Total loudness requires linear scales before integration is valid

Evidence

One important factor may be mentioned again. When the integration of specific loudness leads to the total loudness, we have to be aware of the fact that integration (corresponding to measuring the area below a certain curve) can only be performed if linear scales are used on the abscissa as well as on the ordinate. Therefore, it is not possible to do any integration process on the left part of Fig. 8.19. This can only be done on the right part, where specific loudness is plotted on a linear scale as a function of critical-band rate, also on a linear scale. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1283

Categorization

• DEFINE: Clarifies the methodological constraint that loudness integration is only valid on linear-scale plots of specific loudness versus critical-band rate.
• corroborated: 3 independent passages support this claim — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1283
• XREF: connects to: Total loudness is the integral of specific loudness over critical-band rate — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1250; Third-octave approximations require adjusting the loudness exponent to 0.25; Loudness is the summed specific loudness across critical-band rates, not the raw spectral level (+2 more)

Broader Connections

• Third-octave approximations require adjusting the loudness exponent to 0.25 #corroborates (0.72)
• Loudness is the summed specific loudness across critical-band rates, not the raw spectral level #expands (0.70)
• Loudness depends on more than physical sound intensity alone #complicates (0.70) — Dijk, Pim van, Physiology, Psychoacoustics and…, 2610