ISO 532-1:2017
(Main)Acoustics — Methods for calculating loudness — Part 1: Zwicker method
Acoustics — Methods for calculating loudness — Part 1: Zwicker method
ISO 532-1:2017 specifies two methods for estimating the loudness and loudness level of sounds as perceived by otologically normal persons under specific listening conditions. The first method is intended for stationary sounds and the second method for arbitrary non-stationary (time-varying) sounds, including stationary sounds as a special case. The methods can be applied to any sound recorded as single-channel measurements using a microphone, or as multi-channel measurements, for example by means of a head and torso simulator (see Annex D). Since most important technical sounds are time-varying, a model of time-varying loudness is preferable. The methods are based on the Zwicker algorithm.[14] The method for stationary sounds is provided for reasons of continuity and also offers the use of measured one-third-octave-band levels as input. The more general method for arbitrary sounds calculates the specific loudness pattern based on measured time signals by applying a signal processing model that is directly related to physiological and psychological characteristics of the human hearing system. Loudness is calculated from the specific loudness pattern. It has been shown that this method provides a good match to the results of many loudness experiments using synthetic and technical sounds. No prior knowledge about the properties of the sound (e.g. broadband or narrowband noise, tonal content) and no user interactions are required for the fully automated application of the method. The evaluation of the harmful effect of sound events is outside the scope of ISO 532-1:2017.
Acoustique — Méthode de calcul du niveau d'isosonie — Partie 1: Méthode de Zwicker
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 532-1
First edition
2017-06
Corrected version
2017-11
Acoustics — Methods for calculating
loudness —
Part 1:
Zwicker method
Acoustique — Méthode de calcul du niveau d'isosonie —
Partie 1: Méthode de Zwicker
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
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Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Specification of input signal and instrumentation . 4
5 Method for stationary sounds . 5
5.1 General . 5
5.2 Description of the method . 6
5.3 Calculation of loudness and loudness level . 9
6 Method for time-varying sounds .12
6.1 General .12
6.2 Description of the method .13
6.3 Calculation algorithm .14
6.4 Guidance for determining the loudness of time-varying sounds .15
7 Reporting data .16
Annex A (normative) Numerical details and program code for the calculation of loudness of
stationary and time-varying sounds (test implementation) .17
Annex B (normative) Test signals for the validation of implementation .45
Annex C (informative) Graphical user interface for the calculation of loudness of stationary
and time-varying sounds .48
Annex D (informative) Guidance for determining the loudness when using head and torso
simulator microphones .53
Annex E (informative) Uncertainty considerations .54
Bibliography .57
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
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ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
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URL: www.iso.org/iso/foreword.html
This document was prepared by Technical Committee ISO/TC 43, Acoustics.
This first edition cancels and replaces ISO 532:1975, which has been technically revised.
A list of all parts in the ISO 532 series can be found on the ISO website.
This corrected version of ISO 532-1:2017 incorporates the following correction:
— Table A.9 has been corrected.
iv © ISO 2017 – All rights reserved
Introduction
Loudness and loudness level are two perceptual attributes of sound, describing absolute and relative
sensations of sound strength perceived by a person under specific listening conditions. Due to inherent
individual differences among people, both loudness and loudness level have the nature of statistical
estimators characterized by their respective measures of central tendency and dispersion determined
for a specific sample of the general population.
The object of the ISO 532 series is to specify calculation procedures based on physical properties of
sound for estimating loudness and loudness level of sound as perceived by persons with otologically
normal hearing under specific listening conditions. Each procedure provides single numbers that can be
used in many scientific and technical applications to estimate the perceived loudness and loudness level
of sound, without conducting separate human observer studies for each application. Because loudness
is a perceived quantity, the perception of which may vary among people, any calculated loudness
value represents only an estimate of the average loudness as perceived by a group of individuals with
otologically normal hearing.
ISO 532-1 and ISO 532-2 specify two different methods for calculating loudness which may yield
different results for given sounds. Since no general preference for one or the other method can
presently be stated, it is up to the user to select the method which appears most appropriate for the
given situation. Some major features of each of the methods are described below to facilitate the choice.
The first method of this document describes the calculation of loudness and loudness level of stationary
sounds and is based on DIN 45631:1991. The second method of this document covers the procedures for
calculation of loudness and loudness level of arbitrary non-stationary (time-varying) sounds, including
stationary sounds as a special case, and is based on DIN 45631/A1:2010.
This document also includes a program code for both methods leading to estimates of loudness and
loudness level for stationary and time-varying sounds. An executable computer program is also
provided for both methods. The applied software is normative for calculating loudness values, against
which other implementations can be checked subject to stated tolerances, and provides additional
functionality for the convenience of the user.
The method for stationary sounds in this document differs slightly from the methods included in the
previous ISO 532:1975, method B, by specifying corrections for low frequencies and by restricting the
description of the approach to numerical instructions only, thus allowing a unique software description.
For reasons of continuity, the method given in this document is in accordance with ISO 226:1987 instead
of the later revised version, ISO 226:2003.
Based on the general concept of the method for stationary sounds, the method for time-varying sounds
incorporates a generalization of the Zwicker approach to arbitrary, non-stationary sounds. Of course,
this generalization is compatible with the method for stationary sounds in that it gives the same
loudness values as the method for stationary sounds if applied to stationary sounds.
The Moore-Glasberg method as implemented in ISO 532-2 is limited to stationary sounds and can be
applied to tones, broadband noises and complex sounds with sharp line spectral components. The
method in ISO 532-2 differs from those in ISO 532:1975. ISO 532:1975, method A (Stevens loudness),
was removed as this method was not often used and its predictions were not accurate for sounds with
strong tonal components. The method described in ISO 532-2 also improves the precision of calculated
loudness in the low frequency range and allows for calculation of loudness under conditions where the
sound differs at the two ears. It has been shown that this method provides a good match to the contours
of equal loudness level as defined in ISO 226:2003 and the reference threshold of hearing as defined in
ISO 389-7:2005.
NOTE Equipment or machinery noise emissions/immissions can also be judged by other quantities defined
in various International Standards (see e.g. ISO 1996-1, ISO 3740, ISO 9612 and ISO 11200).
INTERNATIONAL STANDARD ISO 532-1:2017(E)
Acoustics — Methods for calculating loudness —
Part 1:
Zwicker method
1 Scope
This document specifies two methods for estimating the loudness and loudness level of sounds as
perceived by otologically normal persons under specific listening conditions. The first method is
intended for stationary sounds and the second method for arbitrary non-stationary (time-varying)
sounds, including stationary sounds as a special case.
The methods can be applied to any sound recorded as single-channel measurements using a microphone,
or as multi-channel measurements, for example by means of a head and torso simulator (see Annex D).
Since most important technical sounds are time-varying, a model of time-varying loudness is preferable.
[14]
The methods are based on the Zwicker algorithm. The method for stationary sounds is provided for
reasons of continuity and also offers the use of measured one-third-octave-band levels as input. The
more general method for arbitrary sounds calculates the specific loudness pattern based on measured
time signals by applying a signal processing model that is directly related to physiological and
psychological characteristics of the human hearing system. Loudness is calculated from the specific
loudness pattern. It has been shown that this method provides a good match to the results of many
loudness experiments using synthetic and technical sounds.
No prior knowledge about the properties of the sound (e.g. broadband or narrowband noise, tonal
content) and no user interactions are required for the fully automated application of the method.
The evaluation of the harmful effect of sound events is outside the scope of this document.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
IEC 61260-1:2014, Electroacoustics — Octave-band and fractional-octave-band filters — Part 1:
Specifications
IEC 61672-1:2013, Electroacoustics — Sound level meters — Part 1: Specifications
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at http://www.iso.org/obp
— IEC Electropedia: available at http://www.electropedia.org/
3.1
otologically normal person
person in a normal state of health who is free from all signs or symptoms of ear disease and from
obstructing wax in the ear canals, and who has no history of undue exposure to noise, exposure to
potentially ototoxic drugs or familial hearing loss
[SOURCE: ISO 226:2003, 3.1]
3.2
sound pressure level
L
p
ten times the logarithm to the base 10 of the ratio of the square of the sound pressure, p, to the square
of a reference value, p , expressed in decibels
p
L =10lg dB
p
p
where the reference value, p , is 20 μPa
Note 1 to entry: Because of practical limitations of the measuring instruments, p is always understood to
denote the square of a frequency-weighted, frequency-band-limited or time-weighted sound pressure. If specific
frequency and time weightings as specified in IEC 61672-1 and/or specific frequency bands (3.3) are applied, this
should be indicated by appropriate subscripts, for example, L denotes the A-weighted sound pressure level
p,AS
with time weighting S (slow). Frequency weightings such as A-weighting should not be used when specifying
sound pressure levels for the purpose of loudness (3.18) calculation using the current procedure.
Note 2 to entry: This definition is technically in accordance with ISO 80000-8:2007, 8-22.
3.3
frequency band
continuous set of frequencies in the range of two specified limiting frequencies
Note 1 to entry: A frequency band is characterized by two values that define its position in the frequency
spectrum, for instance its lower and upper cut-off frequencies.
Note 2 to entry: Frequency is expressed in Hz.
[SOURCE: IEC 60050-702:1992, 702-01-02]
3.4
filter
device or mathematical operation that, when applied to a complex signal, passes energy of signal
components of certain frequencies while substantially attenuating energy of signal components of all
other frequencies
3.5
cut-off frequency
lowest ( f ) or the highest ( f ) frequency beyond which the response of the filter (3.4) to a sinusoidal
l h
signal does not exceed −3 dB relative to the maximum response measured between f and f
l h
3.6
band-pass filter
filter (3.4) that passes signal energy within a certain frequency band (3.3) and rejects most of the signal
energy outside of this frequency band
3.7
filter bandwidth
Δf
difference between f and f for a band-pass filter (3.6)
h l
2 © ISO 2017 – All rights reserved
3.8
one-third-octave band
frequency band (3.3) with the centre frequency f and the width of one-third of an octave
T
Note 1 to entry: The subscript T instead of c is used to specify the centre frequency in the special case of a one-
third-octave band.
Note 2 to entry: Width of one-third of an octave as specified in IEC 61260-1.
3.9
band-reject filter
filter (3.4) that rejects signal energy within a certain frequency band (3.3) and passes most of the signal
energy outside of this frequency band
Note 1 to entry: A narrow band-reject filter is also called a notch filter.
3.10
one-third-octave-band level
L
T
sound pressure level (3.2) of sound contained within a frequency band (3.3) with the width of one-third
of an octave
3.11
sound spectrum
representation of the magnitudes (and sometimes of the phases) of the components of a complex sound
as a function of frequency
3.12
critical band
auditory filter
filter (3.4) within the human cochlea describing the frequency resolution of the auditory system with
characteristics that are usually estimated from the results of masking experiments
3.13
critical bandwidth
auditory filter bandwidth
bandwidth of a critical band (3.12)
Note 1 to entry: The critical bandwidth values in Hz are as specified in Reference [22].
Note 2 to entry: Each critical bandwidth has a width of one unit on the critical band rate scale (3.14).
3.14
critical band rate scale
transformation of the frequency scale, constructed so that an increase in frequency equal to one critical
bandwidth (3.13) leads to an increase of one unit on the critical band rate scale
Note 1 to entry: Frequencies on the critical band rate scale are expressed in Bark.
EXAMPLE The value of the critical bandwidth for a centre frequency of 1 000 Hz is approximately 160 Hz, so
an increase in frequency from 920 Hz to 1 080 Hz corresponds to a step of one Bark.
3.15
critical band level
L
CB
sound pressure level (3.2) of sound contained within a critical band (3.12)
3.16
loudness level
sound pressure level (3.2) of a frontally incident, sinusoidal plane progressive wave, presented binaurally
at a frequency of 1 000 Hz that is judged by otologically normal persons (3.1) as being as loud as the
given sound
Note 1 to entry: Loudness level is expressed in phons.
3.17
calculated loudness level
L
N
loudness level (3.16) calculated following the procedure of a predictive model
3.18
loudness
perceived magnitude of a sound, which depends on the acoustic properties of the sound and the specific
listening conditions, as estimated by otologically normal persons (3.1)
Note 1 to entry: Loudness is expressed in sones.
Note 2 to entry: Loudness depends primarily upon the sound pressure level (3.2), although it also depends upon
the frequency, waveform, bandwidth, and duration of the sound.
Note 3 to entry: One sone is the loudness of a sound with a loudness level (3.16) of 40 phon.
Note 4 to entry: A sound that is twice as loud as another sound is characterized by doubling the number of sones.
3.19
calculated loudness
N
loudness (3.18) calculated following the procedure of a predictive model
Note 1 to entry: The calculated loudness is denoted N or N , expressed in sones. The letters F and D signify that
F D
the calculation assumes either free field frontal sound incidence (F) or diffuse field incidence (D).
Note 2 to entry: The calculated loudness corresponds to the loudness that would be experienced by an average of
a group of persons with otologically normal hearing whose heads are centred at the position of the microphone.
This is equivalent to diotic listening (same sound at each ear).
3.20
specific loudness
¢
N
loudness (3.18) evoked over a frequency band (3.3) with a bandwidth of a critical band (3.12) centred at
the frequency of interest
Note 1 to entry: Specific loudness is expressed in sones/Bark.
Note 2 to entry: The definition together with the stated unit are different from those in ISO 532-2.
3.21
percentile loudness
N
X
loudness (3.18) that is reached or exceeded in X % of the measuring time intervals
Note 1 to entry: The percentile loudness is expressed in sones.
4 Specification of input signal and instrumentation
The input signal is measured using a sound acquisition system consisting of at least a microphone, pre-
amplifier and amplifier. The instrumentation shall meet the requirements of IEC 61672-1:2013, class
1, as far as applicable. The waveform of the time signal is sampled with an A/D-converter. The test
4 © ISO 2017 – All rights reserved
implementation in A.4 requires a sampling rate of 48 kHz. Signals with other sampling rates shall be
resampled to 48 kHz when using this implementation. For the convenience of the user an additional
source file containing an algorithm for up-sampling signals with sampling rates of 32 kHz or 44,1 kHz is
provided (see ‘// BLOCK Resampling’).
For reasons of convenience, the program code is extended to allow the use of time signals in the form
of WAVE files for the calculation algorithm of loudness. The data format can be 16-bit integer or 32-
bit float format (correct sound pressure values, no normalized data). For a 16-bit integer format, an
appropriate calibration file and the corresponding calibration value shall be given. The corresponding
algorithms are also contained in the additional source file.
The type of sound field [free (F) or diffuse (D)] shall be specified.
The one-third-octave-band sound pressure levels are determined using one-third-octave-band filters
that conform to IEC 61260-1:2014, class 1 with centre frequencies spanning the range between 25 Hz
and 12,5 kHz. In order to reduce uncertainties of loudness calculation the filter coefficients are provided
(A.2). The one-third-octave-band filters are designed as 6th order Chebyshev filters using three 2nd
order sections. These filters are optimized to provide a damping of 20 dB at the centre frequencies
of the adjacent bands (except for 12,5 kHz only the lower band is considered). This means that, for
example, a 1 kHz tone with a sound pressure level of 70 dB produces the following levels at different
centre frequencies: 50 dB at 800 Hz, 70 dB at 1 kHz and 50 dB at 1,25 kHz.
The method for stationary sounds also offers the use of one-third-octave-band levels measured with
a sound level meter according to IEC 61672-1:2013, class 1, and a filter according to IEC 61260-1:2014,
class 1, as input.
NOTE A software package including the listing of the program code can be freely downloaded from http://
standards.iso.org/iso/532/-1/ed-1/en
5 Method for stationary sounds
5.1 General
This specifies a method for calculating loudness and loudness level of stationary sounds using
objective measurement data and a calculation procedure developed by E. Zwicker and his colleagues.
[14]
The calculated data allow the loudness to be specified and thus different stationary sounds to be
quantitatively evaluated according to their individual expected perceived loudness. The procedure
applies to all stationary sounds.
The method for stationary sounds given in this document is an updated version of method B as given in
ISO 532:1975, providing a modified treatment of low-frequency energy. The calculation is based on an
algorithmic approach as opposed to a graphical method. The modified treatment for frequencies below
300 Hz strictly follows the approach given by DIN 45631:1991, introduced to improve the accuracy
of the calculated loudness. Since then, this modified version has achieved widespread use and thus
frequently replaced previous applications of ISO 532:1975, method B. It therefore can be seen as the
direct continuation of the frequently used Zwicker method.
It is this aim of maximum continuity which has prevented any other changes because the benefit of
some smaller adoptions was seen to be smaller than the loss of continuity and comparability of data. For
reasons of continuity, the method given in this document is in accordance with ISO 226:1987 instead of
the later revised version ISO 226:2003.
The procedure involves a sequence of steps. For a precise definition of each step the user is referred
to a detailed description in 5.2 and the program code in A.4. Both descriptions of the procedure are
provided in order to facilitate the comprehension of the procedure. It is envisaged that those wishing to
calculate loudness using the method for stationary sounds will use an implementation of the algorithm
given by the computer program of A.4 or other implementations in conformance with the tolerances
given in the paragraph below.
The implementation given in Annex A shall be used as the test method against which other
implementations shall be tested to determine compliance with this document.
Any specific implementation is permitted if, for all stationary test signals given in B.2 and B.3,
— their calculated specific loudness values differ by not more than ± 5 % of the specific loudness
values calculated by the test implementation or ± 0,1 sone/Bark, and if
— the deviation for total loudness is not more than ± 5 % or ± 0,1 sone.
The supplier of any specific implementation shall provide a declaration of conformance with this
document, indicating the results achieved using the test signals given in Annex B, e.g. as part of the
solution’s user manual. For convenience, the test signals and the tables of the results from the test
implementation (including tolerances) are supplied electronically (as WAVE and EXCEL files). Modifying
the test signals is not allowed.
NOTE A software package including the WAVE and EXCEL files can be freely downloaded from http://
standards.iso.org/iso/532/-1/ed-1/en
5.2 Description of the method
The method for calculating loudness consists of three steps. These steps provide a means of combining
and converting the one-third-octave-band levels to give the total loudness level. These steps are
described below and illustrated by a block diagram in Figure 1. An example for factory noise in a diffuse
sound field is also given for further explanation (see Figure 2). Even though the abscissa gives cut-off
or centre frequencies, Figure 2 is scaled according to critical band rate. At each one-third-octave band,
“ladders” can be seen, the rungs of which represent possible values of the respective one-third-octave-
band levels.
Step 1
This step accounts for the fact that the human hearing system is less sensitive at low frequencies below
300 Hz than at higher frequencies. This is done by appropriately decreasing the respective one-third-
octave- band levels before entering them into the diagram of Figure 2. The details of these corrections
can be taken from Table A.3.
Step 2
The approximation of critical bands by one-third-octave bands is only acceptable for frequencies above
about 300 Hz. For lower frequencies, one-third-octave bands are smaller than the critical bands, so two
or more one-third-octave bands shall be added in order to approximate critical bands. This is the case
for all evaluated one-third-octave bands between 20 Hz and 90 Hz (L ), for the three one-third-octave
CB’ 1
bands between 90 Hz and 180 Hz (L ), and for the two one-third-octave bands between 180 Hz and
CB’ 2
280 Hz (L ). In these cases, the critical band level shall be approximated by power summation in the
CB’ 3
given one-third-octave bands. The thick horizontal lines shown in Figure 2 with the width of about a
critical band at low centre frequencies were produced in this way from the smaller horizontal thin bars
which correspond to the measured one-third-octave-band levels.
Step 3
Before entering the corrected one-third-octave-band levels into the diagram (in order to transform the
levels into their corresponding core loudness, see A.3), it shall be ascertained whether the spectrum
was obtained under diffuse or free field conditions. In the example of Figure 2, this was done by using
the appropriate ladder structure assigning spectral values to specific loudness values. Graphical
representations of different ladder structures for a wide range of one-third-octave-band levels in diffuse
or free field were given in ISO 532:1975 and DIN 45631:1991. In practice, however, the appropriate
values of the ladder structure currently are defined within numerical tables. For reasons of simplicity
and convenience, this document uses a C-implementation of the algorithm instead of particular tables
to specify all numerical allocations. The letters “D” for diffuse and “F” for free field shall be used to
specify the algorithm applied.
6 © ISO 2017 – All rights reserved
Then, for each band a slope towards the higher critical band is added, and the area below the
distribution of specific loudness is summed. The specific value of the slope to be added depends on
the respective one-third-octave-band levels and centre frequencies. Again, detailed information can be
found in the above mentioned graphical representations or in the tables of A.3, respectively. Having
entered the corrected one-third-octave-band levels into the diagram, the shape of the specific loudness
pattern starts with a vertical rise to the one-third-octave-band level measured, stays at the main
value corresponding to the one-third-octave-band level in question and then falls with a slope unless
the level is higher in the next one-third-octave band, in which case the pattern rises vertically to the
level appropriate for the next one-third-octave band. Both the one-third-octave-band spectrum and the
loudness pattern are highlighted by solid curves in the diagram of Figure 2.
If the next one-third-octave-band level is lower, the decrease of the specific loudness towards higher
centre frequencies follows the broken lines, corresponding to the upper slope. In this way, the final
specific loudness versus critical band rate pattern, shortened to “loudness pattern”, is determined
and indicated by the highest thick solid lines in Figure 2. For narrow-band sounds, this upper slope
contributes strongly to the total loudness, i.e. to the total area below the curve. Therefore, it contributes
especially to the total loudness of pure tones. An example is given in Figure 2 by the dotted line for a
1 kHz tone with a sound pressure level of 70 dB. Generally, one-third-octave-band filters show a leakage
towards neighbouring filters of about −20 dB. This means that a 1 kHz tone with a sound pressure level
of 70 dB produces the following levels at different centre frequencies: 50 dB at 800 Hz, 70 dB at 1 kHz
and 50 dB at 1,25 kHz. Therefore, the lower slope of the loudness pattern becomes less steep.
The solid curve in Figure 2 shows the loudness pattern of a factory noise. An area is formed extending
from low to high frequencies. It is bordered by the straight line upwards at the left and right sides of the
overall diagram, and also by the horizontal lower abscissa. The area within these boundaries is marked
by hatching. To calculate the area quantitatively, a rectangular surface of equal area is drawn, which has
the width of the diagram as a basis. The height of this rectangle is a measure of the total area, which is
marked by shading from upper left to lower right. Using this height (the dashed-dotted line), the loudness
or the loudness level can be read from the scales on the right or the left of the diagram. In the diffuse field
example shown in Figure 2, a calculated loudness N of 24 sone and a corresponding loudness level L
D N,D
of 86 phon is found. The sound under test has a relatively broad spectrum. Therefore there is quite a
large difference between the measured sound pressure level of 73 dB or the A-weighted sound pressure
level of 68 dB on the one hand, and the calculated loudness level of 86 phon on the other hand.
The graphical procedure which finally leads to a loudness pattern has the advantage that partial areas
in the diagram correspond to specific parts of the loudness. Therefore, in many cases the diagram
clearly shows which partial area is dominant or which part contributes strongly to the total loudness.
In many applications it is often very important to first reduce that part of the noise which produces the
largest area in the loudness pattern. On the other hand, the diagram shows which parts of the spectrum
are so small in relation to the neighbouring parts that they are partially or even totally masked. In
Figure 2, for example, the one-third-octave-band level of 51 dB at the centre frequency of 630 Hz does
not contribute to loudness because it is totally masked, as indicated by the fact that this one-third-
octave-band level lies below the shaded curve limiting the total area and arising, at this frequency, from
the one-third-octave-band level at 500 Hz.
Figure 1 — Block diagram of the calculation method by this document, method for
stationary sounds
Figure 2 shows a schematic diagram of the graphical calculation algorithm as implemented in this
document, method for stationary sounds, according to DIN 45631:1991.
8 © ISO 2017 – All rights reserved
Key
X1 cut-off frequency of third-octave bands
X2 centre frequency
Y1 scale of total loudness
Y2 scale of corresponding loudness level
Figure 2 — Example of the loudness calculation procedure using charts indicating the
measured one-third-octave-band levels of a factory noise in a diffuse field (see Annex A)
Explanation of Figure 2: Specific loudness is on the ordinate while the critical band rate expressed as
cut-off frequencies of the one-third-octave bands is on the abscissa. The area surrounded by the thick
solid line and hatched from lower left to upper right indicates the total loudness of the noise. This area is
approximated by a rectangular area of the same width but with a height indicated by the area hatched
from upper left to lower right. The height of this rectangular area marks the total loudness on the left
scale and the corresponding loudness level on the right scale. The dotted curve represents the loudness
pattern of a 1 kHz tone with a sound pressure level of 70 dB.
5.3 Calculation of loudness and loudness level
The loudness calculation can be performed from provided one-third-octave-band sound pressure levels
(function ‘f_loudness_from_levels’ in A.4) or from calculated one-third-octave-band levels based on
time signals (function ‘f_loudness_from_signal’ in A.4). The one-third-octave-band levels or the time
signal (as WAVE file) can be easily input using the command line or the graphical user interface of the
software described in Annex C. The appropriate sound field (F or D) shall be specified. For the method
for stationary sounds, loudness is given in sones and loudness level in phons [see Formulae (1) to (3)].
L
N
0,1 − 40
phon
N = 2 sone (1)
where
L ≥ 40 phon
N
and
N
L =+40 33,22 lg phon (2)
N
sone
where
N ≥ 1 sone
respectively.
The relationship for N < 1 sone is
0,35
N
L =+40 0,0005 phon (3)
N
sone
The example in Figure 3 shows the specific loudness versus critical band rate pattern for a single tone
with the frequency f = 1 kHz and with the one-third-octave-band sound pressure level L = 70 dB in
T
a free field. The specific loudness N' in sones/Bark is plotted on the critical band rate scale z. The
F
scale of the critical band rate is subdivided in the unit Bark; each of the 24 critical bands has a width
of 1 Bark. The input for the calculation program is based on a one-third-octave-band level analysis,
providing levels that are reduced by a typical side attenuation of 20 dB/one-third-octave band for
f < 1 kHz and f > 1 kHz. The contribution of one-third-octave-band for f < 1 kHz to the total area
T T T
remains comparably low. For f > 1 kHz, the one-third-octave-bands are masked by the upper slope of
T
f = 1 kHz. The total calculated loudness of the single tone results in N = 8 sone with the calculated
T F
loudness level L = 70,0 phon.
N,F
10 © ISO 2017 – All rights reserved
Key
N' specific loudness, in sones/Bark
F
z critical band rate, in Bark
Figure 3 — Example of the specific loudness versus critical band rate pattern for a single tone
in a free field
The example in Figure 4 shows the specific loudness versus critical band rate pattern for pink noise in a
free field with a constant third-octave-band level L = 78 dB. For the loudness of this broad-band noise
T
the calculation program gives a value of N = 95,0 sone and a loudness level of L = 105,7 phon. For
F N,F
comparison, the A-weighted sound pressure level in this example is L = 90 dB.
A
Key
N' specific loudness, in sones/Bark
F
z critical band rate, in Bark
Figure 4 — Example of the specific loudness versus critical band rate pattern of pink noise in a
free field
6 Method for time-varying sounds
6.1 General
This method specifies the requirements and the procedure to determine the loudness of arbitrary
sounds. When using the procedure for stationary sounds to calculate the loudness of time-varying
sounds, the values obtained are too low. Therefore, a procedure is described in this clause that can
be used to simulate the time processing of sound by the human hearing system when evaluating the
loudness of time-varying sounds.
The procedure involves a sequence of additional steps, as illustrated in Figure 5. For a precise definition
of each step the user is referred to a detailed description in 6.2, 6.3 and the program code in A.4. The
description of the procedure is provided in order to facilitate the comprehension of the procedure.
However, it is envisaged that those wishing to calculate loudness using the method for time-varying
sounds will use the algorithm given by the computer program of A.4 or the executable software given
in Annex C.
The implementation given in Annex A shall be used as the test method against which other
implementations shall be tested to determine compliance with this document.
Any specific implementation is permitted if
— for all time-varying test signals given in B.4, their calculated specific loudness vs. time function
differs by not more than ± 5 % of the specific loudness vs. time function calculated by the test
implementation or ± 0,1 sone/Bark, within a temporal tolerance of ± 2 ms. The tolerance can be
extended to ± 10 % of the specific loudness vs. time function calculated by the test implementation
or ± 0,2 sone/Bark, within a temporal tolerance of ± 2 ms, but only for maximum 1 % of the sampled
specific loudness vs. time function using a time resolution of 2 ms; and if
— for all time-varying test signals given in B.4 and B.5, the deviation for the total loudness vs. time
function is not more than ± 5 % or ± 0,1 sone, within a temporal tolerance of ± 2 ms. The tolerance
can be extended to ± 10 % of the loudness vs. time function calculated by the test implementation
or ± 0,2 sone, within a temporal tolerance of ± 2 ms, but only for maximum 1 % of the sampled
loudness vs. time function using a time resolution of 2 ms.
The supplier of any specific implementation shall provide a declaration of conformance with this
document, indicating the results achieved using the test signals given in Annex B, for example as part of
the solution’s user manual. For convenience, the test signals and the tables of the results from the test
implementation (including tolerances) are supplied electronically (as WAVE and EXCEL files). Modifying
the test signals (e.g. appending zeros) is not allowed.
NOTE A software package including the WAVE and EXCEL files can be freely downloaded from http://
standards.iso.org/iso/532/-1/ed-1/en
12 © ISO 2017 – All rights reserved
NOTE Additional elements with respect to Figure 1 are shown within the boxes with chain dotted lines.
Figure 5 — Block diagram of the calculation method by this document, method for arbitrary
sounds
6.2 Description of the method
The calculation of the loudness of arbitrary sounds is based on the calculation of the loudness of
stationary sounds. The spectral analyses using one-third-octave-band filters are common to both of
these procedures. Although these calculations follow standards (IEC 61260-1) with defined tolerance
bands, the loudness calculation procedure requires the filters to be defined more precisely. An
important prerequisite is a damping of 20 dB at the centre frequencies of the adjacent bands. Thus, this
document intends to reduce the uncertainties of the existing standards by defining all mathematical
facts of the algorithms, starting with the waveform of the time signal and ending with specific and total
[15]
loudness vs. time functions. 16-bit integer data together with a reference signal of known sound
pressure level (for calibration) or 32-bit float data (input as sound pressure in Pascal) can be used. For
processing, a common sampling rate f of 48 kHz is chosen in the test implementation given in Annex A.
s
Signals with other sampling rates shall be resampled to this common sampling rate when using the test
implementation. For the convenience of the user, an additional source file (see ‘// BLOCK Resampling’)
containing an algorithm for up-sampling signals with sampling rates of 32 kHz or 44,1 kHz is provided.
The temporal evaluation of the methods for stationary and time-varying sounds shows significant
differences; the nonlinear decay of the human hearing system needs to be modelled in detail.
Furthermore, a number of very complex hearing characteristics, such as effects of the temporal
summation and forward-masking, shall be taken into account.
The procedure is in principle suitable for calculating the loudness of all time-varying sounds. Sounds
with distinct time structures, such as sounds caused by helicopters and diesel motors as well as spoken
language, yield results which can be used in various fields of application.
6.3 Calculation algorithm
The input signal is filtered by an array of 28 one-third-octave-band filters according to IEC 61260-
1:2014, class 1, with centre frequencies f from 25 Hz to 12 500 Hz, designed as 6th order Chebyshev
T
filters using three 2nd order sections. The filter coefficients are given in Table A.1 and Table A.2
...
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