Psychoacoustics 2 - Perception of Loudness

Alexis Baskind
Psychoacoustics 2
Perception of loudness
Alexis Baskind, https://alexisbaskind.net

Alexis Baskind
Psychoacoustics 2 - Perception of loudness
Course series
Fundamentals of acoustics for sound engineers and music producers
Level
undergraduate (Bachelor)
Language
English
Revision
January 2020
To cite this course
Alexis Baskind, Psychoacoustics 2 - Perception of loudness, course material, license:
Creative Commons BY-NC-SA.
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Psychoacoustics 2 - Perception of Loudness
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NonCommercial-ShareAlike 4.0 International License.

Alexis Baskind
Outline
1. Introduction
2. Absolute threshold of hearing
3. Equal-loudness contours
4. Loudness – the Sone
5. Loudness and duration
6. Complex sounds - Simultaneous masking
7. Just-noticeable differences for loudness
8. Estimating loudness

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Introduction
• The Weber-Fechner law is a rough approximation of
for all sensory impressions, but has to be corrected
and/or fine-tuned for each of them
• Perception of loudness is complex subjective
frequency-dependent phenomenon, that depends
among other on the following factors:
– Frequency content, bandwidth of the sound
– Duration of the sound
– Masking from other sounds
– Attention of the listener

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Absolute threshold of hearing
• The threshold of hearing is the average level in dB
SPL of the softest pure tone that humans can
detect, for each frequency
• Note the
effect of age
(20, 40, 60
years) on the
threshold

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Loudness level is not loudness
• Loudness level (unit: phons) is relative measure of
the frequency dependency of the perceived
loudness for pure tones compared to the 1 kHz-
Reference.
• The Sone (see later) is a psychoacoustical measure
for Loudness that describes the absolute perceived
loudness between pure tones.

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Equal-loudness contours
• The equal-loudness contours are measures of sound
pressure in dB SPL for which a listener perceives a constant
loudness when presented with pure steady tones
Frequency (Hz)
• The phon is a
measure of the
perceptual loudness
level of a pure tone
• Those contours are
also called
isophones
• The phon-value at 1
kHz equals the
sound pressure
level in dB SPL

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Equal-loudness contours
Frequency (Hz)
Music
Speech
Ultrasound
Infrasound
Threshold of pain

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Loudness correction
• Music is often mixed loud, i.e. between 75 and 85
dB SPL, to allow hearing to get all frequencies
• … but music is often listened at a softer level !
 Then the mix will sound different (not even considering the fact
that the speakers and the room are indeed different)
 In particular, some of the low- and high-frequency content will be
missing
• Loudness correction on a consumer’s amplifier
aims at allowing a better listening experience at low
levels by boosting low- and high-frequencies

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Loudness correction
Example: K&H ES-20 Stereo-Amplifier
Frequency response
of the loudness
corrector (contour)
of the ES-20
amplifier

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Limitations of equal-loudness contours
• The phon-scale corresponds to the dB-SPL-scale, therefore
the relation to the perceived loudness is not linear: for
instance, a doubling of the perceived loudness does not
correspond to a doubling of the level in dB SPL (but rather
to+10 dB)
Limitations of the Weber-Fechner-law
• The equal-loudness contours are in principle only relevant for
pure tones, not for complex sounds
• The sound duration is not taken into account
 What is the loudness of complex, time-modulated
sounds?
• The equal loudness contours don‘t allow to know, how loud a
sound will be perceived in a mix

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Loudness – the Sone
• The phon scale describes more precisely the perceived
loudness than the dBSPL scale since it takes its frequency
dependency into account. However, it doesn’t map the
perception linearly.
• As a matter-of-fact, it is known that an increase of the
sound pressure level of 10 dB corresponds ca. to a doubling
of the perceived loudness (except for very soft sounds)
• The sone scale was introduced because of this reason. It’s
based on the phone scale and corrects it in order to
approximate loudness more precisely
• Like the phon scale, the sone scale is based on pure tones,
therefore it’s still not sufficient to estimate the loudness of
more complex sounds

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Loudness – the Sone
Music
notation
Phons Sones
120 256
110 128
fff 100 64
ff 90 32
f 80 16
mf, mp 70 8
p 60 4
pp 50 2
ppp 40 1
32 1/2
25 1/4
19 1/8
14 1/16
(Of course the objective loudness of a mf or a ppp is
very subjective and depends on the context, but
this table gives an order of magnitude)

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Faders
1. A linear volume fader would be almost useless, since it
does not allow to control the loudness in a linear way:
Reference: x 1
Amplification => Loudness change
Reference (+0 dB)
x 1.3 ca. 1.2x louder (+2.3 dB)
x 0 silence
x 0,5 ca. 1.5x softer (-6 dB)
x 0,25 ca. 2x softer (-12 dB)
x 0,125 ca. 3.5x softer (-18 dB)
x 0,06 ca. 5x softer (-24 dB)
(the resolution
for soft levels
is much too
coarse)

Alexis Baskind
Faders
2. A pure dB-Fader would also be not optimal, since
the lower half of it would be almost useless:
Reference: 0 dB
Reference
silence
-10 dB 2x softer
-20 dB 4x softer
-30 dB 8x softer
-40 dB 16x softer
-50 dB 32x softer
-60 dB 64x softer
+10 dB 2x lauter
+20 dB 4x louder(the resolution
in this range is
too coarse: a
few
centimeters
correspond to
a difference of
20 dB
-¥

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Faders
3. The standard for Faders is actually a very good
compromise:
Reference: 0 dB
Reference
silence
-10 dB 2x softer
-20 dB 4x softer
-30 dB 8x softer
-40 dB 16x softer
-60 dB 32x softer
+10 dB 2x louder
-50 dB
-¥
(in this
region, the
fader allows
to control
loudness
almost in a
linear way)

Alexis Baskind
Effect of sound duration
• Below 200-300 ms, the longer the sound, the louder it will
be perceived
• This observation is used in audio level metering
instruments like the VU-meter, which smoothing time is set
to 300 ms.
Loudness /
max loudness
Sound
duration (s)

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Complex Sounds
• In case of sounds more complex than pure steady tones,
the same principle applies (i.e. hearing is less sensitive to
low- and high-frequencies at soft levels)
• But the equal-loudness curves don’t strictly apply, since:
– Overtones and noisy parts of a sound, which are first separated
from each other by the auditory system, are combined afterwards
and perceived as a unique entity
– This loudness summation is complex and depends on the so-
called critical bands (see below)
– Among others, the superposition of single pure tones implies
masking

Alexis Baskind
Critical bands
• The first type of frequency grouping occurs in the midbrain:
adjacent simultaneous frequency components are
combined in frequency bands which are perceived as one
entity
• Those frequency bands are called critical bands
• In many cases, they dictate the frequency resolution of
hearing
• On top of that, the loudness of a broadband sound does
not correspond to the sum of the loudness of all single
components: it depends on the energy in each frequency
band => loudness summation

Alexis Baskind
Critical bands
The critical bandwidth depends
on the center frequency:
• Up to 500 Hz, it equals circa 100
Hz
• Above 500 Hz, it increases
proportionnaly to the center
frequency: the relative bandwidth
is more or less constant (between
1/6 octave and 1/3 octave)
=> This could explain why 1/3 octave
filters are used everywhere inDies
könnte erklären, warum Terzband-
Filter in sound engineering!

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Critical bands and loudness summation
Image: Thomas Görne, “Tontechnik” (based on Feldtkeller and Zwicker)
Bandwidth
Spectral loudness
summation:
loudness level of
noises centered at 1
kHz with variable
bandwidth
Horizontal axis =
noise bandwidth
Vertical axis =
effective sound
pressure level in dB
SPL

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Simultaneous masking
Frequency
(kHz)
If two tones with similar (but not equal) frequencies are played
together, the loudest tone masks the softest partially or totally:
The hearing threshold is locally raised

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• The louder the loudest tone, the bigger the bandwidth of the
masking pattern
• Moreover, the behavior is asymmetric on the frequency axis
Example: Masking
of a soft tone by a
1-kHz pure tone
Increase of the threshold of hearing in presence of an interfering Signal (1 kHz
pure tone)
Threshold of
hearing
Source:
Blauert/Wikipedia

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“Generally speaking, a high-frequency sound can only mask a
low-frequency sound if the frequency spacing is small. A low-
frequency sound can only mask a high-frequency sound if the
former is loud compared to the latter” (Michael Dickreiter)
This means for mixing:
If two sounds share common frequency ranges, components of
the softest are quite often masked by the loudest.
A classical example is masking of a bass drum by an electric
bass or vice-versa: if the bass drum is louder than the bass,
only overtones of the bass remain audible (which also can be
themselves masked by other instruments)

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How to solve/reduce masking in mixing
– With different EQs, so that every instrument has a privileged
space in a given frequency region. For this purpose it‘s not
relevant if the soloed track sounds good or coloured, only the
result in the mix counts. Actually it‘s even often
counterproductive to try to optimize the sound of each
instrument independently from the other ones!
– With less or shorter reverb, a different sounding reverb, and/or
with an EQ at the output of the reverb
– With dynamic processing (potentially with external Side-chain):
the bass drum could for instance dominate during its attack and
right afterwards be made softer to make the resonance of the
bass more audible
– With panning (see later, „Cocktail-Party-Effekt“)

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Just-noticeable level difference
• The just-noticeable difference (JND), describes (of
for all sensory perceptions) the lower threshold of
perception of a difference in the physical stimulus
• For loudness, the just-noticeable difference is about
1 dB
• The JND depends on absolute loudness:
– it is closer to 2 or 3 dB at the threshold of hearing
– it can drop to .3 or .5 dB for loud sounds
• JND depends also on the ear training

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Just-noticeable level difference
Just-Noticeable Level Difference of a 1-kHz tone as a function of sound
pressure level
(From Fastl H., Zwicker E., “Psychoacoustics: Facts and Models”)

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Estimation of Loudness, Frequency Weighting
• Based on the previous observations, it’s clear, that a
precise estimation of loudness with electronic
means is hardly possible
• The standards for loudness estimation are
restrained to a simple correction of the spectral
content
• Those so-called frequency-weighting curves
consists in several filters, that have to be selected
with respect to the absolute sound pressure level

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• The A-weighting (Unit dB(A) ) is designed for very soft sounds
(Loudness level around 40 phon, very soft)
• The B-weighting ( dB(B) ) for ca. 60 phon
• The C-weighting (dB(C) ) for ca. 80 phon

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• The measurement process in a sound level meter
consists in:
1. converting the sound pressure in voltage (with an
omnidirectional microphone)
2. applying the A-, B-, or C-weighting filter
3. calculate the RMS in dB
• In practice, the B-Weighting is not used at all, and C-
Weighting quite rarely
=> dB(A) is de facto a general standard for estimating
loudness, though it is only suitable for soft sounds.
Filter: A-, B-, or
C-weighting
RMS
dB(A), dB(B)
or dB(C)

Psychoacoustics 2 - Perception of Loudness

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