Sharpness is modeled as a weighted first moment of specific loudness

Evidence

Taking into account the factor, g, which increases above 16 Bark to values larger than unity, using the specific loudness versus critical-band rate pattern as the distribution in question, and using the boundary condition that a narrow-band noise centred at 1 kHz has to produce a sharpness of 1 acum, an equation of the following form can be given: … In this equation, S is the sharpness to be calculated and the denominator gives the total loudness N, which has already been discussed in Chap. 8. The upper integral is like the first moment of specific loudness over critical-band rate, but uses an additional factor, g(z), that is critical-band-rate dependent. This factor is shown in Fig. 9.2 as a function of critical-band rate. Only for critical-band rates larger than 16 Bark does the factor increase from unity to a value of four at the end of the critical-band rate near 24 Bark. This takes into account that sharpness of narrow-band noises increases unexpectedly strongly at high centre frequencies. Equation (9.1) is only a weighted first moment of the critical-band rate distribution of specific loudness. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1355

Keeping in mind that sharpness decreases if lower cut-off frequency is reduced (see dotted curve in Fig. 9.1), we may assume that a kind of moment is responsible for the development of sharpness. Taking into account the factor, g, which increases above 16 Bark to values larger than unity, using the specific loudness versus critical-band rate pattern as the distribution in question, and using the boundary condition that a narrow-band noise centred at 1 kHz has to produce a sharpness of 1 acum, an equation of the following form can be given: … In this equation, S is the sharpness to be calculated and the denominator gives the total loudness N, which has already been discussed in Chap. 8. The upper integral is like the first moment of specific loudness over critical-band rate, but uses an additional factor, g(z), that is critical-band-rate dependent. This factor is shown in Fig. 9.2 as a function of critical-band rate. Only for critical-band rates larger than 16 Bark does the factor increase from unity to a value of four at the end of the critical-band rate near 24 Bark. This takes into account that sharpness of narrow-band noises increases unexpectedly strongly at high centre frequencies. Equation (9.1) is only a weighted first moment of the critical-band rate distribution of specific loudness. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1353

Categorization

• DEFINE: Defines the sharpness model as a weighted first moment of specific loudness over critical-band rate, with a weighting factor g(z) rising above 16 Bark.
• XREF: Connects to the earlier loudness model (specific loudness vs critical-band rate pattern from Chap. 8) and the excitation-pattern framework common across psychoacoustic models, parallel to how loudness and roughness are each formalized as integrals over excitation patterns. — connects to: Sharpness depends primarily on spectral content, not on level or bandwidth.; Sharpness is a stable, subject-independent psychoacoustic quantity; Sharpness depends on the spectral envelope, not fine structure
• corroborated: 3 independent passages support this claim — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1355; Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1353

Broader Connections

• Sharpness is a stable, subject-independent psychoacoustic quantity #qualifies (0.75)