# ISO 226:2003 pdf download

ISO 226:2003 pdf download.Acoustics -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 [1] to [12]. In most of the cases, the experimental conditions, such as the stimuli and subject criterion, satisfied the preferred test conditions (see reference [13]). 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 Equation (1) and Equation (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, 1, the following function was applied here:dimensional constant;

p is the sound pressure of the pure tone;

0 is the exponent of the loudness-perception process;

Pt is the threshold of hearing in terms of sound pressure.

This function was given in references [14] and [15], 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 [16]).

Furthermore, it was pointed out in reference [17] 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. 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,

The exponent ar, which is the exponent at 1 000 Hz, is set to 0,25 for the following reason. The typical value obtained by means of the AME (Absolute Magnitude Estimation) method was 0,27 (0,54 for sound pressure) (see reference [15]). 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 arfl in the equations, where fi = 1,08. This value of fi was determined in reference [18]. Therefore, the exponent at 1 000 Hz, ar, is assumed to be 0,25 (= 0,27/1,08).

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

The equal-loudness-level contours can be drawn if the values of the frequency dependent parameters, a,, Lu, and T1. in Equation (1) are obtained. The values were calculated from the experimental data according to the following procedure.

a) With the exception of the two studies (references [19, 21]) where the mean values were used, thresholds of hearing from 20 Hz to 12500 Hz (references [3-9, 11, 12, 20, 22, 23]) 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) Equation (1) was fitted to the mean results of the individual studies (references [1-12]) at each frequency by the nonlinear least-squares method for estimating a and Lu. The obtained values of a, were then smoothed and interpolated by a cubic B-spline function. The resultant values are shown as a1in Table 1.

c) Lu values were then re-estimated by using Equation (1) with the values of a,. The re-estimated Lu values were smoothed and interpolated by a cubic B-spline function. The resultant values are shown as Lr in Table 1.

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

The estimation of the contours was carried out for the frequency range from 20 Hz to 12 500 Hz, because available data at frequencies above 12 500 Hz exhibit large variability. Figure C.2 shows the data from references [1] to [12] and from [19] to [23], together with the fitted normal equal-loudness-level contours and the curve for the threshold of hearing.