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Playing the Numbers Some highlights from Mathema’cs in Music Thomas A. Ivey, College of Charleston October 2009

Transcript

PlayingtheNumbers

SomehighlightsfromMathema'csinMusic

Thomas A. Ivey, College of Charleston October 2009

Page 2: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

Spectrograms

Page 3: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

PerfectIntervals

•  Ra:o2:1isanoctave•  Ra:o3:2isaperfectfi4h•  Ra:o4:3isaperfectfourth•  Ra:o5:4isaperfectthird•  Ra:o5:3isaperfectsixth

Page 4: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

TheBowedViolinString

Page 5: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

Vibra:onalModesforDrums

Page 6: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

ChladniPaIerns

Page 7: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

PythagoreanScale

Page 8: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

ModernTemperamentvs.JustIntona:on

ComparefiMhs: perfect modern

Comparethirds: perfect modern

Comparetriads: perfect modern

Page 9: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

Bosanquet’sHarmonium

Page 10: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

MusicalTransforma:ons

TransposedownafiMh(7semitones):

InvertaboutD:

Retrograde:

Page 11: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

Twelve‐ToneMusic

ArnoldSchoenberg(1874‐1951)

AntonWebern(1883‐1945)

PianoConcerto,Opus42

ConcertoforNineInstruments,Opus24

Page 12: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

TotalSerialismPierre Boulez (1925- )

Structures 1a (1950)

Page 13: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

ChangeRinging

hIp://www.youtube.com/watch?v=Fgm_‐olvSQM

Page 14: Playing the Numbers - College of Charlestoniveyt.people.cofc.edu/MathMusicSlides.pdf · Playing the Numbers Some highlights from Mathemacs in Music Thomas A. Ivey, College of Charleston

PlainBobMinimus

12342143241342314321341231421324

13423124321423412431421341231432

142341324312342132412314213412431234

(AB)(CD)

(BC)

(CD)

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