ISO 532-2:2017

Acoustics - Methods for calculating loudness - Part 2: Moore-Glasberg method

ISO 532-2:2017 specifies a method for estimating the loudness and loudness level of stationary sounds as perceived by otologically normal adult persons under specific listening conditions. It provides an algorithm for the calculation of monaural or binaural loudness for sounds recorded using a single microphone, using a head and torso simulator, or for sounds presented via earphones. The method is based on the Moore-Glasberg algorithm. NOTE 1 Issues of binaural calculations are discussed in Annex A. NOTE 2 Users who wish to study the details of the calculation method can review or implement the source code, which is entirely informative and provided with ISO 532-2:2017 for the convenience of the user. This method can be applied to tones, broadband noises and complex sounds with sharp line spectral components, for example transformer hum or fan noise. NOTE 3 It has been shown (see Reference [15]) 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. The evaluation of the harmful effect of sound events is outside the scope of ISO 532-2:2017.

Acoustique — Méthode de calcul d'isosonie — Partie 2: Méthode Moore-Glasberg

General Information

• Status: Published
• Publication Date: 25-Jun-2017
• ICS: 17.140.01 - Acoustic measurements and noise abatement in general
• Technical Committee: ISO/TC 43 - Acoustics
• Drafting Committee: ISO/TC 43/WG 9 - Method for calculating loudness level
• Parallel Committee: ISO/TC 127/SC 2 - Safety, ergonomics and general requirements
• Current Stage: 9092 - International Standard to be revised
• Start Date: 01-Nov-2024
• Completion Date: 13-Dec-2025

Relations

• Revised: ISO 532:1975 - Acoustics - Method for calculating loudness level
• Effective Date: 17-Nov-2012

Overview

ISO 532-2:2017 - "Acoustics - Methods for calculating loudness - Part 2: Moore‑Glasberg method" specifies a standardized algorithm for estimating the loudness and loudness level of stationary sounds as perceived by otologically normal adults. Based on the Moore–Glasberg model, the method supports monaural and binaural calculations for signals captured with a single microphone, a head-and-torso simulator, or presented via earphones. The standard applies to tones, broadband noises and complex sounds with sharp spectral lines (e.g., transformer hum, fan noise). Informative source code is provided with the publication. Evaluation of harmful effects of sound events is outside its scope.

Keywords: ISO 532-2, Moore‑Glasberg, loudness calculation, acoustics standard, loudness level, binaural loudness, stationary sounds.

Key topics and technical requirements

• Signal specification: Defines allowed input types (complex tones, band-limited noise, mixtures, 1/3‑octave band representations) and measurement conditions.
• Instrumentation: Requirements and guidance for microphones, head-and-torso simulators and earphone presentations.
• Ear transfer and preprocessing: Procedures to determine the sound spectrum at the tympanic membrane and oval window for different capture methods.
• Spectral to perceptual transformation: Converts input spectrum to a series of sinusoidal components, then through four physiologically based transformations to produce an excitation pattern and specific loudness.
• Loudness computation: Rules for calculating monaural and binaural loudness and deriving loudness level.
• Uncertainty and reporting: Guidance on uncertainty of calculated loudness for stationary sounds and recommended data reporting.
• Annexes: Informative material on binaural calculations (Annex A), test results (Annex B), and downloadable software (Annex C).
• Normative references: Links to related electroacoustic standards (e.g., IEC 61260‑1, IEC 61672‑1, IEC/TS 60318‑7).

Applications

ISO 532-2:2017 is practical for:

• Acoustic consultants performing perceptual noise assessments and product noise characterization.
• Product designers and manufacturers evaluating perceived loudness of equipment (motors, HVAC, transformers).
• Audio engineers and researchers conducting loudness modelling and psychoacoustic studies.
• Hearing scientists and audiologists modelling perceived sound strength under controlled conditions.
• Test laboratories implementing reproducible loudness calculations for compliance and R&D.

This method is particularly useful when human listener tests are impractical or when a reproducible metric of perceived loudness is required.

Who should use this standard

• Acoustic engineers, test labs and manufacturers
• Product noise consultants and environmental acousticians
• Hearing science researchers and audiologists
• Standards developers and regulatory bodies

Related standards

• ISO 532-1 (Zwicker method)
• ISO 226:2003 (equal loudness contours)
• ISO 389‑7:2005 (reference threshold of hearing)
• IEC 61260‑1, IEC 61672‑1, IEC/TS 60318‑7

For implementation, users can review the informative source code supplied with ISO 532-2:2017 to reproduce the Moore‑Glasberg loudness algorithm.

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 532-2
First edition
2017-06
Acoustics — Methods for calculating
loudness —
Part 2:
Moore-Glasberg method
Acoustique — Méthode de calcul d’isosonie —
Partie 2: Méthode Moore-Glasberg
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2017 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 General . 5
5 Specifications of signals . 5
5.1 General . 5
5.2 Complex tone . 5
5.3 Noise consisting of bands of pink or white noise of defined width . 5
5.4 Mixture of discrete sinusoidal components and bands of pink or white noise . 6
5.5 Sound specified in terms of the sound pressure levels in 29 adjacent one-third-
octave bands . 6
6 Instrumentation . 6
7 Description of the method . 7
7.1 Introduction . 7
7.2 Determination of sound spectrum at the tympanic membrane . 7
7.2.1 General. 7
7.2.2 Free field and diffuse field transfer functions for sound picked up by a
single microphone . 8
7.2.3 Earphones . 8
7.2.4 Signal recorded at eardrum . 8
7.2.5 Head and torso simulator . 8
7.2.6 Interpolation and extrapolation . 8
7.3 Determination of sound spectrum at the oval window . 9
7.4 Transformation of sound spectrum into excitation pattern .10
7.5 Transformation of excitation pattern into specific loudness .13
7.5.1 Introduction .13
7.5.2 Reference excitation at the reference threshold of hearing . .14
7.5.3 Gain of the cochlear amplifier for inputs with low sound pressure levels .14
7.5.4 Calculation of specific loudness from excitation when E /E ≤ E/E .
THRQ 0 0 15
7.5.5 Calculation of specific loudness from excitation when E /E > E/E .
THRQ 0 0 15
10 15
7.5.6 Calculation of specific loudness from excitation when E > 10 .
8 Calculation of loudness and loudness level .16
8.1 Calculation of monaural and binaural loudness (diotic and dichotic stimuli) .16
8.2 Relationship between loudness level and loudness .17
8.3 Calculation of the reference threshold of hearing .18
9 Uncertainty of calculated loudness for stationary sounds .18
10 Data reporting .19
Annex A (informative) Comments regarding binaural loudness.20
Annex B (informative) Results for specific test signals .21
Annex C (informative) Software for the calculation of loudness .26
Bibliography .27
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
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
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
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO’s adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following
URL: w w w . i s o .org/ iso/ foreword .html
This document was prepared by Technical Committee ISO/TC 43, Acoustics.
A list of all parts in the ISO 532- series, published under the general title Acoustics — Methods for
calculating loudness, can be found on the ISO website.
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 seeks 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.
This document is limited to calculation of loudness and loudness level of stationary sounds and the
calculations are based on the spectral properties of a sound. This calculation method is based on Moore-
[14-17]
Glasberg loudness calculation algorithms . It starts by converting a specified signal spectrum
into a series of sinusoidal components representing that spectrum. This series is then transformed
into a specific loudness pattern by applying four consecutive transformations, each of which is directly
related to physiological and psychological characteristics of the human hearing system. Loudness is
calculated from the specific loudness pattern.
This document describes the calculation procedures leading to estimation of loudness and loudness
level and provides an executable computer program and code. The software provided with this
document is entirely informative and provided for the convenience of the user. Use of the provided
software is not required for conformance with this document.
The Moore-Glasberg method is limited to stationary sounds and can be applied to tones, broadband
noises and complex sounds with sharp line spectral components. The method in this document
[18]
differs from those in ISO 532:1975. Method A of ISO 532:1975 (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 this document 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.
The Zwicker method in ISO 532-1 can be applied for stationary and arbitrary non-stationary sounds.
The method for stationary sounds in ISO 532-1 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 ISO 532-1 is in accordance with ISO 226:1987 instead of
the later revised version, ISO 226:2003.
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 532-2:2017(E)
Acoustics — Methods for calculating loudness —
Part 2:
Moore-Glasberg method
1 Scope
This document specifies a method for estimating the loudness and loudness level of stationary sounds
as perceived by otologically normal adult persons under specific listening conditions. It provides an
algorithm for the calculation of monaural or binaural loudness for sounds recorded using a single
microphone, using a head and torso simulator, or for sounds presented via earphones. The method is
based on the Moore-Glasberg algorithm.
NOTE 1 Issues of binaural calculations are discussed in Annex A.
NOTE 2 Users who wish to study the details of the calculation method can review or implement the source
code, which is entirely informative and provided with this document for the convenience of the user.
This method can be applied to tones, broadband noises and complex sounds with sharp line spectral
components, for example transformer hum or fan noise.
NOTE 3 It has been shown (see Reference [15]) 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.
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
IEC/TS 60318-7, Electroacoustics — Simulators of human head and ear — Part 7: Head and torso simulator
for the measurement of hearing aids
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
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 , in gases 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 (3.2) 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 (3.17) calculation using the current procedure.
Note 2 to entry: This definition is technically in accordance with ISO 80000-8:2007, 8.
3.2
frequency band
continuous set of frequencies lying between 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]
3.3
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
3.4
cut-off frequency
lowest ( f ) or highest ( f ) frequency beyond which the response of the filter (3.3) to a sinusoidal signal
l h
does not exceed −3 dB relative to the maximum response measured between ( f ) and ( f )
l h
3.5
one-third-octave band
frequency band (3.2) 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.
3.6
band-reject filter
filter (3.3) that rejects signal energy within a certain frequency band (3.2) 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.
3.7
band level
L
pb
sound pressure level (3.1) of sound contained within a restricted frequency band (b)
2 © ISO 2017 – All rights reserved

3.8
one-third-octave-band level
L
T
sound pressure level (3.1) of sound contained within a frequency band (3.2) with the width of one-third
of an octave
3.9
sound spectrum
representation of the magnitudes (and sometimes of the phases) of the components of a complex sound
as a function of frequency
3.10
spectrum density level
spectrum level
level of the limit, as the width of the frequency band (3.2) approaches zero, of the quotient of a specified
quantity distributed within a frequency band, by the width of the band, expressed in decibels
Note 1 to entry: The words “spectrum level” should be preceded by a descriptive modifier describing the
measured quantity.
Note 2 to entry: For illustration, the sound pressure spectrum level L at the midband frequency is obtained
ps
practically by
 
Lp=Δ10lg //fp /Δ f dB
pbs ()b0()0
 
 
where p is the time-mean-square sound pressure measured through a filter (3.3) system, p the reference
b 0
sound pressure, Δf the bandwidth of the filter system, and Δ f the reference bandwidth of 1 Hz. For computational
purposes, with L for the band sound pressure level (3.1) observed through the filter, the above relation becomes
pb
LL=− 10lgΔΔff/ dB
ppbs b  0 
3.11
auditory filter
filter (3.3) within the human cochlea describing the frequency resolution of the auditory system, with
characteristics that are usually estimated from the results of masking experiments
3.12
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]
3.13
equivalent rectangular bandwidth of the auditory filter for otologically normal persons
ERB
n
auditory filter (3.11) bandwidth determined by measuring tone detection thresholds in wideband noise
passed through band-reject (notch) filters of various bandwidths
Note 1 to entry: The subscript n indicates that the value applies for persons with otologically normal hearing.
Note 2 to entry: The multi-letter abbreviated term presented in italics and with a subscript is used here instead
of a symbol to maintain an established notation and to avoid confusion.
Note 3 to entry: Bandwidth is measured in Hertz (Hz).
3.14
equivalent rectangular bandwidth number scale
ERB -number scale
n
transformation of the frequency scale constructed so that an increase in frequency equal to one ERB
n
leads to an increase of one unit on the ERB -number scale
n
Note 1 to entry: ERB is measured in Hertz (Hz).
n
Note 2 to entry: The unit of the ERB -number scale is the Cam. For example, the value of ERB for a centre
n n
frequency of 1 000 Hz is approximately 132 Hz, so an increase in frequency from 934 Hz to 1 066 Hz corresponds
to a step of one Cam. The equation relating ERB -number to frequency is given in 7.4.
n
3.15
loudness level
sound pressure level (3.1) of a frontally incident, sinusoidal plane progressive wave, presented binaurally
at a frequency of 1 000 Hz that is judged by otologically normal persons as being as loud as the given sound
Note 1 to entry: Loudness level is expressed in phons.
3.16
calculated loudness level
L
N
loudness level (3.15) calculated following the procedure of a predictive model
3.17
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
Note 1 to entry: Loudness is expressed in sones.
Note 2 to entry: Loudness depends primarily upon the sound pressure level (3.1) 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 (3.15) 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.
3.18
calculated loudness
N
loudness (3.17) calculated following the procedure of a predictive model
3.19
excitation
E
output of an auditory filter (3.11) centred at a given frequency, specified in units that are linearly related
to power
Note 1 to entry: An excitation of 1 unit is produced at the output of an auditory filter centred at 1 000 Hz by a
tone with a frequency of 1 000 Hz with a sound pressure level (3.1) of 0 dB presented in a free field with frontal
incidence.
3.20
excitation level
L
E
ten times the logarithm to the base 10 of the ratio of the excitation (3.19) at the output of an auditory
filter (3.11) centred at the frequency of interest to the reference excitation E
E
L =10lg dB
E
E
4 © ISO 2017 – All rights reserved

where the reference excitation, E , is the excitation produced by a 1 000 Hz tone with a sound pressure
level (3.1) of 0 dB presented in a free field with frontal incidence
3.21
specific loudness
N ‘
calculated loudness (3.18) evoked over a frequency band (3.2) with a bandwidth of one ERB (3.13)
n
centred on the frequency of interest
Note 1 to entry: Specific loudness is expressed in sones/Cam.
Note 2 to entry: The definition together with the stated unit are different from those in ISO 532-1.
4 General
The method described in the main part of this document specifies a method for calculating loudness
and loudness level based on the Moore-Glasberg procedure.
The procedure involves a sequence of stages. Each stage is described below. However, it is envisaged
that those wishing to calculate loudness using this procedure will use the computer program (see
Annex C) provided with this document that implements the described procedure. It is not expected
that the procedure will be implemented by hand. Such computations would be very time consuming.
The source code provided in Annex C gives an example of the implementation of the method. Other
implementations using different software are possible.
NOTE 1 The computational procedure described in this document is an updated version of procedures
[14-17]
published earlier elsewhere .
NOTE 2 Uncertainties are addressed in Clause 9.
5 Specifications of signals
5.1 General
The spectrum of the signal whose loudness is to be determined shall be specified at each ear. The
spectrum can be specified exactly using the methods described in 5.2, 5.3 and 5.4 for the case of a
complex tone, noise consisting of bands of pink or white noise of defined width, or sounds having a
mixture of discrete sinusoidal components or bands of pink or white noise. The sound spectrum can
be specified approximately using one-third-octave-band levels specified in the method described
in 5.5. For this, one-third-octave bands according to IEC 61260-1:2014 should be used. The methods
described in 5.2 to 5.4 may be of interest for synthetic signals or signals analysed by discrete Fourier
transform techniques. The method described in 5.5 will be usually used for practical signals. If the
spectrum is specified exactly, the predicted loudness will be more accurate than when the spectrum is
approximated using one-third-octave-band levels.
5.2 Complex tone
This is a sound with a spectrum that consists of discrete sinusoidal components. The spectrum can be
specified in terms of frequency components that are either harmonically or non-harmonically spaced.
The frequency and sound pressure level of each component shall be specified.
5.3 Noise consisting of bands of pink or white noise of defined width
The number of noise bands and their widths shall be specified. Each band can be composed of either
filtered white noise (with a constant spectrum level within the passband) or filtered pink noise (with
a spectrum level within the passband that decreases with increasing centre frequency at a rate of
3 dB/octave). For each band, the following shall be specified: the lower cut-off frequency, the upper
cut-off frequency and the spectrum level. In the case of pink noise, the frequency at which the spectrum
level is determined shall also be specified. Within the procedure, the spectra of bands of noise are
approximated by a series of discrete sinusoidal components. When the bandwidth of the noise exceeds
30 Hz, the components are spaced at 10 Hz intervals, and the level of each component is set 10 dB higher
than the spectrum level at the corresponding frequency. When the bandwidth of the noise is less than
30 Hz, the components are spaced at 1 Hz intervals, and the level of each component is set equal to the
spectrum level at the corresponding frequency.
EXAMPLE 1 A band of white noise extending from 200 Hz to 500 Hz with a spectrum level of 50 dB would be
approximated by sinusoidal components with frequencies 205 Hz, 215 Hz, 225 Hz, 235 Hz …. 475 Hz, 485 Hz,
495 Hz, each component having a sound pressure level of 60 dB.
EXAMPLE 2 A band of pink noise having lower and upper cut-off frequencies of 100 Hz and 115 Hz, respectively,
with a spectrum level of 65 dB would be approximated by sinusoidal components with frequencies 101 Hz,
102 Hz, 103 Hz, 104 Hz …. 113 Hz, 114 Hz, 115 Hz, with the components having sound pressure levels increasing
progressively from 64,7 dB at 101 Hz to 65,3 dB at 115 Hz.
NOTE The spacing of the components (10 Hz as in Example 1 or 1 Hz as in Example 2) is not a property of
the input signal. The 1 Hz spacing is used to ensure sufficient accuracy in the computation of loudness when the
bandwidth of the spectrum of the signal is narrow, i.e. less than 30 Hz. For signals with wider bandwidth, i.e.
30 Hz or greater, then a 10 Hz spacing will result in sufficient accuracy for the purpose of the computation of
loudness.
5.4 Mixture of discrete sinusoidal components and bands of pink or white noise
For the case of mixtures of sounds, which each have a spectrum consisting of discrete sinusoidal
components, 5.2 is applied for each discrete sinusoidal component that the mixed sound comprises. For
the case of a mixture of bands of pink or white noise, the spectrum of each component of the mixture
can be specified exactly using 5.3. This method is mainly applicable to synthetic signals, although it
could be applicable to signals with strong line components in a noise background.
5.5 Sound specified in terms of the sound pressure levels in 29 adjacent one-third-
octave bands
The nominal centre frequencies of the 29 adjacent one-third-octave bands are as defined by IEC 61260-
1:2014 within the range 25 Hz to 16 000 Hz. Within each band, the spectrum is assumed to be flat, and,
as described for noise bands in 5.3, the spectrum is approximated as a series of sinusoidal components
spaced at 10 Hz intervals or (for centre frequencies of 125 Hz and below) at 1 Hz intervals. The level
of each component is calculated as follows. Let the width of a one-third-octave band at a given centre
frequency be W (e.g. 230 Hz for a centre frequency of 1 000 Hz). The sound pressure level in that band,
L , is converted to the spectrum level in that band as L − 10lg(W/1 Hz) dB. The level of each component
T T
in the approximation is then set 10 dB above the spectrum level, i.e. to L − 10lg(W/1 Hz) dB + 10 dB.
T
NOTE The 1/3 octave filters, as defined by IEC 61260–1:2014, to analyse the spectrum of the input signal
can have errors in their outputs of up to ± 0,7 dB. In a worst-case scenario, if all filter outputs were 0,7 dB higher
than the correct values, this would lead to an error in the estimated loudness (in sones) of approximately +4 %
for a typical broadband sound. If all filter outputs were 0,7 dB lower than the correct values, this would lead to an
error in the estimated loudness of approximately −4 % for a typical broadband sound.
EXAMPLE Consider the one-third-octave band centred at 1 000 Hz, and assume that the band sound pressure
level is 63 dB. The spectrum level is then 63 dB – 10lg(230) dB = 39,4 dB. The spectrum of that one-third-octave
band would thus be approximated by components at 890 Hz, 900 Hz, 910 Hz, 920 Hz …. 1 080 Hz, 1 090 Hz,
1 100 Hz, 1 110 Hz, each with a sound pressure level of 49,4 dB.
6 Instrumentation
For the input signals used in 5.2 to 5.4 instrumentation is not necessarily required as these levels can
be specified without the use of measurement instrumentation. If the input signals from these three
methods are acquired with instrumentation, or if one-third-octave-band sound pressure levels as
described in 5.5 are determined in a sound field, this shall be done through the use of a sound acquisition
system that conforms to IEC 61672-1, in conjunction with one-third-octave filters that conform to
6 © ISO 2017 – All rights reserved

IEC 61260-1:2014. Equipment used to present the one-third-octave spectrum in real time shall meet
the requirements of IEC 61672-1:2013, class 1, or IEC 61260-1:2014, class 1. The microphone(s) shall
have an omnidirectional characteristic or a free-field characteristic, corresponding to the method
being used in 7.2.2. If a head and torso simulator is used it shall conform to IEC/TS 60318-7. For signals
acquired using a head and torso simulator, the transfer function of the simulator shall be allowed for, as
described in 7.2.5. It should be noted that the following procedure described in this document applies to
the sound that has been already acquired.
7 Description of the method
7.1 Introduction
The method of calculating loudness consists of the following discrete steps:
(a) transformation of the recorded sound spectrum into the sound spectrum at the tympanic
membrane for each ear;
(b) transformation of the sound spectrum at the tympanic membrane into the sound spectrum at the
oval window;
(c) transformation of the sound spectrum at the oval window into an excitation pattern on the basilar
membrane;
(d) transformation of the excitation pattern into a specific loudness pattern;
(e) calculation of monaural and binaural loudness using the concept of binaural inhibition.
These steps are illustrated in the flow chart in Figure 1 and are described sequentially in 7.2 to 7.5.
Figure 1 — Flow chart illustrating the sequence of the method
7.2 Determination of sound spectrum at the tympanic membrane
7.2.1 General
The spectrum specified in Clause 5 is transformed to the spectrum of sound reaching the tympanic
membrane. This is done by applying one of the transfer functions specified in 7.2.2 to 7.2.5. Several
different listening situations are possible and the transfer function chosen depends on the situation.
The methods listed are not mutually exclusive.
7.2.2 Free field and diffuse field transfer functions for sound picked up by a single microphone
These transfer functions are applicable when the sound is picked up via a microphone placed at the
centre of the position where the listener’s head would be. The acoustical effects of the head/torso
and outer ear on transmission of sound to the tympanic membrane are represented by two standard
transfer functions. The first, applicable to free field listening with frontal incidence of the sound source,
is specified in column 2 of Table 1. The second, applicable to listening in a diffuse field, is specified in
[19-21]
column 3 of Table 1. The transfer functions represent the mean for adult humans .
The diffuse field transfer function can also be used for sounds presented via earphones that are
designed to have a diffuse field response (see 7.2.3).
The transfer functions given in Table 1 are based on data known to provide good predictions of the equal
loudness contours given in ISO 226:2003 and the absolute threshold values given in ISO 389-7:2005. It
is acknowledged that these transfer functions do not comply with those specified in ISO 11904-1:2002.
7.2.3 Earphones
It is possible to calculate loudness for sounds transmitted via earphones. Note that the sensitivity
level of the earphones (the sound pressure level produced for a given applied voltage) shall be taken
into account when determining the spectra at the tympanic membrane. The transfer function of the
earphones to the tympanic membrane shall be specified. This is done by specifying the deviations
from a flat response at several frequencies. A file containing these deviations is called an “earphone
correction file”. The transfer function of the earphone can be measured using a microphone close to the
tympanic membrane or using the method described in ISO 11904-1:2002.
7.2.4 Signal recorded at eardrum
Spectra at the tympanic membrane can be recorded using a probe microphone in the ear canal. For
sounds with no strong components above 3 000 Hz, a microphone should be within 10 mm of the
tympanic membrane (eardrum). For sounds with strong components above 3 000 Hz, the microphone
should be within 5 mm of the eardrum. In this case, no transfer function is needed. This case is treated
as being equivalent to presentation of the sound via earphones with a flat response at the tympanic
membrane.
7.2.5 Head and torso simulator
Sounds may be recorded using the microphones of a head and torso simulator. If the head and torso
simulator represents an accurate acoustical model of an average adult listener, no transfer function
needs to be specified. Otherwise, this is treated as a special case of earphone presentation, and the
transfer function from the sound field to the microphones of the head and torso simulator shall be
specified in a correction file.
7.2.6 Interpolation and extrapolation
The transfer functions described in 7.2 are specified at discrete frequencies. Linear interpolation on
a decibel versus linear frequency scale is used to determine values at intermediate frequencies. In the
case of earphone correction files, if the lowest frequency specified ( f ) is above 20 Hz then the value of
l
the transfer function for frequencies between 20 Hz and f is set to the value specified at f . If the highest
l l
frequency specified ( f ) is below 18 000 Hz then the value of the transfer function for frequencies
h
between f and 18 000 Hz is set to the value specified at f .
h h
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7.3 Determination of sound spectrum at the oval window
The transmission of sound through the middle ear from the tympanic membrane to the oval window
(the cochlea) is taken into account by a middle ear transfer function specified in column 4 of Table 1.
The shape of the function represents the difference between the sound pressure level in the cochlea
and the sound pressure level at the tympanic membrane. The whole function is scaled so that an input
signal consisting of a 1 000 Hz sinusoid presented in a free field with frontal incidence at a sound
pressure level of 0 dB leads to a sound pressure level at the cochlea of 0 dB. The interpolation procedure
described in 7.2.6 is used to determine values at intermediate frequencies. The values for frequencies
above 12 500 Hz are based on extrapolation and have not been validated, so they are shown in italics
in Table 1. They are included for the user who wishes to predict the loudness of sounds with frequency
components above 12 500 Hz. The end result of this stage is a specification of the spectrum of the
pressure variation applied to the cochlea.
NOTE The transfer function used corresponds to that in Reference [14]; it differs slightly from that in
Reference [17]. The differences are especially noteworthy in the frequency region from 1 250 Hz to 1 600 Hz and
in the region from 4 000 Hz to 6 300 Hz. The transfer function used here provides more accurate predictions of
the reference thresholds of hearing in ISO 389-7:2005 and of the equal-loudness contours in ISO 226:2003.
Table 1 — Transfer functions
Frequency Difference between the Difference between the Scaled transfer function
sound pressure level at sound pressure level at value for the middle ear
the tympanic membrane the tympanic membrane
and the sound pressure and the sound pressure
level measured in the level measured in the
free field for frontal inci- diffuse field (in the ab-
dence (in the absence of sence of a listener)
a listener)
in Hz in dB in dB in dB
20 0,0 0,0 −39,6
25 0,0 0,0 −32,0
31,5 0,0 0,0 −25,85
40 0,0 0,0 −21,4
50 0,0 0,0 −18,5
63 0,0 0,0 −15,9
80 0,0 0,0 −14,1
100 0,0 0,0 −12,4
125 0,1 0,1 −11,0
160 0,3 0,3 −9,6
200 0,5 0,4 −8,3
250 0,9 0,5 −7,4
315 1,4 1,0 −6,2
400 1,6 1,6 −4,8
500 1,7 1,7 −3,8
630 2,5 2,2 −3,3
750 2,7 2,7 −2,9
800 2,6 2,9 −2,6
1 000 2,6 3,8 −2,6
1 250 3,2 5,3 −4,5
1 500 5,2 6,8 −5,4
1 600 6,6 7,2 −6,1
2 000 12,0 10,2 −8,5
Table 1 (continued)
Frequency Difference between the Difference between the Scaled transfer function
sound pressure level at sound pressure level at value for the middle ear
the tympanic membrane the tympanic membrane
and the sound pressure and the sound pressure
level measured in the level measured in the
free field for frontal inci- diffuse field (in the ab-
dence (in the absence of sence of a listener)
a listener)
in Hz in dB in dB in dB
2 500 16,8 14,9 −10,4
3 000 15,3 14,5 −7,3
3 150 15,2 14,4 −7,0
4 000 14,2 12,7 −6,6
5 000 10,7 10,8 −7,0
6 000 7,1 8,9 −9,2
6 300 6,4 8,7 −10,2
8 000 1,8 8,5 −12,2
9 000 −0,9 6,2 −10,8
10 000 −1,6 5,0 −10,1
11 200 1,9 4,5 −12,7
12 500 4,9 4,0 −15,0
a
14 000 2,0 3,3 −18,2
a
15 000 −2,0 2,6 −23,8
a
16 000 2,5 2,0 −32,3
a
20 000 2,5 2,0 −45,5
a
Values are in a range that has not been validated.
7.4 Transformation of sound spectrum into excitation pattern
To obtain a representation of the distribution of excitation produced by the sound within the cochlea,
the sound spectrum at the oval window (the cochlea) is transformed into an excitation pattern along
the basilar membrane. The procedure used here is essentially the same as described by Reference [14].
Reference [14], pages 135 to 138, gives FORTRAN code implementing the procedure. The only change
is that the constant D in Formula (5) of this document has the value 0,35, whereas in the FORTRAN
code a value of 0,38 was used. The cochlea is modelled as an array of band pass auditory filters with
overlapping pass bands. The bandwidths and shapes of the filters depend on both the input sound
pressure level and the centre frequency, f , of the filter. The excitation pattern of a given sound is defined
c
as the output of the auditory filters represented as a function of f . The output can be specified either as
c
excitation ratio, E/E , or as excitation level, L .
0 E
The equivalent rectangular bandwidth, ERB in Hz, of the auditory filter for otologically normal persons
n
and for an input sound pressure level to the cochlea of 51 dB, is specified as a function of the centre
frequency of the band pass auditory filter, f , by Formula (1):
c
ERB = 24,673 (0,004368 f + 1 Hz) (1)
n c
The characteristics of the auditory filter for other input levels are derived as described below.
For a given auditory filter (with a specific f ), the excitation is calculated by summing the power of the
c
output in response to all of the different frequency components in the input. A first stage in this process
is to sum the powers of the components of the input spectrum within each band which has a width
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as defined by Formula (1). The resulting power, converted to decibels (using the reference excitation
defined in 3.20), is denoted X. It is assumed that the sharpness of the auditory filter depends on X.
The value of X is calculated using a rounded-exponential weighting function (called hereafter a filter)
rather than a rectangular weighting function. The rounded-exponential filter is defined by
W(g, f ) = (1 + pg)exp(-pg) (2)
c
where the value of g at frequency f is
g = ∣( f − f )∣ / f (3)
c c
and p is a dimensionless parameter determining the bandwidth and slope of the filter. For calculating
X, the value of p in Formula (2) is set to 4f /ERB . The output power of the rounded-exponential filter is
c n
calculated over the following ranges:
For f < f g = 0 to 1
c     (4)
For f > f g = 0 to 4
c
The calculation of X is performed with the filter centred in turn on every component in the input
spectrum, as specified in Clause 5.
To calculate the output of a give
...