ISO 226

Acoustics — Normal equal-loudness-level contours

This International Standard 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: the sound field in the absence of the listener consists of a free progressive plane wave; the source of sound is directly in front of the listener; the sound signals are pure tones; 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; listening is binaural; the listeners are otologically normal persons in the age range from 18 years to 25 years inclusive.

Acoustique — Lignes isosoniques normales

L'ISO 266:2003 spécifie les combinaisons de niveaux de pression acoustique et de fréquences de sons purs continus qui sont perçus comme isosoniques par des auditeurs humains. Les spécifications sont basées sur les conditions suivantes : le champ acoustique en l'absence de l'auditeur consiste en une onde plane progressive libre ; la source de bruit fait directement face à l'auditeur ; les signaux sonores sont des sons purs ; le niveau de pression acoustique est mesuré en la position du centre de la tête de l'auditeur en l'absence de ce dernier ; l'écoute est binaurale ; les auditeurs sont des sujets otologiquement normaux âgés de 18 ans à 25 ans inclusivement.

General Information

• Status: Not Published
• ICS: 13.140 - Noise with respect to human beings
• Technical Committee: ISO/TC 43 - Acoustics
• Drafting Committee: ISO/TC 43 - Acoustics
• Current Stage: 6000 - International Standard under publication
• Completion Date: 17-Feb-2023

Relations

• Revises: ISO 226:2003 - Acoustics — Normal equal-loudness-level contours
• Effective Date: 06-Jun-2022

Standards Content (Sample)

2022-12-29
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ISO/DISPRF 226:20222023(E)
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2023-xx
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ISO TC 43/WG 1
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Secretariat: DIN
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Style Definition: ANNEX
Acoustics — Normal equal-loudness-level contours
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Acoustique — Lignes isosoniques normales
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ISO/PRF 226:20222023(E)
© ISO 20222023
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All rights reserved. Unless otherwise specified, or required in the context of its implementation,

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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.
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ISO/PRF 226:20222023(E)
Contents

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

C.1 Experimental data ....................................................................................................................................... 9

C.2 Derivation of Formula (1) and Formula (2) ........................................................................................ 9

C.3 Derivation of the frequency dependent parameters shown in Table 1 ................................... 11

C.4 Comparison between equal-loudness-level contours and experimental data ...................... 11

Bibliography ............................................................................................................................................................. 19

Foreword ..................................................................................................................................................................... iv

Introduction ................................................................................................................................................................. v

1 Scope ................................................................................................................................................................ 1

2 Normative references ................................................................................................................................ 1

3 Terms and definitions ................................................................................................................................ 1

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ISO/PRF 226:20222023(E)

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

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ISO/PRF 226:20222023(E)
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/directiveswww.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/patentswww.iso.org/patents).

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www.iso.org/iso/foreword.htmlwww.iso.org/iso/foreword.html.
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

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revised.
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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;
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— correction of systematic errors that lead to minor changes in the entire data up to 0,6 dB.

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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.htmlwww.iso.org/members.html.
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ISO/PRF 226:20222023(E)
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 International Standard, 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:

[1][2] [2][3]

ISO 532-1, , for loudness of arbitrary stationary sounds: ISO 532-2, , for tonal loudness and tonality: ECMA-

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[34]

-418--2 ). The tonal loudness is the loudness of the tonal components of a complex sound as the basis for the

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tonality calculation in Reference [4].
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During the technical revision of this document, it was decided to maintain separate documents for the

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specification of the threshold and supra-threshold data. The threshold values are specified in ISO 389-

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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

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document.
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NOTE 3 The equal-loudness-level values given by this document differ from those of the previous edition of

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ISO 226:2003, 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 Formatted: Pattern: Clear

normal equal-loudness-level contours for pure tones in this document are essentially identical to those described

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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 Formatted: Pattern: Clear

normative hearing threshold at that frequency.
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INTERNATIONAL STANDARD ISO/PRF 226:20222023(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

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frequencies in the one-third-octave series from 20 Hz to 12 500 Hz, inclusive, in accordance with

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ISO 266.
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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
ISO 266, Acoustics — Preferred frequencies
3 Terms and definitions Formatted: English (United States)
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For the purposes of this document, the following terms and definitions apply.
Latin and Asian text, Adjust space between Asian text
and numbers, Tab stops: Not at 19.85 pt + 39.7 pt +

ISO and IEC maintain terminology databases for use in standardization at the following addresses:

59.55 pt + 79.4 pt + 99.25 pt + 119.05 pt + 138.9 pt

— ISO Online browsing platform: available at https://www.iso.org/obphttps://www.iso.org/obp

+ 158.75 pt + 178.6 pt + 198.45 pt
Formatted: English (United States)

— IEC Electropedia: available at https://www.electropedia.org/https://www.electropedia.org/

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3.1
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otologically normal person
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States)
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ISO/PRF 226:20222023(E)

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 (3.2) 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
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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

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(3.1) within the age limits from 18 years to 25 years inclusive
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Note 1 to entry: The method for deriving the normal equal-loudness-level contours is described in Annex C.

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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,

f N
is given by Formula (1) [see also Formula (C.3)]:
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ISO/PRF 226:20222023(E)
T +L
 αα− LT f U 
( )   
r f  Nr 
α α α
 f
 rr 
10    
o  10 phon 10 dB  10 dB
    
L·lg · 10−+10 10 dB− L
f     U
 
α p
f  a  
 
 
 
T +L
L f U
   
N
0,03 f
0,3−α  
10  ( ) 
−10 f 0,072 10 dB
10 phon
  
··lg 4 10 · 10−+10 10 dB− L
( )
  U
f 
 
 
T +L
αα− LT f U Field Code Changed
( )   
r f Nr
 α α f
 rr 
10  
10 dB
o  10 phon 10 dB  
L·lg  · 10−+10 10 dB− L
f   U
α p
f  a
T +L
L f U
   
 N 
0,03 
0,3−α  
10  ( ) 
f 10 dB
−10  10 phon 0,072
  
··lg 4 10 · 10−+10 10 dB− L (1)
 
( ) U
 
f  
 
 
 
where
is the threshold of hearing in dB as in Reference [41];
is the threshold of hearing at 1 000 Hz in dB;
α is the exponent for loudness perception;
is the exponent for loudness perception at 1 000 Hz;
L is a magnitude of the linear transfer function normalized at 1 000 Hz in dB
is 20 μPa.

These values are all given in Table 1 for the preferred third-octave frequencies defined in ISO 266.

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Formula (1) applies, at each frequency, for values from a lower limit of 20 phon to the following upper Formatted: Pattern: Clear

limits:
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20 Hz to 4 000 Hz: 90 phon
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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

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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):
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ISO/PRF 226:20222023(E)
LL++T L
  
f UUf
  
10 dB 10 dB
  
100 10 −10
0,072
L=⋅+lg 10 phon
(0,3−α )
3 f
−10
4⋅10
( )
LL++T L
  
ffUU Field Code Changed
 ff 
10 dB 10 dB
  
100 10 −10
0,072
(2)
L=⋅+lg 10 phon
0,3−α
3 ( )
−10
4⋅10
( )
where T , α and L are the same as in 4.1. Formatted: Pattern: Clear
f f U
The same restrictions, which apply to Formula (1), also apply to Formula (2).
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Table 1 — Parameters of Formula (1) used to calculate the normal
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equal-loudness-level contours
Frequency, α L T
f U f Formatted: Lowered by 3 pt
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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
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ISO/PRF 226:20222023(E)
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

The data are given in graphical form in Annex A and in numerical form in Annex B for the preferred

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frequencies in the one-third-octave series from 20 Hz to 12 500 Hz, inclusive, in accordance with

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ISO 266.
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ISO/PRF 226:20222023(E)
Annex A
(normativeinformative)
Normal equal-loudness-level contours for pure tones under free-field
listening conditions
226_ed3figA1.EPS
Key
X frequency, expressed in Hz
Y sound pressure level, expressed in dB
T hearing threshold

NOTE 1 The hearing threshold under free-field listening condition, T , is indicated by a dashed line as defined in

[41]
ISO 389-7 .
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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

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data from only one institute are available at this loudness level.
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ISO/PRF 226:20222023(E)
Figure A.1 — Normal equal-loudness-level contours for pure tones
(binaural, free-field listening, frontal incidence)
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ISO/PRF 226:20222023(E)
Annex B
(normativeinformative)
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
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ISO/PRF 226:20222023(E)
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
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
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)
© ISO 20222023 – All rights reserved 9
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ISO/PRF 226:20222023(E)
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
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.
10 © ISO 20222023 – All rights reserved
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ISO/PRF 226:20222023(E)
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

Formatted: Pattern: Clear
[5]

References [6] to [17] as summarized in. Reference [5]. In most of the cases, the experimental

Formatted: Pattern: Clear

conditions, such as the stimuli and subject criterion, satisfied the preferred test conditions (see

Formatted: Pattern: Clear

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.
Formatted: Pattern: Clear
Formatted: Pattern: Clear
C.2 Derivation of Formula (1) and Formula (2)
Formatted: Pattern: Clear
Formatted: Pattern: Clear

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 Formatted: Pattern: Clear

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]):

Formatted: Pattern: Clear
2θ 2θ 2θ 2θ
Formatted: Pattern: Clear
  
p p
p   p  
   
t t
lc −  lc− (C.1)
       
Formatted: Adjust space between Latin and Asian text,
 
Pa Pa Pa Pa
       
  
Adjust space between Asian text and numbers, Tab
stops: Not at 19.85 pt + 39.7 pt + 59.55 pt + 79.4 pt
where
+ 99.25 pt + 119.05 pt + 138.9 pt + 158.75 pt +
178.6 pt + 198.45 pt
is a dimensional constant;
Field Code Changed
is the sound pressure of the pure tone;
θ is the exponent of the loudness-perception process;
is the threshold of hearing in terms of sound pressure.

This function was given in References [20] and [21] and is known to describe very well the loudness

Formatted: Pattern: Clear

function of a pure tone in the absence of masking noise, in spite of its simple form (see Reference [22]).

Formatted: Pattern: Clear

Furthermore, it was pointed out in Reference [23] that there are two different processes in assessing

Formatted: Pattern: Clear

loudness: one is a “loudness perception process”; the other is a “number assignment process.” Based on

Formatted: Pattern: Clear

this idea, a two-stage model was proposed in which the outputs of both processes are described by

separate power transformations (se
...

INTERNATIONAL ISO
STANDARD 226
Third edition
Acoustics — Normal equal-loudness-
level contours
Acoustique — Lignes isosoniques normales
PROOF/ÉPREUVE
Reference number
ISO 226:2023(E)
© ISO 2023
---------------------- Page: 1 ----------------------
ISO 226:2023(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2023

All rights reserved. Unless otherwise specified, or required in the context of its implementation, 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
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
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ISO 226:2023(E)
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 .............................................................................................................................................................................................................................20

iii
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ISO 226:2023(E)
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 of 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

www.iso.org/iso/foreword.html.
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.
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ISO 226:2023(E)
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 International Standard, 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.
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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

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ISO 226:2023(E)
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 αα  
  f
 r   r 
10    
10dB
o 10phon 10dB
      
L = ··lg   10 −10 +10 dB−LL
 
f   U
 
α p
 
f  a 
 
 
 
 
 
TL+
 
L f U
   
 
00, 3  
03, −α  
10  
f 10dB
−10  10phon 00,72
    
= ··lg 4101· 01− 0 +10 dB−L (1)
() 
 
 
 
 
 
where
T is the threshold of hearing in dB as in Reference [1];
T is the threshold of hearing at 1 000 Hz in dB;
α is the exponent for loudness perception;
α is the exponent for loudness perception at 1 000 Hz;
L is a magnitude of the linear transfer function normalized at 1 000 Hz in dB
p is 20 μPa.
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ISO 226:2023(E)

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
 
   
f f
 10dB 10dB 
   
100 10 −10
0,072
 
L =⋅lg +10 phon (2)
 
003, −α
3 ()
−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
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
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ISO 226:2023(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Frequency α L T
f U f
Hz dB dB
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

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.
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ISO 226:2023(E)
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

NOTE 1 The hearing threshold under free-field listening condition, T , is indicated by a dashed line as defined

[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)
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ISO 226:2023(E)
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
NOTE Values in brackets are for information only.
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ISO 226:2023(E)
TTabablele B B..11 ((ccoonnttiinnueuedd))
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
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
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
2 000 2 500 3 150 4 000 5 000 6 300 8 000 10 000 12 500
NOTE Values in brackets are for information only.
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ISO 226:2023(E)
TTabablele B B..22 ((ccoonnttiinnueuedd))
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.
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ISO 226:2023(E)
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  
 
lc=  −  (C.1)
 
 
Pa Pa
 
 
 
 
where
is a dimensional constant;
is the sound pressure of the pure tone;
is the exponent of the loudness-perception process;
p is the threshold of hearing in terms of sound pressure.

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

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ISO 226:2023(E)

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):

  
22ααt
lb=−cU() ()U (C.2)
 
 
Pa Pa
  
where
is an extended linear transfer function;
c ,α

are extended dimensional constants and an exponent for the “loudness perception process,”

respectively;
b,β
are those for the “number assignment process,” respectively;
pp, are as defined in Formula (C.1).
Figure C.1 — Block diagram of a loudness‑rating‑process model

In addition to sound pressure, the equal-loudness relationship along the frequency axis must be also

expressed by a function. When the loudness of a 1 000 Hz pure tone is equal to the loudness of an f Hz

pure tone, the following Formula (C.3) can be derived from Formula (C.2):
2 2α
2α 2α
 r α
 r 
p p f
  p p  
f      tf 
r tr
= − + U (C.3)
 
     
    f
Pa Pa Pa PPa
   
U  
     
f  
 
where

p is the sound pressure of an f Hz pure tone when its loudness is equal to that of a 1 000 Hz

pure tone with a sound pressure, p ;
p is the threshold of hearing at a frequency of f Hz;
p is the threshold of hearing at 1 000 Hz;
αα, are the exponents for the f Hz and 1 000 Hz pure tones, respectively;
f r
U is a magnitude of the linear transfer function normalized at 1 000 Hz.

That is, U at 1 000 Hz is set to 1. In these derivations, it is assumed that the variables for the “number

assignment process”, b and β, do not depend on frequency. With these equations, the sound pressure

level of an f Hz pure tone whose loudness is equal to that of a 1 000 Hz pure tone can be calculated.

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ISO 226:2023(E)
2 2
2 2
p p
  p   p
fft  
 
r tr
Formula (C.3) can be transformed into Formula (1) by substituting ,, , by
   
   
Pa Pa Pa Pa
   
   
L T T
     
f f rf
 
2 2
2 2 2 2 2 2
     
p   p
  p p p   p pp
f   10dB     tf   10dB     10dB
0 r 0 10phon 0 tr 0
       
= 10 , = 10 , = 10 , = 10
   
           
Pa Pa Pa Pa Pa Pa Pa Pa
          
   
2 10dB

and U =10 , respectively, where p is 20 μPa and 0,3 is substituted for α and the threshold value

f 0 r
of 2,4 dB is substituted for T .
Formula (2) can be derived from Formula (C.3) with the same replacements.

The exponent α , which is the exponent at 1 000 Hz, is set to 0,3 for the following reasons.

The loudness function based on a method of magnitude estimation and production is determined by

the output of the ‘‘number assignment process.’’ On the other hand, loudness functions based on other

methods based on the additivity of loudness are determined by the output of the ‘‘loudness perception

process.’’ Since judgment of equal loudness between two sounds must be based on the comparison of

the output of the ‘‘loudness perception process,’’ the exponent value based on the loudness additivity

may be used as it is in Reference [5].

The typical value obtained by means of the AME (Absolute Magnitude Estimation) method was 0,27

(0,54 for sound pressure) (see Reference [21]). Loudness obtained by an AME experiment seems to be

suitable for the output of the two-stage model. Thus, the exponent of 0,27 is adopted as the value that

corresponds to αβ in the equations, where β = 1,08. This value of β was determined in Reference [24].

Therefore, the exponent at 1 000 Hz, α , is assumed to be 0,25 (= 0,27/1,08) for values from experiments

based on the method of magnitude estimation and production. This value was used in the previous

edition of ISO 226.

On the other hand, loudness functions based on other methods based on the additivity of loudness

are determined by the output of the ‘‘loudness perception process’’. Since judgment of equal loudness

between two sounds must be based on the comparison of the output of the ‘‘loudness perception

process’’ where the exponent value based on the loudness additivity may be used as it is.

The average of all available data for the α values achieved by the different procedures is 0,296, as

described in Reference [5], rounded to a value of 0,30.
C.3 Derivation of the frequency dependent parameters shown in Table 1

The equal-loudness-level contours can be drawn if the values of the frequency dependent parameters,

α , L , and T in Formula (1) are obtained. The values were calculated from the experimental data

f U f
according to the following procedure.

a) With the exception of the two studies (References [25][27]) where the mean values were used,

thresholds of hearing from 20 Hz to 12 500 Hz (References [8] to [14][16][17][26][28][29]) are

represented by taking the mean of the median results of the individual studies for each frequency

and then smoothed and interpolated by a cubic B-spline function. The resulting values are shown

as T in Table 1. The number of subjects was not taken into account in the calculation of the spline

function.

b) Formula (1) was fitted to the mean results of the individual studies (References [6] to [17]) at each

frequency by the nonlinear least-squares method for estimating α and L . The obtained values of α

f U f

were then smoothed and interpolated by a cubic B-spline function. The resultant values are shown

as α in Table 1.
c) L values were then re-estimated by using For
...