2nd Order Audiometry

In the course of careful listening with my Crescendo system, I have noticed a significant difference in Left/Right hearing at the higher frequencies. I have decruitment hearing at high frequencies, and it is more severe in my right ear than my left.

Decruitment is the condition that even at loud levels, the sound never grows as loud as expected. This is easily corrected, as my algebra of hearing operators has shown. It requires a post-EQ boost at those decruitment frequencies, after going through milder recruitment corrections in Crescendo.

Showing recruitment (red) vs 10 dB decruitment (magenta). While both intercept at the elevated threshold of 60 dB, the normal recruitment curve is steeper (more nearly vertical) at threshold levels.

This figure illustrates a situation with a threshold elevation of 60 dB, for normal recruitment (red), and with 10 dB of decruitment (magenta). The green reference line shows the perception of normal hearing – what comes in is what you perceive.

Consider that since decruitment is the condition that, for whatever reason, prior to reaching the hair cells the signal is diminished, while the hair cells exhibit some milder damage than indicated by threshold determination, so pure tone audiometry (PTA) will have incorrectly determined the Crescendo correction curve, when based solely on your elevated threshold.

Crescendo assumes that all hearing corrections are based on normal recruitment. If your hearing were normal recruitment, then after Crescendo corrections the sound would become the same as with unimpaired hearing. But with a decruitment curve at the same elevated threshold, those Crescendo corrections will never be enough. The affected high frequencies in the music will never seem quite loud enough in relation to the bass and midrange.

A zoomed-in view focusing on normal audible loudness ranges. The red and magenta curves are the same as in the previous graph. The light blue curves illustrate what happens as we vary the Crescendo threshold elevation from below the nominal setting to above it. None of these produce satisfactory results with decruitment hearing.
Here we show what happens if you apply Crescendo processing with 60 dB elevation, plus varying amounts of post-Crescendo gain at this frequency. None of these work properly, since the aim is to match the normal hearing line.

Standard PTA is incapable of discerning this condition. What we need is some kind of diagnostic test that can determine not only your elevated threshold, but also some measure of the steepness of your recruitment hearing curve. Decruitment has less steep curvature near threshold than normal recruitment. But there are currently no such tests.

Critical listening to music will pretty clearly point out when you have this condition. In an attempt to regain those diminished highs, you might try to add post-Crescendo EQ boost at those frequencies, or increase the threshold elevation for Crescendo at those frequencies. But when you do, the faint levels in music become overly bright and crunchy. There becomes too much correction at low levels.

The correct approach is to post-boost the signal by some amount at those higher frequencies, and simultaneously lower the estimated hearing threshold by the same amount. This has the effect of acknowledging an elevated threshold, while also moderating the steepness in the recruitment corrections. High frequencies in the music at faint levels should become more apparent for you while avoiding the crunchy overly bright condition. And the affected frequencies remain correct at louder levels too.

By varying both the Crescendo threshold setting and adding complementary post-gain, we can converge on a correct solution.

It becomes a process of trial and error, being unguided by any measurements. All you have are your subjective sense that the music quality is improving while being able to hear more of it. But if you hear more of the music while the low level portions sound crunchy to you, then you probably have too much threshold elevation indicated for Crescendo, and then if the music never sounds loud enough after backing off, then you may have decruitment hearing at the higher frequencies. In that case, try a bit more post-Crescendo boost using a high shelving filter, and lower the correction strength in Crescendo at the same time by about the same amount.

For myself, I find through experimentation that, I need about 4 dB post-boost in the left channel, and 9 dB post-boost in the right channel, using a high shelving filter at 1250 Hz, Q = 1. With this post-gain, I also find that I need to reduce my Crescendo setting from 60 dB down to around 52 dB. Some music has more high hiss noise floor than others, and I found my Crescendo setting by reducing it until the audible hiss disappeared. I found the differential post-gain by keeping a mono signal centered as its frequency climbed.

Post-Crescendo gains for my hearing. This EQ is inserted just after Crescendo processing. +4 dB/left, +9 dB/right, Q = 1, Fc = 1250 Hz.

At some point in this process you will reach a more satisfactory setting on both post-Crescendo boost and lowered threshold in Crescendo, and the music will sound about as good as you can get. Plenty of high frequency extension, compared to unassisted hearing, while the low level sounds are not too crunchy.

  • DM

In fact, there is really only one recruitment curve, since to first order the recruitment curve is a function solely of the [dB] difference between presentation level and elevated threshold.

While the shape of the curves appears to grow in steepness with threshold elevation, that is an artifact of where along the curve we are looking, and the curvature induced by taking the logarithm (for dB measure presentation) of a value approaching zero, as we approach threshold levels.

In Sones measure the curve looks like this:

The green curve shows normal hearing, while the red curve shows hearing with a 60 dB threshold elevation. Threshold level here is just slightly more than 0 Sones (= 0.0021 Sones). [Negative Sones are unphysical, but serve a useful mathematical purpose.]

An impaired hearing curve has exactly the same underlying curve, but displaced downward so that the same threshold Sones level appears at the elevated threshold presentation level. This is the fundamental premise of Crescendo: that the growth in Sones is governed entirely by the mechanics of our hearing, while the sensation is governed by neurological and physiological effects. At any particular presentation level, all normal recruitment hearing curves exhibit identical shape [derivatives of all orders], regardless of the depth of hearing impairment.

[This downward displacement of the (green) curve is just a mathematical convenience. In physical terms, the threshold level is elevated and the sole (green) Sones curve remains intact. But for comparison of impaired with normal hearing it is convenient to normalize the situation by producing two curves through a downward displacement. The displaced curve corresponds to our impaired perception, and we simply cannot hear anything below threshold Sones level. But physically, they are all the same sole Sones curve.]

A hearing correction, at any particular presentation level, is that amount of additional gain needed to make the red curve present the same Sones level as heard by unimpaired hearing. At higher presentation levels the Sones curve grows steeper, meaning that less additional gain is needed to reach comparable levels between the two curves.

It is the job of Crescendo to produce these hearing correction gains, based on the instantaneous presentation levels in the music, on the assumption that you have a normal recruitment curve with some indicated threshold elevation, and assuming its result is going through a spectrally flat transducer to your ears.

And so given the shallow slope of the Sones curve, at low presentation levels, it isn’t terribly surprising then, that PTA is inaccurate. It only takes a small vertical displacement in Sones, to produce a relatively larger variation in measured threshold presentation level. So while the audiologist may claim a measured threshold elevation of 60 dB at some frequency, perhaps it is really only 40 dB? or 50 dB? And then you have to consider that there may be decruitment masking some of the hearing…

Conditions of Decruitment or Hyper-Recruitment shift the impaired response to the right or left, respectively. So now slope of Sones growth is no longer the same as for a normal response. Yet the measured threshold elevation is the same 60 dB in each case. Pre- or post-gain attempts to remove the lateral shift in the response, allowing Crescendo to work as though we have normal recruitment.

[dB Gains are additive, and Crescendo corrections depend only on the dB difference between the presentation level and the elevated threshold. This Crescendo approximation breaks down only at sound levels below those normally encountered in daily experience. So it should not matter if you apply pre- or post-gain along with Crescendo. Pre/post-gains and correction gains commute.

But where you apply the gain does dictate how the Crescendo threshold ought to be set. If you apply gains ahead of Crescendo, then leave the threshold settings unchanged. But if you apply post-gain, then the Crescendo threshold ought to be decreased by the amount of post-gain.

In theory, these two arrangements are equivalent. But pragmatically, applying pre-gain will magnify the noise floor going into Crescendo processing, thwarting its internal noise gating. For positive gains, it is probably cleaner to apply the gains after Crescendo processing with a lowered threshold setting. For Hyper-recruitment compensation the opposite would be true, using pre-Crescendo attenuation with unchanged threshold settings.]

Author: dbmcclain

Astrophysicist, spook, musician, Lisp aficionado, deaf guy