A Special Quality of Hearing Corrections

One of the things that stood out to me, from early on, was the near-fact that hearing corrections depend only on the difference between presentation level and threshold elevation, for levels expressed in Phon measure.

C(P_{thr},P)=c(P - P_{thr})


where C(P_{thr},P) is the required hearing correction for sounds at presentation level P, when the threshold elevation is P_{thr}. And c(x) is a function of one variable.

I call it a near-fact because it is not entirely true. But it is mostly true over the range of sound levels that actually matter in our daily lives.

The dividing line is actually a narrow fuzzy zone around the 40 dB  level, where our hearing transitions from its near-linear threshold level behavior, to its more familiar cube-root compressive behavior. And we live in a world that mostly contains sounds above the 40 dB level.

For instance, the sound level in an empty auditorium is around 30 dB. But the sound level in my room where I’m writing this posting is right now measuring 43 dB, and it is nighttime and quiet as I’m the only one active at the moment.

Where the special relationship is true, we see that the correction gain needed at some level plus an increment, for a given threshold elevation, is the same correction needed for the original level when the threshold elevation is that same increment lower:

C(P_{thr},P + \Delta P) = C(P_{thr}- \Delta P, P )


It is this near-fact which makes possible the uniform treatment of HyperRecruitment and Decruitment by way of a simple Pre-EQ ahead of normal Crescendo corrections.

Without this special behavior we would have to use Post-EQ after a Crescendo correction based on some guessed level of departure from the threshold actually measured with audiology. That would make trial and error even more of a stab in the dark than it already is.

  • DM

[ Note: I’m being intentionally vague here, about sound levels in dB measure. That 40 dB level really applies to Phon measure, which is the same as dBSPL at 1 kHz. At other frequencies this remains approximately the same between 500 Hz and 6 kHz. But beyond those frequencies, Phons and dBSPL depart significantly.

When I stated the room was measured at 43 dB, that was dBA SPL, meaning dB through A-weighted filtering, in microphone units of SPL (sound pressure level).

SPL is what you measure with a microphone – a linear  device (hopefully!). Quite unlike our ears which are distinctively nonlinear.

I remain intentionally vague… ]

Author: dbmcclain

Astrophysicist, spook, musician, Lisp aficionado, deaf guy

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