The Measurement of Loudness

Harry F. Olson*

T !jHE ultimate significant sub-I jective destination of original or_1_ reproduced sound and noise is

the human ear. Therefore, the variedresponses of the auditory system areparticularly important factors in the reproduction of sound. One of the response functions of the human hearingmechanism is loudness. The purpose ofthis paper is to describe a loudnessmeter based upon the fundamentalprinciples of the loudness response ofthe human hearing mechanism.

When a sound or noise of any qualityor structure impinges upon the humanear, the magnitude of the resultantsensation is termed the loudness. It isthe intensive attribute of an auditorysensation in terms of which sounds maybe ordered on a scale extending fromsoft to loud. Loudness depends primarily upon sound pressure but it alsodepends upon frequency and waveformof the stimulus. The units on the scaleof loudness should agree with commonexperience estimates about the magnitude of the sensation. The measurementof loudness is a significant part of theaudio art because the loudness of asound or noise plays an important rolein the reproduction of sound.

Loudness is functionally related tosound pressure level, frequency, andwaveform. Turning this around, thesound pressure level as measured by asound level meter does not indicate theloudness of a sound. However, a conversion can be made in the readings ofa sound level meter employing octaveband pass filters to obtain the loudness.This is indeed a long and tedious process, as the exposition in this paperwill show. What is required is a loud-

■RCA Laboratories, Princeton, N.J.

18

ness meter that indicates the loudnessof a sound in real time. Furthermore,the loudness indication should agreewith the loudness as perceived by thelistener.

There are many uses for a loudnessmeter. For example, the loudness metercan be used to monitor the loudness ofan audio program so that the peak permissible levels of all manner of audioprogram material will provide the sameloudness to the listener. In the production of contemporary recorded musicone of the objectives is to obtain themaximum loudness. For a certain maximum amplitude level of the signal,which is determined by the constraintsof the record, a loudness meter can beemployed to obtain the maximum program loudness by modifications of thefrequency balance and timbre present

in the signal. There are many otheruses for the loudness meter in the measurement of sounds and noises.

Loudness ScaleThe establishment of a loudness scale

is a very complicated matter. A largenumber of investigators in many countries have carried out research on theloudness of a complex sound. A detaileddescription of the work is beyond thescope of this paper. Therefore, only thebasic data on loudness required for thedevelopment of a loudness meter willbe presented.

The unit of loudness is the sone. Asone is defined as the loudness heardby typical listeners when confrontedwith a 1000 Hz tone at a sound pressure level of 40 phons.

byThe loudness level of a sound is given

P= 201og10pB

where p = loudness level, in phons,P = measured sound pressure,

in microbars, andpo = a sound pressure of

0.0002 microbars

The loudness level ' of a sound ornoise.is expressed as n phons, when it isjudged by normal listeners to be equallyloud compared to a pure tone of frequency 1000 Hz consisting of a planeprogressive sound wave radiating to theobserver, the sound pressure of whichis n (decibels) above the standard ref-

AUDIO • OUR 25TH YEAR • FEBRUARY 1972

/100 - / /

// '

/ /

8/

t

/21

/ /

/ /

10080

40

20

108

4

2

1

0 10 20 30 40 50 60 70 80 90 100110120130LOUDNESS LEVEL P IN PHONS

Fig. 1—The relation between the loudness in sones and the loudness level inphons.

/,/

7

/

/

1 2 4 812 4 812 4. 0 0 1 . 0 1 . 1

11 2 4 81 2 4 811 1 0 1 0 0

SOUND PRESSURE IN MICROBARS

Fig. 2—The relation between loudnessin sones and the sound pressure inmicrobars.

3 4 5 6 7 89103 3 4 5 6 7 8 9 1 0 =

FREQUENCY IN HERTZ

3 4 5 6 7 8 9 1 0 *

erence sound pressure of 0.0002 micro-bars.

The relation1 between loudness insones and loudness level in phons isgiven by

s = 2(P-40)/10where S = loudness, in sones and

P = sound pressure level, inphons, given by equation 1.

The relation between the loudness insones and the loudness level in phonsis shown by the graph of Fig. 1.

The relation between loudness insones and sound pressure in microbars,shown by the graph of Fig. 2, indicatesthat there is a nonlinear relationshipbetween the loudness in sones andsound pressure in microbars.

Measurement Of LoudnessIn order to provide a measure of the

loudness for the complex sounds ofspeech, music, and noise, there mustbe a means to separate the complexsounds into manageable segments. Inparticular, to establish the loudness ofa complex sound, at least three specifications must be available as follows:

1. A scale of subjective loudness. Thisis termed the sone scale described inthe preceding section.

2. The equal loudness contours fordiscrete frequency bands of the complex sound.

3. The rule by which loudness addsas the discrete frequency bands of thecomplex sound are added.If specifications 1, 2 and 3 can beestablished, then the loudness of the

Fig. 3—The frequency response characteristics of the octave band pass filters.

AMPLIFIER

MICROPHONE

- V X / V

ATTENUATORCALIBRATED

INDECIBELS

CENTER BANDFREQUENCY

IN HERTZ

uj 100

3 5 1 2 5 1 2 5 1 21 0 0 1 0 0 0 1 0 . 0 0 0

FREQUENCY IN HERTZ

Fig. 4—Schematic diagram of a sound level meter for measuring the sound level inan octave.

Fig. 5—Contours of equal loudness index for octave bands in the audio frequency range.

20 AUDIO • OUR 25TH YEAR • FEBRUARY 1972

complex sounds of speech, music, ornoise can be determined. The objectiveand subjective information23,4 relatingto the specifications of items 1. 2 and 3have been established by investigatorsconcerned with the subject of loudness.Furthermore, these investigators haveshown that the loudness of a complexsound can be determined from the physical data on the complex sound in conjunction with the specifications of items1, 2 and 3.

The specific method for determiningthe loudness of a complex sound is tosplit the audio frequency range intofrequency bands. This is a complex procedure in which the complexity increaseswith the number of frequency bands.From a practical standpoint there shouldbe as few frequency bands as possiblewithout sacrificing frequency selectivity.A suitable frequency band appears tobe the octave. The frequency responsecharacteristics of the octave band pass

CENTER BANDFREQUENCY

MICROBARSTO

LOUDNESS INDEXCONVERTERS

DIFFERENTIAL

-ego—1>—*H 2 5 0 | 1 > *

IN HERTZ AMPLIFIERSA 6 3 I 0 H

i n p u t . - p o p — 0 — +■

A M P L I F I E R H ' 0 0 ° I t > * "

H 2000 | O-H 4000 | {>-

- i > H E I }

GATES

S5E5mm

OCTAVEBAND PASS

FILTERS

RECTIFIERS DCAMPLIFIERS

DIFFERENTIALGATES

ATTENUATOR

INTEGRATINGNETWORK

ATTENUATORSONES

Fig. 6—Schematic diagram of the elements of a loudness meter.

filters employed in this developmentproject are shown in Fig. 3.

The system for determining the soundpressure level in the eight differentoctave bands in the audio frequencyrange is shown in Fig. 4.

When the sound pressure level in eachoctave band has been measured, thenext step is the proper summation ofthese data to provide the total or overall loudness of the complex sound. Inthis investigation and development, theprocedure selected for calculating theloudness of a complex sound is the onedeveloped by S.S. Stevens.- This is alsothe standardized procedurer' as givenin ISO-R532 Method A. In accordancewith this Standard, the relation betweenthe total loudness and the loudness index in each octave band is given by

ST = 0.7 SM + 0.3 ZSwhere St = total loudness of the com

plex sound, in sones,S = loudness index in each oc

tave band,andSm = greatest of the loudness

indices.The loudness index is obtained from

the graph of Fig. 5. The sound pressurelevel in each octave band is determinedby means of the system of Fig. 4. Employing the geometric mean frequencyfor each octave band, the loudness index for each octave band is determinedfrom Fig. 5. Then the total loudness ofthe complex sound in sones is computedby means of equation 3.

1 ? 4 8 1 ? 4 8 1 2 4 8 1 2 4 8 1 2 4 8 1001 .01 . 1 1

SOUND PRESSURE IN MICROBARS10 100

Fig. 7—The relation between the loudness index and the sound pressure in micro-bars for the octave bands of Fig. 3.

L o u d n e s s M e t e rTo provide a loudness meter requires

an automated instrumentation of Fig. 4incorporating the data of Fig. 5 and theprocedures of the preceding sectionoperating in real time. Specifically,equation 3 shows that the loudness meter must provide the following: themeasurement of the loudness index ineach channel, the summation of theloudness indices in all the channels, theselection of the channel with the greatest loudness index, the proper relationand summation of the sum of the loudness indices and the highest loudnessindex, and an indicating meter with theproper dynamics to depict the loudnessof the complex sound in sones from thesummation input.

A schematic diagram of the loudnessmeter'1 is shown in Fig. 6. The signal input is fed to eight octave band pass filters. The frequency response characteristics of the filters are shown in Fig. 3.The output of each band pass filter isfollowed by an amplifier coupled to arectifier, which in turn is followed by

AUDIO • OUR 25H YEAR • FEBRUARY 1972 21

a microbar-to-loudness-index converter.The input-output characteristics of theeight microbar-to-loudness-index converters are shown in Fig. 7. These converters are in the form of nonlinearactive elements as a part of operationalamplifiers and their output is fed to ad.c. amplifier. The output of these amplifiers provides the loudness index foreach octave channel, and the loudnessindex outputs from the eight channelsare added by means of separate directcurrent amplifiers and fed to the attenuator coupled to integrating networkand the sone meter. In order to determine the channel with the highest output, the eight microbar-to-loudness-index converters are fed to differentialelectronic gates in the form of a net-

■7SMSONE SIGNAL

J N f J I L32s

INTEGRATINGNETWORK

SONES

HIGHSPEEDMETER

^1 0 2 0 5 0 1 0 0 2 0 0 4 0 0

LENGTH OF TONE PULSE IN MILLISECONDS

Fig. 8—The integrating network andhigh speed meter of the loudness meter.The graph depicts the relation betweenthe loudness in sones and the length ofthe tone pulse in milliseconds.

work tree, the output of which is fed toan attenuator coupled to the integratingnetwork and the sone meter. The twoattenuators are adjusted to obtain thecorrect values of 0.7Sm and 0.3 2 S. Under these conditions the sone meter willindicate the loudness in sones of anaudio signal input to the loudness meter.

The remaining and very importantsubject is the dynamics of the amplitudecharacteristic of the indicating meter.The amplitude response of the indicating meter system should correspond tothe ear response to individual, repetitive and overlapping short, medium, andlong time pulses of sound and continuous sounds. Since most sounds ofspeech and individual musical instruments are of short duration, this thenbecomes a very important problem. Thebasic question is the loudness of a complex sound as a function of the time thesound persists. Obviously, a short pulseof sound of amplitude equal to a longpulse of sound will exhibit a lowerloudness level. From published dataand data obtained from this develop

ment (loudness as a function of the timelength of the sound pulse), the graphshown in Fig. 8 was drawn. As wouldbe expected, the loudness of a relativelyshort time pulse of sound decreases withthe duration of the time of the pulse.This data was used to develop an integrating network in conjunction with ahigh speed indicating meter. A blockdiagram of the integrating network andthe high speed meter for indicating theoutput of the loudness meter in sones isshown in Fig. 8. The integrating network consists of active growth and decaynetworks applied to an operational amplifier. Since the main intended application for this meter was the determination of the loudness of speech andmusic, the integrating network wastailored to provide the correct indicationof loudness for this type of programmaterial.

The signal input to the loudness metershould correspond to the level of thereproduced sound. For example, theaverage listener prefers a loudness levelof the reproduced sound of 80 phons.The input to the loudness meter shouldbe adjusted so that a level of 80 phonswill give an indication of 16 sones.

P e r f o r m a n c e O f T h e L o u d n e s sM e t e r

A large number of subjective testshave been carried out to determine theperformance of the loudness meter employing reproduced speech and music.A few of the tests and results will bedescribed.

Test No. I. The reproduced soundlevel of a musical program was variedover wide limits. The observers agreedthat the indication of the loudness meter agreed with their sensation of loudness.

Test No. 2. The reproduced soundlevel of a speech program was variedover wide limits. The observers agreedthat the indication of the loudness meteragreed with sensation of loudness.

Test No. 3. The same musical programwas reproduced in highly compressedand uncompressed conditions. The compressed program was reproduced at alevel of 2 dB lower than the uncompressed program as read on a conventional volume indicator (VU meter).The loudness meter indicated a level3 sones higher for the compressed program. Here the two meters indicated areversal in the readings. The subjectiveevaluation by the observers agreed withthe loudness meter. This shows the conventional volume indicator does not indicate loudness.

Test No. 4. Speech was recorded ata low speaking level and at an almost

shouting level. The two were reproducedat the same top level of 80 dB as indicated by a conventional volume indicator (VU meter). The shouting speechindicated a higher loudness on the loudness meter. Again the observers agreedwith the loudness meter.

Test No. 5. Employing a contemporary musical program, the loudness meter was used to provide the maximumloudness for the same peak level as theunchanged program. The main operations were compression and changesin the frequency distribution. Employing a reproduction peak level of 85 dBas indicated on a peak reading levelmeter, the modified program indicateda loudness 6 sones higher than the unmodified program. This is an increasein loudness level of 6.7 phons which isindeed a considerable increase in thesensation of the loudness.

S u m m a r y A n d C o n c l u s i o nA loudness meter has been described

which indicates the loudness of an audiosignal. Since the ultimate significantsubjective destination of all original orreproduced sound is the human ear, ameter which indicates the loudness asperceived by the ear is an importantaudio instrument. For example, theloudness meter will become a very useful tool for determining the loudness ofany simple or complex sound or noise,for monitoring the maximum permissible level of all manner of audio programs, for obtaining the maximum loudness of an audio program for a certainmaximum peak level, etc.

The author'wishes to express his appreciation to R. A. Hackley, D. S.McCoy, and D. G. Murray for contributions to the development work oft h e l o u d n e s s m e t e r . A L

REFERENCES1. ISO-R131. Standard of the InternationalOrganization for Standards. 1959.2. S. S. Stevens, Jour. Acous. Soc. Amer.,Vol. 33, No. 11, p. 1577, 1961.3. B. B. Bauer, E. L. Torick, A. J. Rosenheckand R. G. Allen, "A Loudness Level Monitorfor Broadcasting," IEEE Transactions onAudio and Electroacoustics, Vol. AU-15,No. 4, p. 177, 1967.4. B. B. Bauer and E. L. Torick, "Researchesin Loudness Measurement," IEEE Transactions on Audio and Electroacoustics, Vol.AU-14, No. 3, p. 141, 1966.5. ISO-532 Method A. "Measurement ofLoudness," International Organization forStandardization, 1967.6. R. A. Hackley, H. F. Olson and D. S.McCoy, Audio Engineering Society, Preprint No. 636. April 29, 1969.

22 AUDIO • OUR 25TH YEAR • FEBRUARY 1972