The Physics of SoundSound begins with a vibration of an objectVibrating object transfers energy to air mediumAll complex vibration patterns seen as a combination of many simple vibration patterns

Simple harmonic motionElastic restoring forceMove object from equilibrium point, force returns it to equilibrium pointForce is proportion to distance from equilibrium Displacement

Simple Harmonic MotionHarmonic oscillations, or sinusoid (sine) curves

Simple Harmonic Motion, contAmplitude: Maximum displacement from one extreme to resting positionPeriodic vibration: Wave repeats itselfFrequency (F): Number of cycles per sec (Hz)Period (T): Time (sec) to complete one cycleF = 1 / TPhase: Progression of wave through one cycle (measured in degrees)

Simple Harmonic Motion, contDecay of harmonic motion

Additivity and Superposition of Sine Waves

Additivity and Superposition of Sine Waves, cont

Fourier Decomposition or Fourier Analysis

Fourier Decomposition, contSystems for Naming Frequency ComponentsFreq.HarmonicsOvertonesPartials

f0FundamentalFundamental1st Partial2f0 2nd Harmonic1st Overtone2nd Partial3f0 3nd Harmonic2st Overtone3nd Partial4f0 4nd Harmonic3st Overtone4nd Partial

Fourier Decomposition, cont

The Perception of PitchThe physiology of the ear

The Perception of Pitch, contThe place theory of pitch perception

The basilar membrane as a set of independently tuned resonatorsTone of single frequency causes corresponding place on basilar membrane to vibrate

The Perception of Pitch, contThe frequency theory of pitch perception

Basilar membrane vibrates to match frequencyBecause of refractory period, nerve fibers cannot encode high frequencyVolley principle: nerve fibers working together can encode high frequencies

The Perception of Pitch, contThe psychophysics of frequency

The Mel Scale: Perceived pitch as a function of frequencyNon-linear relation between frequency and pitch

The Perception of Pitch, contThe Cognitive-Structural approach

Octave equivalenceTones in a 2:1 frequency ratio have a special relationEvidence for octave equivalence:The harmonic seriesThe musical pitch set

The Perception of Pitch, contThe Cognitive-Structural approach

Psychological evidence for octave equivalenceDeutsch (1973) Standard Intervening SequenceComparison

The Perception of Pitch, contThe Cognitive-Structural approach

Psychological evidence for octave equivalenceOctave-scramble nursery rhymes

The Perception of Pitch, contA bi-dimensional approach

Tone / Pitch Height: A continuous dimension that increases with frequencyTone / Pitch Chroma: Circular component representing tones with 2:1 freq. ratioThe pitch helix

The Perception of Pitch, contA bi-dimensional approach

Shepard / Circular tones

Single tones:

Continuous glide:

Tritone paradox:

The Perception of LoudnessThe psychophysics of loudness

Audibility curves

The Perception of Loudness, contThe psychological scale of loudness

Sones scale

The Perception of TimbreThe steady state component approach

Components that remain the same over timeProblems with the steady state view of timbre

The Perception of Timbre, contThe importance of transient components

Onset rapidity: Rate of onset of the toneNoise bursts: Amount/type of noise in beginning of toneSpectral energy shift: Changes in relative intensity of harmonics over time

The Perception of Timbre, contThe perceptual similarity of musical timbreJohn Greys studies of musical timbre