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RESEARCH BYELAINE CHEW AND CHING-HUA CHUAN
UNIVERSITY OF SOUTHERN CALIFORNIA
PRESENTATION BYSEAN SWEENEY
DIGIPEN INSTITUTE OF TECHNOLOGY
CS 582 / APRIL 17 , 2011DR. DIMITRI VOLPER
Polyphonic Audio Key Finding Using the Spiral Array CEG
Algorithm
Presentation Flow
Musical Pitch and KeyHuman Perception of PitchThe Spiral Array Model
Pitches Chords Keys
The CEG Algorithm Algorithm Visualization
Musical Pitch and Key
Pitch The perceived value of a tone, “Low” to “High” Psycho-acoustic (subjective) perception of Frequency
Frequency (Hz) is a scientific measurement of period
Key (Western music) Labels the “center” tone in a section of music Standard smallest interval: Semitone or “half-step” Standard pattern of semitones around “center”
Ascending: 2,2,1,2,2,2,1
Human Perception of Pitch
Limited range of perception Typically 20Hz – 20,000Hz Range tends to decrease with age
Noticable Difference is coarser at low Hz Less distance (Hz) between lower sounds Around 1400 perceivable intervals
Certain frequency distances sound relatively close Thirds, Fifths, Octaves
The Spiral Array Model
Helical Structure
Toroidal across Octaves
Distance in 3D model approximates perceived closeness between pitch
Pitch, chord and key can all map to the same space
Chords in the Spiral Array
Standard chords are based on three supporting tones
Create Triangles in 3D relative to the model
Triangles are effectively continuous, as pitch is
Major and Minor chords’ centers thus form helixes
Key in the Spiral Array
Simple keys are based on three supporting chords
Creates triangles in 3D, based on supporting chords’ triangular centers
Triangles are effectively continuous, as chords are
Major and Minor keys’ centers thus form helixes
Center of Effect
Center of Effect (CE) Relative location of a chord based on its supporting
tones
Notes of different strength change the CE location Complex chord CE’s will not line up exactly on the
model
Center of Effect Generator (CEG) Key-Finding
Center of Effect relates position of multiple pitches in model
Spatially closest chord is most likely key Correlates input music
to standard key structure
Helping Visualize the CEG Algorithm
Keys exist as a triangle in 3-space
Keys’ centers-of-effect make up two helixes in the 3D model
In standard intonation, keys are discrete (12 minor, 12 major)
Helping Visualize the CEG Algorithm
From a complex audio signal, weighted values are calculated for bins on each discrete tone
The weighted values approximate the current key’s location on the model
The spatially-closest key is the most likely match
CEG Key-Finding Algorithm
Pitch detection Extract pitch class and strength from signal
Key finding Nearest Neighbor Search in Spiral Array
Fast Fourier Transform
Efficient algorithm to compute Discrete Fourier Transform
O(n log n) vs O(n2)
Transforms function into its Frequency Domain representation
Widely used across many fields
Solving Partial Differential Equations
Data Compression
Polynomial Multiplication
Spectral Analysis
Frequency bands
Algorithm for Pitch Class/Strength from FFT
For each frequency spectrum in a 0.37 second period:
1. For each frequency band find peak value2. For each pitch-class, k, and its strength at time
j: Fjk, is the sum of all peak values for that frequency band (and others related by octaves)
3. Normalize1. Divide all pitch-strength values by the largest:
2. Divide all pitch-strength values by their sum:(k = 0, 1, …, 11)
CEG Key-Finding Algorithm
Pitch detection Extract pitch class and strength from signal
Key finding Nearest Neighbor Search in Spiral Array
CEG Algorithm
For pitch class and strength from each 0.37 seconds:
1. Assign pitch-names to pitch classes:1. Generate CE for previous 5 seconds; and2. Assign pitch-names to current pitch-classes by
nearest neighbor search in Spiral Array Space
2. Determine Key based on pitch names:1. Generate the cumulative CE from beginning to
current
2. Perform nearest-neighbor search to find closest key
BIBLIOGRAPHY:
• Po l yphon i c Aud io Key F ind ing Us ing the Sp i ra l A r ray CEG A lgor i thm
Chuan , C. and Chew, E .IEEE In te rna t i ona l Con fe rence on Mu l t imed ia & Expo
2005
• Towards a Mathemat i ca l Mode l o f Tona l i t y Chew, E .Doc tora l d i s se r ta t i on , MI T 2000
Questions?