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IS0
INTERN AT1 O NA L ORGAN IZ AT1 ON FOR STANDARDIZATION
IS0 RECOMMENDATION
R 532
METHOD FOR CALCULATING LOUDNESS LEVEL
1st EDITION
December 1966
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The copyright of IS0 Recommendations and IS0 Standards
belongs to IS0 Member Bodies. Reproduction of these
documents, in any country, may be authorized therefore only
by the national standards organization of that country, being
a member of ISO.
For each individual country the only valid standard is the national standard of that country.
Printed in Switzerland
Also issued in French and Russian. Copies to be obtained through the national standards organizations.
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BRIEF HISTORY
The IS0 Recommendation R 532, Method for Calculating Loudness Level, was drawn
up by Technical Committee ISO/TC 43, Acoustics, the Secretariat of which is held by the British
Standards Institution (BSI).
Work on this question by the Technical Committee began in 1958 and led, in 1963, to
the adoption of a Draft IS0 Recommendation.
In December 1963, this Draft IS0 Recommendation (No. 675) was circulated to all the
IS0 Member Bodies for enquiry. It was approved, subject to a few modifications of an edito-
rial nature, by the following Member Bodies:
Netherlands
Australia Denmark
Austria Finland New Zealand
Belgium Germany Sweden
Brazil Greece Switzerland
Canada Hungary United Kingdom
Chile India U.S.A.
Colombia Italy U.S.S.R.
Czechoslovakia Korea, Rep. of Yugoslavia
One Member Body opposed the approval of the Draft: France.
The Draft IS0 Recommendation was then submitted by correspondence to the IS0 Coun-
cil, which decided, in December 1966, to accept it as an IS0 RECOMMENDATION.
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ISO/R 532 .I 1966 (E)
IS0 Recommendation R 532 December
METHOD FOR CALCULATING LOUDNESS LEVEL
INTRODUCTION
It is often desirable to seek a single number that corresponds to the loudness or to the IOU
level of a given sound. Such a number can be calculated if there is available a spectrum an
It has to be understood that the calci
of the sound obtained by physical measurement.
number is a statistic, i.e. it conveys less information than the spectrum measurements from '
it is derived.
Such analysis is often accomplished in terms of either octave bands or one-third octave t:
Sounds in which the spectra do not have discontinuities as a function of frequency, c,
represented adequately in terms of octave bands, but sounds which contain such discontir
may require one-third octave-band analysis if they are to be described adequately.
This IS0 Recommendation specifies two methods for calculating the loudness or loudness
of a complex sound, which differ not only in the method of analysis of the sound, but a
the principles of computation. The first, Method A, utilizes physical measurements ob1
from spectrum analysis in terms of octave bands. The second, Method B, utilizes spei
analysis in terms of one-third octave bands.
In addition to the different band widths involved in the basic physical measurements, th'
methods differ in other respects, and the results obtained do not always agree. Meth
generally gives slightly higher results than those obtained for the same sounds by Methc
the difference being possibly as much as 5 phons; but it would seem to take better into ac,
those variations in sound spectra that occur within narrow ranges of frequency.
The quantities calculated by either method should be designated with specific reference tl
or other method using the system of symbols and abbreviations given in Table 1.
TABLE 1. - Designations for calculaüng loudnesses and loudness levels
Quantity measured
Band width Sound
Method
of analysis field
Loudness I Loudness level
~~ ~~
A octave diffuse
sones (OD) 1 phons (OD) 1
diffuse
B
1 free
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ISO/R 532 - lgs6 (E)
PART I
METHOD A FOR CALCULATING THE LOUDNESS OF A COMPLEX
SOUND THAT HAS BEEN ANALYSED IN TERMS OF OCTAVE BANDS
1. GENERAL
This Part of this IS0 Recommendation specifies a procedure, Method A, for calculating
the loudness of steady complex sounds for which octave-band analyses are appropriate. (Octave-
band analyses may, of course, be reconstructed from more detailed analyses). The level in
each octave band is converted into a loudness index, and the total loudness in sones (OD) is
then calculated by means of an empirical formula. The total loudness thus calculated may
then be converted into a calculated loudness level in phons (OD) by means of the relation
specified in IS0 Recommendation R 131, Expression of the Physical and Subjective Magnitudes
of Sound or Noise.
Method A also yields a graph that provides a valuable guide for the further study of the sound,
particularly if the loudness index is plotted as the ordinate (see Note to clause 4.3).
Method A also contains extensions for analyses made in terms of bands of one-third octave and
one-half octave. For calculating the loudness of noises that require one-third octave-band
analysis, however, Method B is recommended.
This Method A has the advantage of simplicity and is specified for sounds for which octave-
band analyses are appropriate. Many noises of practical interest fall in this class.
Since the purpose of this Part is to provide a simple and convenient method by which com-
plex sounds of diverse levels and spectra may be ordered on a scale of subjective magnitude,
certain simplifying assumptions and linear approximations have been made. The procedure
is derived from three relations:
A loudness function relating loudness in sones to loudness level in phons, which is identical
(1)
to that in IS0 Recommendation R 131.
An empirical set of equal-loudness contours for bands of noise in a diffuse sound field.
(2)
A rule relating the total loudness of a sound to the loudness indices of the frequency bands
(3)
composing it.
On the basis of these empirical relations, the total loudness of a sound may be calculated with
the aid of a table or a chart, together with a linear equation. Subject to certain restrictions
specified below, the recommended method may be expected to assess loudness or loudness level
with an accuracy that is sufficient for engineering purposes.
2. SCOPE
Part of this IS0 Recommendation specifies a method for calculating the loudness experienced
by a typical (median) listener under the following conditions:
2.1 Diffuse sound field. The sound is assumed to reach the listener’s ears from all directions
at the same intensity. This condition is approximated in an ordinary room.
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ISO/R 532 - 1966 (E)
2.2 Kind .of spectrum. The method is designed specifically for the types of broad band
spectra most commonly encountered. Errors may arise if it is applied to certain types of
line spectra, or to spectra having two or more sharp maxima that are separated by
more than an octave. The magnitude of the error that may result from an unusual
spectrum can only be determined experimentally.
2.3 Steady state. The method is designed for noises that are steady rather than intermittent.
Nevertheless, in a diffuse field, many noises of impulsive origin behave effectively as
steady noises, because reverberation serves to diminish temporal discontinuities.
NOTES
1. The error that may result with intermittent noises is not necessarily attributable to
the calculation procedure. It may also be affected by the averaging characteristics of
the meter used to determine the sound pressure levels.
2.
Since the loudness of a sound depends upon the nature of the enclosure in which it
is heard, it is important that comparative evaluations of different noise sources should
be based on measurements made in essentially similar enclosures.
3. The band levels in the diffuse field should be measured by means of an omni-direc-
tional microphone located in the unobstructed sound field at the position of the
listener's head.
3. DEFINITIONS
For the purposes of this IS0 Recommendation the following definitions apply (the definitions
in clauses 3.1 and 3.4 are common to both methods):
3.1 Sound pressure level (L). Sound pressure level in decibels is 20 log,, (PIP,) dB, where
p is the measured sound pressure and p, is a reference sound pressure having the value
2 x 10-5 N/m2 = 2 x lO-* dyn/cm2 (cf. IS0 Recommendation R 131).
3.2 Band pressure level. Sound pressure level corresponding to the part of the spectrum
(octave) under measurement.
3.3 Loudness (S) in sones. Numerical designation of the strength of a sound which is pro-
portional to its subjective magnitude as estimated by normal observers. 1 sone is the
loudness of a sound whose loudness level is 40 phons.
3.4 Loudness-loudness level relation. Loudness level P in phons of a sound is related to the
loudness S in sones by the relation:
," = 2(P40)/10
NOTE. - When loudness levels are computed from calculated loudness values, the results
may differ from those obtained by direct subjective judgement. It is important, therefore,
to state whether the values have been calculated or have been measured by other means.
3.5 Loudness index. Number determined by the geometric mean frequency and the band
pressure level of the octave band, according to the curves of Figure A, page 7.
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ISO/R 532 - 1968 (E)
4. SPECIFICATION
Calculated loudness. The method for calculating loudness is embodied in a table and a
4.1
formula. For convenience, Table 2, page 8, is also presented graphically as a chart
(Fig. A, page 7). The table or chart provides a means for converting each band level to
a loudness index, and the formula provides a rule for combining the loudness indices to
obtain the calculated total loudness.
The procedure is as follows:
(1) Enter the geometric mean frequency of each band in the table or in the abscissa of
Figure A. Then, from the band level (the ordinate in Figure A), determine the loud-
ness index of each band.
(2) Compute the total loudness in sones (OD) S, by means of the formula:
st = s, + F(CS - S,)
where S, is the greatest of the loudness indices and ÇS is the sum of the loudness
indices of all the bands. For octave bands the value of Fis 0.3.
NOTE. - Method A has also been applied to analyses made in terms of one-half
octave and one-third octave bands, and may be so used in cases where the sound
A. In such cases the value of Fis
spectrum would fall under the restrictions of Method
as follows :
One-third-octave O. 15
One-half-octave 0.2
4.2 Calculated loudness level. The total loudness may be converted into calculated loudness
level in phons (OD) by means of the formula:
s - 2(P-40)110
t-
or P = 40 + 10 log, St
A nomogram giving this relation is included in Figure A.
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ISO/R 532 - 1966 (E)
U I .I11 1 1 I - llll
I ""I I I
100 10 O00 HZ (c/s)
1 O00
FREQUENCY
FIG. A
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ISO/R 532 - 1966 (E)
4.3 Table of loudness index. In Table 2 values of the loudness index are tabulated for the
frequency of 1000 Hz. Values at other frequencies can be obtained by means of the
following rules. The value of the loudness index is constant on the contour having a
slope of -3 dB/octave. Above 9000 Hz the contour has a slope of 12 dB/octave.
Below a certain frequency the contour has a slope of -6 dB/octave. The frequency at
which this change
...