Loudness Scaling Research Articles

Subjective Interpretation of Loudspeaker Frequency Response Curves in terms of Loudness

In objective measurements of the overall response of sound reproducing systems, the need is continually felt of a method of interpreting them subjectively. We have found it possible, by utilising Kingsbury's scale of loudness and his measurements at different frequencies connecting the sensation level of a pure tone with its loudness,1 to derive loudness-frequency characteristics. By way of example, in Fig. 1, is shown a typical measured acoustical response curve for a high quality loudspeaker. This type of curve can refer to the loudspeaker when supplied with constant current or when associated with its amplifier, or to the overall response characteristic corrected for different factors such as the change in the polar distribution of radiation with frequency.

Physical Measurements of Audition and Their Bearing on the Theory of Hearing*

The author states his purpose to be the presentation of certain facts of audition which have been determined recently with considerable accuracy and the discussion of the theory which best explains these facts. Making use of data of Knudsen's as well as his own measurements of the auditory sensation area, the author estimates that the normal ear can perceive approximately 300,000 different pure tones. This is taking account of all possible variations in both pitch and intensity. Knudsen's data show that for considerable ranges the minimum perceptible difference in intensity bears a constant ratio to the intensity and the minimum perceptible difference in frequency bears a constant ratio to the frequency. These relations have been termed by psychologists “The Law of Weber and Fechner.” A loudness scale is proposed such that the difference in loudness between two tones is equal to ten times the common logarithm of their intensity ratio. A pitch scale is proposed such that the difference in pitch is equal to one hundred times the logarithm to the base two of the frequency ratio. A method for measuring the loudness of complex sounds is mentioned but is to be discussed in a later paper. A method is proposed for expressing quantitatively different degrees of deafness. Reference is made to data obtained by the author on the masking of one pure tone by another. The minimum audible intensity of a pure tone depends upon the presence of another tone of different frequency. A low pitched note will, in general, exert a surprisingly large masking effect upon notes of higher frequency. The masking of a low note by a higher is not nearly as pronounced. From his observations, the author draws certain interesting conclusions. For example, given a complex tone consisting of three frequencies 400, 300 and 200 cycles with relative loudness values of 50, 10 and 10, respectively, the ear would hear only the 400 cycle tone and the 200 cycle tone. If the sound is now increased 30 loudness units, without distortion, the 400 cycle tone and the 300 cycle tone only, will be heard. Binaural masking in which each ear receives one of the two sounds is considered and the conclusion reached that the masking effect noted results from conduction of the masking tone through the bones of the head to the ear receiving the masked tone. It is stated on the basis of data obtained by Wegel and Lane that the oscillatory system of the ear, comprised by the membranes and little bones of the middle and inner ears, does not obey Hooke's Law regarding the proportionality of stress and strain. Consequently, the ear, when stimulated by a pure tone, introduces harmonics and the workers cited have observed harmonics as high as the 4th order. The non-linear transmission characteristic of the vibratory system of the ear is held to account for the greater masking of a high frequency by a lower. A theory of hearing is advanced which pictures the basilar membrane as being caused to vibrate by incident sound waves. In the case of a pure tone, the membrane is supposed not to vibrate uniformly throughout its length but the region of maximum amplitude determines the pitch of the tone as interpreted by the ear and the maximum amplitude determines the intensity. — Editor.

Physical measurements of audition and their bearing on the theory of hearing

The author states his purpose to be the presentation of certain facts of audition which have been determined recently with considerable accuracy and the discussion of the theory which best explains these facts. Making use of data of Knudsen's as well as his own measurements of the auditory sensation area, the author estimates that the normal ear can perceive approximately 300,000 different pure tones. This is taking account of all possible variations in both pitch and intensity. Knudsen's data show that for considerable ranges the minimum perceptible difference in intensity bears a constant ratio to the intensity and the minimum perceptible difference in frequency bears a constant ratio to the frequency. These relations have been termed by psychologists “The Law of Weber and Fechner.” A loudness scale is proposed such that the difference in loudness between two tones is equal to ten times the common logarithm of their intensity ratio. A pitch scale is proposed such that the difference in pitch is equal to one hundred times the logarithm to the base two of the frequency ratio. A method for measuring the loudness of complex sounds is mentioned but is to be discussed in a later paper. A method is proposed for expressing quantitatively different degrees of deafness. Reference is made to data obtained by the author on the masking of one pure tone by another. The minimum audible intensity of a pure tone depends upon the presence of another tone of different frequency. A low pitched note will, in general, exert a surprisingly large masking effect upon notes of higher frequency. The masking of a low note by a higher is not nearly as pronounced. From his observations, the author draws certain interesting conclusions. For example, given a complex tone consisting of three frequencies 400, 300 and 200 cycles with relative loudness values of 50, 10 and 10, respectively, the ear would hear only the 400 cycle tone and the 200 cycle tone. If the sound is now increased 30 loudness units, without distortion, the 400 cycle tone and the 300 cycle tone only, will be heard. Binaural masking in which each ear receives one of the two sounds is considered and the conclusion reached that the masking effect noted results from conduction of the masking tone through the bones of the head to the ear receiving the masked tone. It is stated on the basis of data obtained by Wegel and Lane that the oscillatory system of the ear, comprised by the membranes and little bones of the middle and inner ears, does not obey Hooke's Law regarding the proportionality of stress and strain. Consequently, the ear, when stimulated by a pure tone, introduces harmonics and the workers cited have observed harmonics as high as the 4th order. The non-linear transmission characteristic of the vibratory system of the ear is held to account for the greater masking of a high frequency by a lower. A theory of hearing is advanced which pictures the basilar membrane as being caused to vibrate by incident sound waves. In the case of a pure tone, the membrane is supposed not to vibrate uniformly throughout its length but the region of maximum amplitude determines the pitch of the tone as interpreted by the ear and the maximum amplitude determines the intensity. — Editor.