playing the numbers - college of charlestoniveyt.people.cofc.edu/mathmusicslides.pdf · playing the...
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PlayingtheNumbers
SomehighlightsfromMathema'csinMusic
Thomas A. Ivey, College of Charleston October 2009
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Spectrograms
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PerfectIntervals
• Ra:o2:1isanoctave• Ra:o3:2isaperfectfi4h• Ra:o4:3isaperfectfourth• Ra:o5:4isaperfectthird• Ra:o5:3isaperfectsixth
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TheBowedViolinString
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Vibra:onalModesforDrums
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ChladniPaIerns
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PythagoreanScale
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ModernTemperamentvs.JustIntona:on
ComparefiMhs: perfect modern
Comparethirds: perfect modern
Comparetriads: perfect modern
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Bosanquet’sHarmonium
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MusicalTransforma:ons
TransposedownafiMh(7semitones):
InvertaboutD:
Retrograde:
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Twelve‐ToneMusic
ArnoldSchoenberg(1874‐1951)
AntonWebern(1883‐1945)
PianoConcerto,Opus42
ConcertoforNineInstruments,Opus24
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TotalSerialismPierre Boulez (1925- )
Structures 1a (1950)
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ChangeRinging
hIp://www.youtube.com/watch?v=Fgm_‐olvSQM
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PlainBobMinimus
12342143241342314321341231421324
13423124321423412431421341231432
142341324312342132412314213412431234
(AB)(CD)
(BC)
(CD)