PlayingtheNumbers

SomehighlightsfromMathema'csinMusic

Thomas A. Ivey, College of Charleston October 2009

Spectrograms

PerfectIntervals

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

TheBowedViolinString

Vibra:onalModesforDrums

ChladniPaIerns

PythagoreanScale

ModernTemperamentvs.JustIntona:on

ComparefiMhs: perfect modern

Comparethirds: perfect modern

Comparetriads: perfect modern

Bosanquet’sHarmonium

MusicalTransforma:ons

TransposedownafiMh(7semitones):

InvertaboutD:

Retrograde:

Twelve‐ToneMusic

ArnoldSchoenberg(1874‐1951)

AntonWebern(1883‐1945)

PianoConcerto,Opus42

ConcertoforNineInstruments,Opus24

TotalSerialismPierre Boulez (1925- )

Structures 1a (1950)

ChangeRinging

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

PlainBobMinimus

12342143241342314321341231421324

13423124321423412431421341231432

142341324312342132412314213412431234

(AB)(CD)

(BC)

(CD)