ISO 226:2023

INTERNATIONAL ISO
STANDARD 226
Third edition
2023-03
Acoustics — Normal equal-loudness-
level contours
Acoustique — Lignes isosoniques normales
Reference number
© ISO 2023
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Formula for derivation of normal equal-loudness-level contours .2
4.1 Deriving sound pressure level from loudness level . 2
4.2 Deriving loudness levels from sound pressure levels . 3
Annex A (informative) Normal equal-loudness-level contours for pure tones under free-
field listening conditions . 5
Annex B (informative) Tables for normal equal-loudness-level contours for pure tones
under free‑field listening conditions . 6
Annex C (informative) Notes on the derivation of the normal equal-loudness-level contours .9
Bibliography .19
iii
Foreword
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This document was prepared by Technical Committee ISO/TC 43, Acoustics.
This third edition cancels and replaces the second edition (ISO 226:2003), which has been technically
revised.
The main changes are as follows:
— clarification of the scope in the introduction;
— updated bibliography;
— alignment with ISO 389-7 regarding the 0 phon data;
— correction of systematic errors that lead to minor changes in the entire data up to 0,6 dB.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
Introduction
Curves defining combinations of pure tones in terms of frequency and sound pressure level, which are
perceived as equally loud, express a fundamental property of the human auditory system and are of
basic importance in the field of psychoacoustics. Such equal-loudness-level contours were specified in
the previous editions of this document.
NOTE 1 In this document, only the equal-loudness-level contours for pure tones are specified because of
insufficient equal-loudness-level data for other sounds. Nevertheless, this International Standard could be
applicable to one-third-octave or narrower bands of noise. It may be less valid for broader bands of noises or
noises with prominent tones.
NOTE 2 For the calculation of loudness of arbitrary signals or the calculation of the tonal loudness other
standards must be applied (e.g., for loudness of arbitrary stationary and non-stationary (time-varying) sounds:
[2] [3]
ISO 532-1 , for loudness of arbitrary stationary sounds: ISO 532-2 , for tonal loudness and tonality: ECMA-418-
[4]
2 ). The tonal loudness is the loudness of the tonal components of a complex sound as the basis for the tonality
calculation in Reference [4].
During the technical revision of this document, it was decided to maintain separate documents for
the specification of the threshold and supra-threshold data. The threshold values are specified in
[1]
ISO 389 7 , as a part of the series of International Standards concerning reference zero values for
the calibration of audiometric equipment. The equal-loudness-level contours are presented in this
document.
NOTE 3 The equal-loudness-level values given by this document differ from those of the previous edition
of ISO 226, although the differences are small, i.e., up to 0,6 dB for the entire range of data. This change was
caused by the application of an improved model for the perception of loudness as described in Reference [5]. The
normal equal-loudness-level contours for pure tones in this document are essentially identical to those described
in Reference [5] since both are based on the same equal-loudness-level data. The only difference is the low equal-
loudness levels at 20 Hz caused by the revision of ISO 389-7 in 2019, which introduced a 0,4 dB change in the
normative hearing threshold at that frequency.
v
INTERNATIONAL STANDARD ISO 226:2023(E)
Acoustics — Normal equal-loudness-level contours
1 Scope
This document specifies combinations of sound pressure levels and frequencies of pure continuous
tones which are perceived as equally loud by human listeners. The specifications are based on the
following conditions:
a) the sound field in the absence of the listener consists of a free progressive plane wave;
b) the source of sound is directly in front of the listener;
c) the sound signals are pure tones;
d) the sound pressure level is measured at the position where the centre of the listener's head would
be, but in the absence of the listener;
e) listening is binaural;
f) the listeners are otologically normal persons in the age range from 18 years to 25 years inclusive.
The data are given in graphical form in Annex A and in numerical form in Annex B for the preferred
frequencies in the one-third-octave series from 20 Hz to 12 500 Hz, inclusive, in accordance with
ISO 266.
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.
ISO 266, Acoustics — Preferred frequencies
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// 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
3.2
free field
sound field where the boundaries of the room exert a negligible effect on the sound waves
3.3
loudness level
value in phons that has the same numerical value as the sound pressure level in decibels of a reference
sound, consisting of a frontally incident, free sinusoidal plane wave at a frequency of 1 000 Hz, which is
judged as loud as the given sound
3.4
equal-loudness relationship
curve or function expressing, for a pure tone of a given frequency, the relationship between its loudness
level (3.3) and its sound pressure level
3.5
equal-loudness-level contour
curve in the sound pressure level/frequency plane connecting points whose coordinates represent pure
tones judged to be equally loud
3.6
normal equal-loudness-level contour
equal-loudness-level contour (3.5) that represents the average judgment of otologically normal persons
(3.1) within the age limits from 18 years to 25 years inclusive
Note 1 to entry: The method for deriving the normal equal-loudness-level contours is described in Annex C.
3.7
threshold of hearing
level of a sound at which, under specified conditions, a person gives 50 % of correct detection responses
on repeated trials
4 Formula for derivation of normal equal-loudness-level contours
4.1 Deriving sound pressure level from loudness level
The sound pressure level L in dB of a pure tone of frequency, f, which has a loudness level, L , in phon, is
f N
given by Formula (1) [see also Formula (C.3)]:
TL+
 
αα− L T f U
 ()     
r f  N r 
α
α αα  
  f
 r   r 
p
10    
10dB
o 10phon 10dB
      
L = ··lg   10 −10 +10 dB−LL
 
f   U
 
α p
 
f  a 
 
 
 
 
 
TL+
 
L f U
   
N
 
α
00, 3  
f
03, −α  
()
10  
f 10dB
−10  phon 00,72
    
= ··lg 4101· 01− 0 +10 dB−L (1)
() 
U
 
α
f
 
 
 
 
where
T is the threshold of hearing in dB as in Reference [1];
f
T is the threshold of hearing at 1 000 Hz in dB;
r
α is the exponent for loudness perception;
f
α is the exponent for loudness perception at 1 000 Hz;
r
L is a magnitude of the linear transfer function normalized at 1 000 Hz in dB
U
p is 20 μPa.
These values are all given in Table 1 for the preferred third-octave frequencies defined in ISO 266.
Formula (1) applies, at each frequency, for values from a lower limit of 20 phon to the following upper
limits:
20 Hz to 4 000 Hz:          90 phon
5 000 Hz to 12 500 Hz:     80 phon
Formula (1) is only informative for loudness levels below 20 phon because of the lack of experimental
data between 20 phon and the hearing thresholds. The same holds for loudness levels above 90 phon
up to 100 phon from 20 Hz to 1 000 Hz because data from only one institute are available at 100 phon.
4.2 Deriving loudness levels from sound pressure levels
The loudness level L in phon of a pure tone of frequency f, which has a sound pressure level L in dB, is
N f
given by Formula (2):
LL+ TL+
   
f UUf
 
αα
   
f f
 10dB 10dB 
   
100 10 −10
0,072
 
L =⋅lg +10 phon (2)
N
 
003, −α
3 ()
f
−10
41⋅ 0
 () 
 
where T , α and L are the same as in 4.1.
f f U
The same restrictions, which apply to Formula (1), also apply to Formula (2).
Table 1 — Parameters of Formula (1) used to calculate the normal
equal-loudness-level contours
Frequency α L T
f U f
f
Hz dB dB
20 0,635 −31,5 78,1
25 0,602 −27,2 68,7
31,5 0,569 −23,1 59,5
40 0,537 −19,3 51,1
50 0,509 −16,1 44,0
63 0,482 −13,1 37,5
80 0,456 −10,4 31,5
100 0,433 −8,2 26,5
125 0,412 −6,3 22,1
160 0,391 −4,6 17,9
200 0,373 −3,2 14,4
250 0,357 −2,1 11,4
315 0,343 −1,2 8,6
400 0,330 −0,5 6,2
500 0,320 0,0 4,4
630 0,311 0,4 3,0
800 0,303 0,5 2,2
1 000 0,300 0,0 2,4
1 250 0,295 −2,7 3,5
1 600 0,292 −4,2 1,7
2 000 0,290 −1,2 −1,3
2 500 0,290 1,4 −4,2
3 150 0,289 2,3 −6,0
4 000 0,289 1,0 -5,4
5 000 0,289 −2,3 −1,5
6 300 0,293 −7,2 6,0
8 000 0,303 −11,2 12,6
10 000 0,323 −10,9 13,9
12 500 0,354 −3,5 12,3
For a graphical and numerical representation of the data for the preferred frequencies in the one-third-
octave series from 20 Hz to 12 500 Hz, inclusive, in accordance with ISO 266, information according to
Annex A and Annex B shall be used.
Annex A
(informative)
Normal equal-loudness-level contours for pure tones under free-
field listening conditions
Key
X frequency, expressed in Hz
Y sound pressure level, expressed in dB
T hearing threshold
f
NOTE 1 The hearing threshold under free-field listening condition, T , is indicated by a dashed line as defined
f
[1]
in ISO 389-7 .
NOTE 2 The contour at 10 phon is drawn by dotted lines because of the lack of experimental data between
20 phon and the hearing thresholds. Moreover, the 100-phon contour is also described by a dotted line because
data from only one institute are available at this loudness level.
Figure A.1 — Normal equal‑loudness‑level contours for pure tones
(binaural, free‑field listening, frontal incidence)
Annex B
(informative)
Tables for normal equal-loudness-level contours for pure tones
under free‑field listening conditions
Table B.1 — Sound pressure level corresponding to a given loudness level of pure tones ranging
in frequency from 20 Hz to 12 500 Hz
Loudness Sound pressure level, dB
level
Frequency, Hz
phon
20 25 31,5 40 50 63 80 100 125 160
10 (83,7) (76,1) (68,7) (61,7) (55,5) (49,5) (43,7) (38,6) (33,9) (29,2)
20 89,5 82,9 76,3 69,9 64,3 58,8 53,4 48,6 44,1 39,6
30 94,8 88,6 82,5 76,6 71,4 66,2 61,2 56,7 52,6 48,4
40 99,7 93,9 88,2 82,7 77,8 73,0 68,3 64,2 60,4 56,6
50 104,6 99,1 93,7 88,5 83,9 79,4 75,2 71,4 68,0 64,6
60 109,4 104,2 99,1 94,2 89,9 85,8 81,9 78,5 75,4 72,4
70 114,1 109,2 104,4 99,8 95,9 92,1 88,5 85,5 82,8 80,1
80 118,9 114,2 109,7 105,4 101,8 98,3 95,1 92,5 90,1 87,8
90 123,6 119,2 115,0 111,0 107,7 104,6 101,7 99,4 97,4 95,5
100 (128,3) (124,2) (120,2) (116,6) (113,6) (110,8) (108,3) (106,3) (104,7) (103,2)
Loudness Sound pressure level, dB
level
Frequency, Hz
phon
200 250 315 400 500 630 800 1 000 1 250 1 600
10 (25,1) (21,5) (18,3) (15,4) (13,2) (11,3) (10,0) 10,0 (11,2) (10,5)
20 35,6 32,1 28,9 25,9 23,6 21,6 20,1 20,0 21,4 21,5
30 44,7 41,4 38,4 35,7 33,5 31,6 30,0 30,0 31,6 32,1
40 53,3 50,3 47,6 45,1 43,1 41,4 40,0 40,0 41,8 42,6
50 61,6 58,9 56,5 54,3 52,6 51,1 49,9 50,0 52,0 52,9
60 69,7 67,4 65,4 63,5 62,1 60,8 59,8 60,0 62,1 63,2
70 77,8 75,9 74,2 72,6 71,5 70,4 69,7 70,0 72,3 73,5
80 85,9 84,3 82,9 81,8 80,9 80,1 79,6 80,0 82,5 83,8
90 94,0 92,7 91,7 90,9 90,2 89,7 89,5 90,0 92,6 94,1
100 (102,0) (101,1) (100,4) (99,9) (99,6) (99,4) (99,4) 100,0 — —
Loudness Sound pressure level, dB
level
Frequency, Hz
phon
2 000 2 500 3 150 4 000 5 000 6 300 8 000 10 000 12 500
10 (7,3) (4,5) (3,0) (3,9) (7,6) (14,4) (20,9) (23,7) (22,4)
20 18,2 15,5 14,2 15,3 18,7 25,0 31,4 34,7 33,0
30 28,7 26,1 24,9 26,1 29,5 35,5 41,6 44,7 42,4
40 39,2 36,6 35,5 36,7 40,1 45,8 51,6 54,4 51,3
50 49,6 47,0 45,9 47,2 50,5 56,1 61,6 63,9 60,0
60 60,0 57,4 56,4 57,7 61,0 66,4 71,5 73,2 68,6
70 70,4 67,8 66,8 68,1 71,4 76,6 81,4 82,6 77,1
80 80,7 78,1 77,2 78,5 81,8 86,9 91,3 91,9 85,6
90 91,1 88,5 87,5 88,8 — — — — —
100 — — — — — — — — —
NOTE  Values in brackets are for information only.
Table B.2 — Loudness levels corresponding to a given sound pressure level of pure tones
ranging in frequency from 20 Hz to 12 500 Hz
Sound Loudness level, phon
pressure level
Frequency, Hz
dB
20 25 31,5 40 50 63 80 100 125 160
0 — — — — — — — — — —
10 — — — — — — — — — —
20 — — — — — — — — — (3,5)
30 — — — — — — — (4,1) (7,0) (10,7)
40 — — — — — (3,5) (7,1) (11,2) (15,7) 20,4
50 — — — — (5,6) (10,4) (16,2) 21,7 26,8 31,9
60 — — (2,7) (8,4) (14,7) 21,6 28,4 34,3 39,4 44,2
70 — (3,5) (11,5) 20,1 28,0 35,6 42,4 48,0 52,7 56,9
80 (4,7) (15,5) 25,8 35,5 43,6 50,9 57,2 62,1 66,2 69,8
90 20,8 32,6 43,2 52,6 60,1 66,7 72,2 76,5 79,9 82,8
100 40,5 51,8 61,8 70,3 76,9 82,6 87,4 (90,9) (93,6) (95,8)
110 61,3 71,6 80,6 88,1 (93,9) (98,7) — — — —
120 82,4 (91,6) (99,5) — — — — — — —
Sound Loudness level, phon
pressure level
Frequency, Hz
dB
200 250 315 400 500 630 800 1 000 1 250 1 600
0 — — — — — — — — — —
10 — — (3,4) (5,4) (7,1) (8,8) (10,0) 10,0 (8,8) (9,5)
20 (6,0) (8,7) (11,5) (14,2) (16,4) (18,4) 19,9 20,0 (18,6) (18,6)
30 (14,4) (17,9) 21,1 24,1 26,4 28,4 30,0 30,0 28,4 28,0
40 24,7 28,4 31,7 34,6 36,7 38,6 40,0 40,0 38,2 37,5
50 36,1 39,7 42,7 45,3 47,2 48,9 50,1 50,0 48,1 47,2
60 48,1 51,3 53,9 56,2 57,8 59,2 60,2 60,0 57,9 56,9
70 60,3 63,0 65,3 67,1 68,4 69,6 70,3 70,0 67,7 66,6
80 72,7 74,9 76,7 78,1 79,1 79,9 80,4 80,0 77,6 76,3
90 85,1 86,8 88,1 89,1 89,7 (90,3) (90,5) 90,0 87,4 86,0
100 (97,5) (98,7) (99,5) — — — — 100,0 — —
110 — — — — — — — — — —
120 — — — — — — — — — —
Sound Loudness level, phon
pressure level
Frequency, Hz
dB
2 000 2 500 3 150 4 000 5 000 6 300 8 000 10 000 12 500
0 (3,5) (6,0) (7,4) (6,7) (3,6) — — — —
10 (12,5) (14,9) (16,2) (15,3) (12,1) (6,0) — — —
20 21,7 24,2 25,4 24,3 21,2 (15,2) (9,1) (7,0) (8,0)
30 31,2 33,7 34,8 33,6 30,5 24,7 (18,6) (15,6) (17,0)
40 40,8 43,3 44,3 43,1 39,9 34,4 28,4 25,2 27,4
50 50,4 52,9 53,9 52,7 49,5 44,1 38,4 35,4 38,5
60 60,0 62,5 63,5 62,3 59,1 53,8 48,4 45,9 50,0
70 69,7 72,2 73,1 71,9 68,7 63,5 58,5 56,5 61,7
80 79,3 81,8 82,7 81,5 78,3 73,3 68,6 67,3 73,4
90 89,0 — — — — — 78,7 78,0 —
100 — — — — — — — — —
110 — — — — — — — — —
120 — — — — — — — — —
NOTE  Values in brackets are for information only.
Annex C
(informative)
Notes on the derivation of the normal equal-loudness-level
contours
C.1 Experimental data
Normal equal-loudness-level contours for pure tones under free-field listening conditions specified in
ISO 226 are obtained from the results of twelve independent experimental investigations as given in
References [6] to [17] as summarized in Reference [5]. In most of the cases, the experimental conditions,
such as the stimuli and subject criterion, satisfied the preferred test conditions (see Reference [18]).
The deviation from the preferred test conditions can be regarded as negligible. Brief descriptions of the
investigations are given in Table C.1.
C.2 Derivation of Formula (1) and Formula (2)
Equal-loudness-level contours are drawn in the two-dimensional plane described by frequency and
sound pressure level axes. Since experimental data to draw the contours are given discretely, the data
must be appropriately smoothed and interpolated. To this end, a model function representing the
equal-loudness relations is derived. Values of the parameters of the function are obtained by fitting the
function to the experimental data using the method of least squares.
The interpolation along the sound pressure level axis was based on a model loudness function. A
loudness function denotes the loudness of a sound as a function of the sound pressure level of the
sound. While several functions have been proposed as the model loudness function for a pure tone, l,
the following function, given by Formula (C.1), was applied here (see Reference [19]):
2θ 2θ
 
p
p  
 
t
lc=  −  (C.1)
 
 
Pa Pa
 
 
 
 
where
c
is a dimensional constant;
p
is the sound pressure of the pure tone;
θ
is the exponent of the loudness-perception process;
p is the threshold of hearing in terms of sound pressure.
t
This function was given in References [20] and [21] and is known to describe very well the loudness
function of a pure tone in the absence of masking noise, in spite of its simple form (see Reference [22]).
Furthermore, it was pointed out in Reference [23] that there are two different processes in assessing
loudness: one is a “loudness perception process”; the other is a “number assignment process.” Based
on this idea, a two-stage model was proposed in which the outputs of both processes are described
by separate power transformations (see Reference [5]). Moreover, in an actual hearing system, the
sound emitted from a sound source is transformed by a linear transfer function such as a head-related
transfer function and transfer functions of the outer ear, the middle ear, and the linear mechanical part
of the inner ear. The linear transfer function describes a comprehensive transfer function between a
sound source and the stage just before the loudness perception process. According to these ideas, the
process of loudness rating consists of three parts:
— a linear transfer function,
— a loudness perception, and
— a number assignment.
Figure C.1 shows a block diagram describing this model. The loudness response on the basis of this
model together with the loudness function of Formula (C.1) is given by Formula (C.2):
β
p
p
  
22ααt
lb=−cU() ()U (C.2)
 
 
Pa
...