiatura) numbers show how many g# 4x bars a chord is repeated; the E 6x It’s tricky when chorus’ pattern is more g# 4x you feel someone regular than the verse’s. E 3x (inner appoggiatura) (g#/E) 4x (bass) has done something E 6x on your behalf g# 4x It’s E 3x slippery (g#/E) 4x (bass) when your sense of E 6x justice murmurs g# 4x underneath E 3x and it’s d# 3x asking you (transition) CHORUS E 3x How am I going to make it d# 3x right? E 3x d# 3x E 3x How am I going to make it d# 4x right? INTERLUDE - metric modulation Monday, February 8, 2010 Example 7. “Desired Constellation,” interlude and metric modulation.
Monday, February 8, 2010 Monday, February 8, 2010 Example 9. “Desired Constellation,” intro and part of first verse; rhythmic interpretation 2, after hearing the whole song.
Monday, February 8, 2010 Monday, February 8, 2010 hemiola, rhythm necklace and illusion 0 11 1 15 0 1 14 2 10 2 13 3 3 9 12 4
8 4 11 5
7 5 10 6 6 9 8 7
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Monday, February 8, 2010 hemiola, rhythm necklace and illusion 0 11 1 15 0 1 14 2 10 2 13 3 3 9 12 4
8 4 11 5
7 5 10 6 6 9 8 7
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Monday, February 8, 2010 rhythm necklace [2 2 2 1 2 2 2 2 1] in Radiohead and UI student composer Taylor Briggs
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Monday, February 8, 2010 2 2 2 2 2 1 2 2 2 2 2 2 1
Bell pattern from Zoboko, a song by the Aka Pygmies from the CD “Ligeti and Africa”
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Monday, February 8, 2010 Rhythm ostinato for Flow (2006) for recorder quartet and chamber orchestra
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Monday, February 8, 2010 0 n = 28 p = 7
6 1
5 2
4 3
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Monday, February 8, 2010 0 n = 28 p = 7
6 1
5 2
4 3
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Monday, February 8, 2010 0 n = 28 p = 7 k = 5 6 1
5 2
4 3
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Monday, February 8, 2010 0 n = 28 p = 7 k = 5 6 1
5 2
4 3
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Monday, February 8, 2010 The Machine Awakes for soprano & chamber orchestra, 2007/09 Words by Richard Powers, from Galatea 2.2
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Monday, February 8, 2010 30 Full Score in C, World without Words New Tempo q = 144 88 *$ +*$ , - non dim., stop suddenly Sno. ! ! # . $" " / 0 0 %
stop suddenly on downbeat ! # $" % % " % %
stop suddenly on downbeat Sop. ! # $" % % " % % non dim., slap tongue, hollow tone - little pitch World *$ 1*$ , - stop suddenly ! # . & & & & & & & & & $" " / 0 0 2 / 2 / 2 / / 2 2 / without 1- 1-' - - -' - -' - -' p(' ' ' (' ' Words 1* 3- - * , - non dim., stop suddenly ! # . for 13 $" " / 0 0 % slap tongue, hollow tone - little pitch saxes stop suddenly on downbeat Alto ! # & & & & & & & & & & & & & & (2009) $" % % " / 2 / 2 / 2 / 2 0 0 2 / 2 / 2 / 2 / / 2 2 / +- - - 1-' -' -' p(' - -' ' (' ( 1-' -' -' -' ' non dim., stop suddenly 1-' ( -' - 3- 1- - 3- , - ! $ . $ $ # . $" " / 0 0 % * +- - * , - non dim., stop suddenly ! # . $" " / 0 0 % # slap tongue, hollow tone - little pitch stop suddenly on downbeat & & Ten. ! # 2 $" % % " 4 4 0 0 - / 4 4 0 0 2 / (p' +-' # slap tongue, hollow tone - little pitch stop suddenly on downbeat (& & & & & & & & & & & &' & & & & & ! % % #+-' / 2 / / - / -' / / 2 / 2 / 1- / 2 / 2 2 / $" " . - 2 - ' 2 - -' . . 1-' -' -' p ' - ' - ' 1-' -' ( -' -' # slap tongue, hollow' tone - little(' pitch ( stop suddenly on downbeat & & +-&' & -&' & &' &' 1-' ) ! # (' &2 & & - & &' 1- . & " % % " - / / . / -' / . -' . / / 2 / 1- / . / 0 0 2 / p. - - - 3- . - slap tongue,' hollow' tone - little pitch' ' ' Bari. ( ( &' &' & &' & & & & & & +- &' - & (' - &' & & &' 1-' & (' & -' ) ! % % # 2 / . / - / ' / - - 2 / 2 / 1- / . / - / - - . / " " -' . - . -' - . ' - . - ' p( (' ' ' 38 Bass ) ! % % # % % " " " Monday, February 8, 2010 World without 0 7/4 time sig Words for 13 saxophones (2009) n = 14 1 6 k = 12
5 2
4 3
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Monday, February 8, 2010