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Re: Spreading in bark scale

Dear Goran,
Dear list,

the frequency spreading you refer to comes from a simple masking model published by Maiwald in 1967 and used by Terhardt in his virtual pitch model in 1979. It is based on the assumption that masking/the excitation of a tone is to a first approximation of triangular shape if the frequencies are expressed as critical-band rate in Bark. In this approximation the lower slope of the masking pattern is relatively independent of frequency and level with a value of about 27dB/Bark, whereas the upper slope shows frequency dependence at very low frequencies as well as the "upward spread of masking" depending on masker level (main excitation). The formula you have describes the slope of this upper part of the masking/excitation pattern. Obviously, modeling complex masking patterns with just two lines can only be a coarse approximation, but it can cover some of the main effects at the benefit of being computationally extremely cheap. As far as I can assume, Maiwald derived this formula with the Bark scale as published in tabulated form in Zwicker's first book. The arctan-approximation of the Bark scale was published years later in 1980. However, the error introduced by using the formula instead of the table is very small and negligible compared to the coarseness of the masking model and the variability seen in psychoacoustic masking studies.

I hope that helps you a bit,

Bernhard Seeber

AUTHOR={ Maiwald, D. },
TITLE={{Ein Funktionsschema des Geh"ors zur Beschreibung der Erkennbarkeit kleiner Frequenz- und Amplituden"anderungen}},
PAGES={ 81-92.}}

ARTICLE{Ter79, AUTHOR = {Terhardt, E.}, TITLE = {Calculating virtual pitch}, YEAR = {1979}, JOURNAL = "Hearing Research", VOLUME = {1}, NUMBER = {2}, PAGES = {155-182} }

AUTHOR = {Zwicker, E. and Terhardt, E.},
TITLE = {Analytical expressions for critical band rate and critical bandwidth as a function of
YEAR = {1980},
VOLUME = {68},
NUMBER = {6},
PAGES = {1523-1525}

Date:    Sat, 8 Apr 2006 00:14:56 +0200
From:    Goran Bozidar Markovic <mr97411@xxxxxxxxxxxxxxxxxx>
Subject: Spreading in bark scale

Dear list,

I am unable to get books from Zwicker, Terhardt and other relevant books
about psychoacoustics. So I can not check one thing:
Frequency spreading used in ITU-R BS.1387 is based on Terhardt:

24+230/fc+0.2*L   db/Bark

Is this spreading based on assumption that exact bark scale is used, or is
it based on assumption that bark scale aproximation by Terhardt is used?

Please help.

Dr.-Ing. Bernhard U. Seeber
Department of Psychology                   office: +1 510-643-8408
University of California, Berkeley         lab:    +1 510-642-5352
3210 Tolman Hall #1650                     fax:    +1 510-642-5293
Berkeley, CA 94720-1650, USA               web:    http://www.bseeber.de