MUSI-6201 | Computational Music Analysis...2015/10/05 · overview intro perception music features summary intensity, magnitude & loudness features: root mean square 2/2 common variants

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

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6331121&

https://github.com/alexanderlerch/ACA-Slides





github repository








github repository








github repository





intensity, magnitude & loudnessintroduction

intensity-related descriptors commonly usedwaveform view

t [s]

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level monitoring (PPM, VU,. . . )

terms and definitions

magnitudeintensityenvelopelevelvolumevelocityloudness


intensity, magnitude & loudnessintroduction

intensity-related descriptors commonly usedwaveform view

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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

(v(n)

v0

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





vdB(n) = 20 · log10

(v(n)

v0






vdB(n) = 20 · log10

(v(n)

v0



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]

0

5

10

15

20

ǫ = 1e − 01

ǫ = 1e − 02

ǫ = 1e − 03

ǫ = 1e − 04

b add if statement

vtrunc(n) =


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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

SPL

[dB]

0

20

40

60

80

100

120

0 phon

20 phon

40 phon

60 phon

80 phon

90 phon

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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:






score:






score:





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

vRMS(n) =

√√√√√ 1

K

ie(n)∑i=is(n)

x(i)2



vRMS(n) =

√√√√√ 1

K

ie(n)∑i=is(n)

x(i)2

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



vRMS(n) =

√√√√√ 1

K

ie(n)∑i=is(n)

x(i)2

5 10 15 20 25

f [k

Hz]

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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

v(n)

H(z):

A, B, C weighting

RLB (BS.1770)

. . .



x(i)H(z) RMS

v(n)

H(z):

A, B, C weighting

RLB (BS.1770)

. . .



x(i)H(z) RMS

v(n)

H(z):

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

f [Hz]

102 103 104

|H(f

)|[dB]

-20

-10

0

10

BS.1770 MC

ITU-R BS.468

A Weighting

C Weighting

Z Weighting ma

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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

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

⊕ ⊗ ⊕ ⊕

z−1

⊗

x(i) |x(i)|

−

αAT

λ

−

vPPM(i)



⊕ ⊗ ⊕ ⊕

z−1

⊗

x(i) |x(i)|

−

αAT

λ

−

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)



⊕ ⊗ ⊕ ⊕

z−1

⊗

x(i) |x(i)|

−

αAT

λ

−

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)



⊕ ⊗ ⊕ ⊕

z−1

⊗

x(i) |x(i)|

−

αAT

λ

−

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)



⊕ ⊗ ⊕ ⊕

z−1

⊗

x(i) |x(i)|

−

αAT

λ

−

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)



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discuss differences between peak meter and maxper block

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intensity, magnitude & loudnessfeatures: zwicker loudness

Stimulus Outer EarTransferFunction

ExcitationPatterns

SpecificLoudness

OverallLoudness

vLoud




ExcitationPatterns

SpecificLoudness

OverallLoudness

vLoud

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

vLoud

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).

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




ExcitationPatterns

SpecificLoudness

OverallLoudness

vLoud

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).

https://www.salford.ac.uk/computing-science-engineering/research/acoustics/psychoacoustics/sound-quality-making-products-sound-better/sound-quality-testing/customised-metrics






ExcitationPatterns

SpecificLoudness

OverallLoudness

vLoud

overall loudnessvloud =

∑∀i

zi


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











Documents

MUSI-6201 | Computational Music Analysis...2015/10/05 · overview intro perception music features summary intensity, magnitude & loudness features: root mean square 2/2 common variants