specific loudness calculation: ambiguity of excitation

["Rossi Mark (PA-ATMO/EES21) *" <Mark.Rossi@xxxxxxxxxxxx>]

Dear list,

I spent 2 days now searching for the answer to my question, reading tens of papers and articles, asking lots of people... I hope you're not offended by the triviality of it.


The specific loudness as defined by Zwicker & Fastl in [1] (page 224; equation 8.5) reads
N'(z) = N'_0 *((E_{TQ}(z))/s(z)*E_0))^{0.23} * [(1-s(z)+s(z)*E(z)/E_{TQ}(z))^{0.23} -1] sone/Bark

I found N'_0 and s(z) in [1] and an equation to calculate the threshold in quiet E_{TQ} in [2]. But it seems impossible to me to figure out, what the excitations E(z) and E_0 exactly are. In [1] you can read: "...and E_0 is the excitation that corresponds to the reference intensity I_0 = 10^{-12} W/m^2."
?

The questions are (given I already calculated the excitation pattern):
- when E_0 is the _intensity_ ratio between the measured intensity at a critical band rate I_M and I_0 ( E_0 = I_M/I_0 ): what is E(z) supposed to be? and should the threshold in quiet in the first parenthesis be given as intensity (10^L) too, in order to keep the term nondimensional?
- if the first assumption is correct: is E(z) the excitation _level_ at the considered critical band rate?
- when E(z) = E_0: why they used different expressions?
The mentioned chapter in [1] leaves this completely open and me in frustration.

I hope someone here can help me with my 'simple' question.


Thanks and regards,
Mark Rossi


[1] E.Zwicker, H.Fastl: "Psychoacoustics" 2nd updated edition
    Springer,
    1999
[2] E.Terhardt: "Calculating Virtual Pitch",
    Hearing Research,
    vol. 1,
    p. 155-182
    1979


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Mark Rossi
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