The General Implications of Equal Loudness Contours

It isn’t too hard to accept that the frequency response of our hearing isn’t flat. Whatever it is, hey, we’re used to it, and we like our sound just fine, thank you. The problem that is revealed by the Equal Loudness Contours lies in the fact that they aren’t parallel at all levels. Uh-oh!

Think about it for second. When you measure the frequency response of an amplifier, you get a curve that is the response of that amplifier. Period. Nothing to do with level. Change the gain by 30 dB and you are still going to have the same response, down (or up) 30 dB. The response of the amplifier, at various levels, will be the same. If you publish the response curves at the various levels (which we don’t, because they don’t tell us anything we didn’t already know), they will all be parallel curves. Frequency response generally doesn’t change as a function of amplitude.

Except with hearing.

You heard me. With hearing.

In our hearing system, the frequency response of our hearing changes as the loudness changes. The EQ of our hearing mechanism is being tweaked on an ongoing realtime basis for each different loudness level we encounter. Hoo boy!!

And the difference isn’t subtle. Take a look.

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	A rendering of the Equal Loudness Contours as generated by Robinson and Dadson in the late ‘50s, expressed in 1/3 octave increments. Just so you know, I’ve extended the curves (using interpolation) on the bottom and on the top ends. Robinson and Dadson only went to 16 kHz. on the top, and as far as I can tell, didn’t take any measurements above 130 dB SPL (which seems like a reasonable and prudent course to me).

Now, in this illustration, we’re painting with a very coarse brush, so the differences look minor. Keep in mind that our vertical range is 180 dB (oh, about a billion-to-1 amplitude ratio!). The equal loudness curves are anchored to actual sound pressure levels at 1 kHz., and each such curve is called a Phon Line, as in “The 90 Phon Line passes through 90 dB SPL at 1 kHz.” A Phon is a sound that is “equally loud.” Huh? The bottom line is called “MAF,” which stands for “Minimum Audible Frequency.”

Anyway, several things jump out. First, the low frequency end of the spectrum is seriously skewed, so that (a) equal loudness generally requires much more Sound Pressure Level at low frequencies. Second, the subjective loudness range of 120 dB at 20 Hz. is a great deal less than the physical range (75 dB as opposed to 120 dB). Third, things get very funny between 1 kHz. and 8 kHz. Finally, we have a similar but less expanded skewing of the high end.

Because my teaching experience has been that this set of curves is a little hard to get a grip on, I’ve taken the liberty of creating a set of inverse curves, which I am going to call Hearing Response Curves. Here they are.

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	An expression of the changing frequency response of hearing at various sound pressure levels, anchored to physical reality at 1 kHz. These curves were generated as the inverse values of the various Equal Loudness Contours.

These curves make at least a little more sense. Take a look at the top one, the 120 dB SPL Hearing Response curve. It’s flat from 1 kHz. down to 200, and rolls off fairly steeply below that, ending up some 12 dB down at 50 Hz. and 30 dB down at 20 Hz. Above 1 kHz., there is a broad peak (1.7 octaves wide) centered at 3200 Hz., with a steep rolloff above that that includes a little plateau. Our hearing appears to be down approximately 40 dB at 20 kHz.

Welcome to the the comparatively crummy response of our hearing system.

Note that low frequency rolloff gets progressively worse as levels get softer, so that by the time we’re down to the 10 dB SPL Response curve, our Hearing Response at 20 Hz. is almost 70 dB down! Really shabby!

Now take a look at the response at 90 dB SPL.

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	Shows the Hearing Response curve at 90 dB SPL. I chose 90 dB SPL because it is close to my working level, and I find it a useful reference point. The bottom end is down 30 dB, there is a 3 dB mudrange peak, a nasty little 10 dB peak at 4 kHz. and a steep but lumpy rolloff above that.

Do you understand, from looking at this, just how critical 4 kHz. is to our hearing mechanism? And just how vulnerable we are to loud sounds in that range?

In any case, at this reference level, our hearing response is neither very good (to the extent that that means anything) nor particularly linear. The 400 Hz. and 4 kHz. bumps are troublesome, and our lack of sensitivity at frequency extremes is actually quite severe.

Now comes the interesting part. Let’s compare the 90 dB Response Curve with the 100 dB response curve. Take a look.

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	Hearing response curves at 100 dB SPL as well as 90 dB SPL.

Now these curves have some interesting differences. The mudrange and 4 kHz. peaks are different in terms of both frequency and amplitude, and the high-frequency roll-off of the 100 dB curve is considerably steeper. Notice also that at 20 Hz. the difference between the two curves is at least 15 dB, even though we only subjectively perceive them as 10 dB.

To make this clearer, let’s look at the difference between the two. We’ll use 90 dB SPL Hearing Response as the baseline.

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	Shows the difference in Hearing Response between 100 and 90 dB SPL.

Figure 5 shows the difference in Hearing Response between 100 and 90 dB SPL. Now this really reveals some interesting details. If I were to characterize the response at 100 dB SPL vs. 90 dB SPL, I’d say it has a nice little rising bass response that gives it some added deep punch, a dip in the mudrange that makes it a little clearer, and a nice 3 dB peak around 2 kHz. that hypes the presence. On the downside, the top octave is really badly rolled off.

Which Hearing Response curve sounds better? 90 dB SPL or 100 dB SPL? I bet you never thought of it in quite these terms before, eh?

Let’s take a look at the difference between the 80 dB SPL curve compared to the 90 dB SPL curve.

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	Hearing response at 80 dB SPL in comparison to 90 dB SPL.

Figure 6 shows hearing response at 80 dB SPL in comparison to 90 dB SPL. There’s a little bottom end rolloff (4 dB) and a 1 dB boost in the top octave. Otherwise, pretty much the same. Which do you think sounds better?

Now let’s compare response at 70 dB SPL compared to 90.

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	70 dB SPL compared to 90.

Now, to me, Figure 7 looks a little like the response curve of an Auratone! Broad and fairly deep low frequency rolloff, beginning at 500 Hz. and getting down 8 dB by 32 Hz. (Auratones, of course, are much further down by 32 Hz.). Then a really troublesome 3 dB dip in the ultra-important 4 kHz. range. Oddly, there’s a slight boost finally at around 16 kHz. Overall, this curve is a serious and quite audibly deleterious change in frequency response. It is not trivial.

Finally, let’s look at 60 and 50 dB SPL Hearing Response curves compared to 90 dB SPL.

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	60 and 50 dB SPL Hearing Response curves compared to 90 dB SPL.

These curves in Figure 8 pretty much complete the picture, covering the range of playback levels we normally encounter in recording. We see more of the same, with increasing deterioration in response, particularly in the low end. The top end really begins to get irrational, with big variations in the that critical 4 kHz. range.