Preeti Rao 2 nd CompMusic Workshop, Istanbul 2012
o Music signal characteristics o Perceptual attributes and acoustic properties o Signal representations for pitch detection o STFT o Sinusoidal model o Pitch detection algorithms o Polyphonic context and predominant pitch tracking o Applications in MIR 2
Digital audio format: PCM • Sampling rate: 44.1 kHz, 22.05 kHz • Amplitude resolution: 16 bits/sample *The Physics Classroom:http://www.glenbrook.k12.il.us/gbssci/ phys/Class/sound/u11l2a.html WiSSAP 2007
Interesting sounds are typically coded in the form of a temporal sequence of “atomic sound events”. E.g. speech -> a sequence of phones music -> an evolving pattern of notes An atomic sound event, or a single gestalt, can be a complex acoustical signal described by a set of temporal and spectral properties => an evoked sensation. Department of Electrical Engineering , IIT Bombay
A sound of given frequency components and sound pressure levels leads to perceived sensations that can be distinguished in terms of: o loudness <-- intensity o pitch <-- fundamental frequency o timbre (“quality” or “colour”) <--ther spectro-temporal properties Department of Electrical Engineering , IIT Bombay
low pitch tone Frequency = 100 Hz ������������������������ T 0 = 10 msec 1 Hertz = 1 vibration/sec high pitch tone Frequency = 300 Hz T 0 = 3.3 msec Department of Electrical Engineering , IIT Bombay
Musical pitch scale low pitch high pitch semitone = 2 1/12 Department of Electrical Engineering , IIT Bombay
o The construction of a musical scale is based on two assumptions about the human hearing process: o The ear is sensitive to ratios of fundamental frequencies (pitches), not so much to absolute pitch. o The preferred “musical intervals”, i.e. those perceived to be most consonant, are the ratios of small whole numbers. o A musical sound is typically comprised of several frequencies. The frequencies are evident if we observe the “spectrum” of the sound Department of Electrical Engineering , IIT Bombay
300 Hz 600 Hz 900 Hz 300 Hz + 600Hz 300 Hz + 600Hz + 900Hz Department of Electrical Engineering , IIT Bombay
Sound “atoms” : Single tone signal ( ) ( ) x 1 t X 1 f 0.7 0.8 t ( ms ) 0 50 f ( Hz ) -0.6 500
Non-tonal Signal ( ) ( ) x 2 t X 2 f 0.7 0.2 t ( ms ) 0 50 f ( Hz ) -0.5 500
Complex tone signal ( ) ( ) x 3 t X 3 f 0.5 0.2 t ( ms ) 0 50 f ( Hz ) -0.4 1000 500
Bandpass noise signal ( ) ( ) x 4 t X 4 f 0.3 1 t ( ms ) 0 50 f ( Hz ) -0.3 800 250
A flute note ( ) dB ( ) X 1 f x 1 t -20 0.5 t ( ms ) 0 50 f ( kHz ) -70 -0.5 5
o We see that the distinctive signal characteristics are more evident in the frequency domain. o The ear is a frequency analyzer. It represents a unique combination of analysis and synthesis => we do not perceive spectral components but rather the composite sounds. o We observe that a single “note” is perceived as one entity of well-defined subjective sensations. This is due to the spatial pattern recognition process achieved by the central auditory system. 15
Major dimensions of music for retrieval are melody, rhythm, harmony and timbre. o Melody, harmony -> based on pitch content o Rhythm -> based on timing information o Timbre -> relates to instrumentation, texture A representation of these high-level attributes can be obtained from pitch, timing and spectro-temporal information extracted by audio signal analysis. Representations are then compared via a similarity measure to achieve retrieval. 16
o The temporal pattern of frame-level features can offer important cues to signal identity Audio signal Texture <= duration: 0.5 – 1.0 s windows Analysis <= duration: 50 – 100 ms windows Feature Extraction Frame-level features M. F. Martin and J. Breebaart, "Features Feature summary for Audio and Music Classification," in Feature Proc.ISMIR , 2003 . vector 17
Melody: pitch related feature Melody is the temporal sequence of notes usually played by a single instrument (fixed timbre). The discrete notes (pitches) are typically selected from a musical scale. frequency/note time
o Typical implementation : o Pitch detection is carried out on the audio signal at uniformly spaced intervals o The pitch sequence is segmented into notes (regions of relatively steady pitch) o Notes are labeled o Note patterns are matched to determine melodic similarity o Challenges : o Note segmentation can be a difficult task o Pitch detection in polyphonic music is tough 19
Monophonic Signal: cues to perceived pitch Spectrum Waveform A. de Cheveigne. Multiple F0 estimation. In D.-L. Wang and G.J. Brown, editors, Computational Auditory Scene Analysis : Principles, Algorithms and Applications, IEEE Press / Wiley, 2006 . “Schroeder histogram” PDA Department of Electrical Engineering , IIT Bombay
o Time (Lag) domain : maximise autocorrelation value o Frequency domain : minimise error between estimated and predicted harmonic structures o Other 21
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Music and speech signals are typically time-varying in nature => a time-frequency representation is required to visualize signal characteristics. The short-time Fourier transform (STFT) affords such a representation based on an assumption of signal quasi- stationarity. The window shape dictates the time and frequency resolution trade-off. ∑ ∑ ∑ ∑ ∞ ∞ ∞ ∞ − − − − j ω ω ω ω m X ( ω ω ω ω , n ) = = = = x ( m ) w ( n − − − − m ) e S m = = = = −∞ −∞ −∞ −∞ Department of Electrical Engineering , IIT Bombay
w(n-m) x(m) x(m)w(n-m) X n ( , ) ω DFT π ω 0
I t [ ] ∑ ˆ[ ]= x t a t [ ]cos [ ] t e t [ ] Φ + i i i 1 = a t [ ] - amplitude variation of i th sinusoidal component (“partial”) i Φ [ ] t - total phase (represents both frequency and phase variation) i I t [ ] - Number of partials, can vary with time [ ] t [ ] t t [ ] t Φ = ω + ϕ i i i { a , , } ω ϕ Model parameters to be estimated: i i i l
Sinusoid Audio Peak Peak x DFT parameters signal detection tracking { a , , } ω ϕ i i i l Additive Window synthesis _ Tonal component Σ Residual + For the smooth evolution of the signal, sine components are detected in each frame and linked to tracks from the previous frame based on frequency proximity.
50 Spectral magnitude Fixed threshold (MaxPeak - 40 dB) 40 Final peaks picked 30 20 ) agnitude (dB 10 0 -10 M -20 -30 -40 -50 0 500 1000 1500 2000 2500 3000 Frequency (Hz) 50 Spectral magnitude 40 Envelope - 20 dB Envelope - 25 dB 30 Envelope - 30 dB 20 ) B (d 10 e d itu 0 n g -10 a M -20 -30 -40 -50 0 500 1000 1500 2000 2500 3000 Frequency (Hz)
Match spectrum around peak with that of ideal sinusoid. Apply threshold to the error. Department of Electrical Engineering , IIT Bombay
Peak tracking D sine peak C Frequency track born B track dies A 0 1 2 3 4 Time
Singer (main melody) Tanpura (drone) Harmonium (secondary melody) Tabla (percussion) 2000 Tun Na Ghe 1500 Frequency (Hz) 1000 500 0 0 5 10 15 20 Time (sec)
Predicted Measured o Input : magnitudes + locations of Components Components sinusoids a b 800 800 o For a range of trial fundamentals, 700 700 generate predicted harmonics 600 500 o Minimise TWM error w.r.t. trial 420 400 fundamentals 375 300 200 200 Err Err 100 100 p → m m → p Err = + ρ total N K Nearest Neighbour Matching Department of Electrical Engineering , IIT Bombay
Department of Electrical Engineering , IIT Bombay
E(p,j) p W(p,p') E(p',j+1) j p → Pitch candidates, j → Frame (time instant) E → Measurement cost (local), W → Smoothness cost Minimize the Global transition cost over the singing spurt Department of Electrical Engineering , IIT Bombay
Department of Electrical Engineering , IIT Bombay
Multi-F0 Signal Polyphonic analysis representation audio signal Singing voice Predominant-F0 Voice F0 detection trajectory extraction contour
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“ Pitch class profile ” o Pitch histogram o Similarity measure involves match between histograms 38
Positive Positive Positive Positive Negative Negative Negative Negative phrases phrases phrases phrases phrase phrase phrase phrase
Detects phrases melodically similar to ‘Guru Bina’ pitch contour Swaras: S S N R Emphatic beat Negative Positive sam phrase phrases
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Multi-F0 Signal Polyphonic analysis representation audio signal Singing voice Predominant-F0 Voice F0 detection trajectory extraction contour
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