Transcript Presentation

Polyphonic Audio Key Finding
Using the Spiral Array CEG
Algorithm
RESEARCH BY
ELAINE CHEW AND CHING-HUA CHUAN
U NIVERSITY OF S OUTHERN C ALIFORNIA
PRESENTATION BY
SEAN SWEENEY
D IGIP EN I NSTITUTE OF T ECHNOLOGY
CS 582 / A PRIL 17, 2011
DR. DIMITRI VOLPER
Presentation Flow
 Musical Pitch and Key
 Human Perception of Pitch
 The 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
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 value
2. 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. Normalize
1.
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.
2.
Generate CE for previous 5 seconds; and
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
Questions?
BIBLIOGRAPHY:
• Polyphonic Audio Key Finding Using the Spiral Array CEG
Algorithm
Chuan, C. and Chew, E.
IEEE International Conference on Multimedia & Expo 2005
•
Towards a Mathematical Model of Tonality
Chew, E.
Doctoral dissertation, MIT 2000