Re: Spreading in bark scale

["Bernhard U. Seeber" <seeber@xxxxxxxxxxxxxxxxxxxx>]

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



ARTICLE{GW-Mai67,
AUTHOR={ Maiwald, D.  },
TITLE={{Ein Funktionsschema des Geh"ors zur Beschreibung der 
Erkennbarkeit kleiner Frequenz- und Amplituden"anderungen}},
YEAR={1967},
JOURNAL="Acustica",
VOLUME={18},
NUMBER={},
PAGES={ 81-92.}}


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

@article{Zwi_Ter80,
   AUTHOR   = {Zwicker, E. and Terhardt, E.},
   TITLE    = {Analytical expressions for critical band rate and 
critical bandwidth as a function of
      frequency},
   YEAR     = {1980},
   JOURNAL  = JASA,
   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