11-7 Loudness analysis (Loudness, Sharpness)

Loudness level is a sound evaluation parameter that considers auditory masking effect which has not been considered by A-weighted sound pressure level (L_A) and, as such, represents more closely the loudness of sound perceived by humans.

These days, some home electrical appliances are publicized as "half as loud as conventional products" in brochures and related media. The criterion used in such comparisons is loudness.

Ono Sokki’s LA-3000 series sound level meters, offer a loudness analysis based on real-time 1/3 octave analysis data. Ono Sokki also offers the Sound Quality Evaluation software that quantifies sound using six psychoacoustic parameters of sharpness, roughness, fluctuation strength, AI, tonality and loudness.

(1) What is loudness?

When we hear sound, a range of factors are involved as shown in Figure 11-12. How we feel about the sound we hear depends on our psychological conditions and are different from person to person: some people do not mind sounds that are familiar to them. There have been many attempts to evaluate sound while considering psychological factors, Ono Sokki has been using the OS-2000 sound quality evaluation software for that purpose.

From the viewpoint of auditory sense, loudness, which is one of the sound quality evaluationparameters, is heavily dependent on sound pressure level. A-weighted sound pressure level, which is commonly used to evaluate noise, was devised as a sound pressure level with frequency weighting approximated to 40-phon pure tone loudness characteristics (equal-loudness-level contours (ISO R 226)) to simulate auditory sense. However, when two different pure tones with the same loudness are heard, the combined tone is twice as loud as the individual pure tones when their frequencies are wide apart and is less loud than that when their frequencies are close to each other. This is called the masking effect.

A-weighted sound pressure level is a quantity with weighting approximated to pure-tone loudness curves. As such, the parameter does not agree with the level of loudness perceived by humans for ordinary noise with various frequencies. Thus, in order to determine a loudness more akin to auditory sense, ａmethod calculating the loudness of steady noise accounting for the masking effect was developed and standardized in ISO 532. This standard consists of ISO 532A by S.S. Stevens and ISO 532B by E. Zwicker. Ono Sokki uses ISO 532B. Please also read the supplement below.

(2) Equal loudness curve, Loudness level (phon) and Loudness (sone)

Figure 11-13 shows pure-tone loudness curves (ISO 226:2003). This figure is the same as the one presented in Section 6-4 "Loudness level"; please also refer to the descriptions there.

The numbers near the curves indicate the loudness levels. One phon corresponds to the sound pressure level (dB) of 1 kHz pure tone. An equal loudness curve is a line that connects the points of sound pressure level at various frequencies that have the same auditory loudness as 1 kHz pure tone. This is A-weighting approximated to 40-phon equal loudness curves. Loudness, however, is not a psychological quantity. Ordinary 50-phon noise does not sound twice as loud as 40 phon. Two 40-phon sounds occurring at the same time do not sound the same as 50 phon. Meanwhile, the loudness of a pure tone (1 kHz) with a sound pressure level of 40 dB is defined as 1 sone. Loudness twice the level of 1 sone is defined as 2 sone.

Just as sound pressure level L_p and noise level L_A are both shown in dB, loudness is also converted and shown in dB and phon used as the unit of measurement for loudness. The relationship between loudness level L (phon) and loudness S (sone) can be expressed using the following equation as long as L is between 40 and 120 phon.

This means that every 10-phon increase in loudness level makes the sound twice as loud (when S = 2 sone, L = 50 phon). When S < 1, the following equation applies

(3) Critical band and Loudness

The human ear feels sound in different parts depending on the sound’s frequency. The human ear functions like a frequency analyzer. A band that corresponds to a bandwidth for frequency analysis is called a critical band. It appears that each critical band has a masking effect. For example, combining 250 Hz pure tone and 1 kHz pure tone creates a tone twice as loud as these tones as shown in the left part of Figure 11-14. On the other hand, combining 250 Hz pure tone and 500 Hz pure tone does not create a tone two times louder than these tones. That is because of the critical bands, resulting in the 250 Hz tone masking the 500 Hz tone.

The Loudness of the 250 Hz tone is represented by the hatched area. The loudness of the 250 Hz tone and that of the 500 Hz tone are determined by their hatched areas. The area of the 500 Hz tone masked (covered) by the area of the 250 Hz tone is excluded, making the 500 Hz tone less loud than when it was 1 kHz and closer to its auditory loudness. As shown by the hatched area of the 250 Hz tone, the masking effect is light (approximated as negligible) on the lower frequency side and pronounced on the higher frequency side. Another characteristic of the masking effect is that the louder the tone, the wider the reach of the masking.

(4) Sharpness

Sharpness is a measure of the high frequency content of a sound, and is calculated as a ratio of Loudness with a focus on wide-band to normal Loudness. The unit of measurement is acum. Generally, Loudness is associated with overwhelming power (loud, powerful, strong, etc.) while sharpness is associated with something metallic (hard, annoying, shrieking).

(5) Examples of measurements

Figure 11-15 shows display examples of loudness (sone) and loudness level (phon) using a simplified measurement while factoring in the masking effect.

ISO 532B specifies that loudness shall be determined based on FLAT-weighted, 1/3 octave real-time analysis.

Loudness can be measured in two ways depending on the environment in which measurements are taken: in a free sound field like an anechoic chamber or an open field where there is no reflection of sound; and in a diffuse sound field like a gymnasium or an ordinary room where sound is reflected. These methods use different calculations and their measurements are distinguished from each other using the codes GF and GD respectively.