MUSI-6201 | Computational Music Analysis...2015/10/05 · overview intro perception music features...

overview intro perception music features summary

MUSI-6201 — Computational Music AnalysisPart 5.1: Intensity

alexander lerch

November 4, 2015

instantaneous featuresoverview

text bookChapter 4: Intensity (pp. 71–78)

sources: slides (latex) & Matlab

github repository

lecture contentloudness perception and decibelsdynamics in musicinstantaneous features

github repository

intensity, magnitude & loudnessintroduction

intensity-related descriptors commonly usedwaveform view

0 5 10

level monitoring (PPM, VU,. . . )

terms and definitions

magnitudeintensityenvelopelevelvolumevelocityloudness

intensity, magnitude & loudnessintroduction

intensity-related descriptors commonly usedwaveform view

0 5 10

level monitoring (PPM, VU,. . . )

terms and definitionsmagnitudeintensityenvelopelevelvolumevelocityloudness

intensity, magnitude & loudnesshuman perception 1/2

perception has non-linear relation to intensity:

model: logarithmic relation

vdB(n) = 20 · log10

)v0: reference constant (0 dB point)digital: v0 = 1 ⇒ dBFSscaling factor: 1 dB ≈ JNDL

vdB(n) = 20 · log10

intensity, magnitude & loudnessexcursion: level computation

if v(n) = 0 ⇒: computation of log10(0)

work-aroundsa add constant ε

vdB(n) = 20 · log10(v(n) + ε)

b add if statement

vtrunc(n) =

{v(n), if v(n) ≥ εε, otherwise

if v(n) = 0 ⇒: computation of log10(0)work-arounds

a add constant ε

vdB(n) = 20 · log10(v(n) + ε)

vdB [dB]

-40 -35 -30 -25 -20 -15 -10 -5 0

v′ dB−

vdB[dB]

ǫ = 1e − 01

ǫ = 1e − 02

ǫ = 1e − 03

ǫ = 1e − 04

b add if statement

vtrunc(n) =

if v(n) = 0 ⇒: computation of log10(0)

work-aroundsa add constant ε

vdB(n) = 20 · log10(v(n) + ε)

b add if statement

vtrunc(n) =

decibel scale is not loudness scale:

equal-sized steps on the decibel scale not perceived asequal-sized loudness steps

perceptual loudness depends on

frequencycochlear resolutionmasking effects

decibel scale is not loudness scale:

equal-sized steps on the decibel scale not perceived asequal-sized loudness steps

perceptual loudness depends on

frequencycochlear resolutionmasking effects

f [Hz]

102 103 104

0 phon

20 phon

40 phon

60 phon

80 phon

90 phon

intensity, magnitude & loudnessdynamics in music

score:

only several rough dynamic steps,e.g.:pp, p, mf, f, ffcomparably vague instructions on volume modifications, e.g.:crescendo, decrescendo, sfdynamics influenced by

instrumentationtimbrenumber of voicescontext and musical tension

MIDI:128 velocity stepsno standardized relation to magnitude, power, . . .

score:

intensity, magnitude & loudnessfeatures: root mean square 1/2

vRMS(n) =

√√√√√ 1

ie(n)∑i=is(n)

vRMS(n) =

√√√√√ 1

ie(n)∑i=is(n)

value of this feature for the hypothetical prototype signalssilencesinusoidal (Amplitude A)

vRMS(n) =

√√√√√ 1

ie(n)∑i=is(n)

5 10 15 20 25

0 5 10 15 20 25

common variants (sample processing only):

reduce computational complexity

v 2RMS(n) =

x(ie(n))2 − x(is(n − 1))2

ie(n)− is(n) + 1+ v 2

RMS(n − 1)

vRMS(n) =√

v 2RMS(n)

single pole approximation

vtmp(i) = α · vtmp(i − 1) + (1− α) · x(i)2

v∗RMS(i) =

√vtmp(i)

common variants (sample processing only):

reduce computational complexity

v 2RMS(n) =

x(ie(n))2 − x(is(n − 1))2

ie(n)− is(n) + 1+ v 2

RMS(n − 1)

vRMS(n) =√

v 2RMS(n)

single pole approximation

vtmp(i) = α · vtmp(i − 1) + (1− α) · x(i)2

v∗RMS(i) =

√vtmp(i)

intensity, magnitude & loudnessfeatures: weighted root mean square

x(i)H(z) RMS

A, B, C weighting

RLB (BS.1770)

x(i)H(z) RMS

A, B, C weighting

RLB (BS.1770)

x(i)H(z) RMS

A, B, C weightingRLB (BS.1770). . .

f [Hz]

102 103 104

)|[dB]

BS.1770 MC

ITU-R BS.468

A Weighting

C Weighting

Z Weighting ma

intensity, magnitude & loudnessfeatures: peak envelope (max)

vPeak(n) = maxis(n)≤i≤ie(n)

|x(i)|

intensity, magnitude & loudnessfeatures: peak envelope (max)

vPeak(n) = maxis(n)≤i≤ie(n)

|x(i)|

5 10 15 20 25

0 5 10 15 20 25

intensity, magnitude & loudnessfeatures: peak envelope (PPM) 1/2

⊕ ⊗ ⊕ ⊕

x(i) |x(i)|

vPPM(i)

⊕ ⊗ ⊕ ⊕

x(i) |x(i)|

vPPM(i)

release state (|x(i)| < vPPM(i − 1)⇒ λ = αRT)

vPPM(i) = vPPM(i − 1)− αRT · vPPM(i − 1)

= (1− αRT) · vPPM(i − 1)

⊕ ⊗ ⊕ ⊕

x(i) |x(i)|

vPPM(i)

release state (|x(i)| < vPPM(i − 1)⇒ λ = αRT)

vPPM(i) = vPPM(i − 1)− αRT · vPPM(i − 1)

= (1− αRT) · vPPM(i − 1)

⊕ ⊗ ⊕ ⊕

x(i) |x(i)|

vPPM(i)

attack state (|x(i)| ≥ vPPM(i − 1)⇒ λ = 0)

vPPM(i) = αAT ·(|x(i)| − vPPM(i − 1)

)+ vPPM(i − 1)

= αAT · |x(i)|+ (1− αAT) · vPPM(i − 1)

⊕ ⊗ ⊕ ⊕

x(i) |x(i)|

vPPM(i)

attack state (|x(i)| ≥ vPPM(i − 1)⇒ λ = 0)

vPPM(i) = αAT ·(|x(i)| − vPPM(i − 1)

)+ vPPM(i − 1)

= αAT · |x(i)|+ (1− αAT) · vPPM(i − 1)

5 10 15 20 25

0 5 10 15 20 25

discuss differences between peak meter and maxper block

5 10 15 20 25

0 5 10 15 20 25

5 10 15 20 25

0 5 10 15 20 25

intensity, magnitude & loudnessfeatures: zwicker loudness

Stimulus Outer EarTransferFunction

ExcitationPatterns

SpecificLoudness

OverallLoudness

ExcitationPatterns

SpecificLoudness

OverallLoudness

outer ear transfer function1

1D. Hammershøi and H. Møller, “Methods for Binaural Recording and Reproduction,” Acta Acustica united

with Acustica, vol. 88, no. 3, pp. 303–311, May 2002.

ExcitationPatterns

SpecificLoudness

OverallLoudness

excitation patterns1

1M. Schleske, Vibrato of the musician, [Online]. Available:

http://www.schleske.de/en/our-research/handbook-violinacoustics/vibrato-of-the-musician.html

(visited on 07/29/2015).

ExcitationPatterns

SpecificLoudness

OverallLoudness

specific loudness1

1U. of Salford, Customised metrics, [Online]. Available: https://www.salford.ac.uk/computing-science-

engineering/research/acoustics/psychoacoustics/sound-quality-making-products-sound-

better/sound-quality-testing/customised-metrics (visited on 07/29/2015).

ExcitationPatterns

SpecificLoudness

OverallLoudness

overall loudnessvloud =

∑∀i

intensity, magnitude & loudnessderived features

number or ratio of pauses

dynamic range

statistical features from (RMS) histogram

summarylecture content

1 why are intensity-related features often in dB

2 how does the dB-Scale relate to loudness

3 what are typical intensity-related features

MUSI-6201 | Computational Music Analysis...2015/10/05 · overview intro perception music features...

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