posted 27 March 2002 01:06            

imd_tests.kym

The IMD intercept points are interesting in their own right because, whether you are aware of it or not, you are hearing these IMD product tones in your music. And when the music is as loud as these IMD intercept levels then the IMD product tones are as loud as the musical content itself.

There is a bank of 3 attenuators that attenuate the input parent tones (this is a 2-tone test with equal amplitudes on 300 Hz and 500 Hz) by 1, 2, and 4 dB. The amplitude of these parent tones is controlled by the fader labeled !Amp.

The next two faders, labeled Probe2 and Probe3 control the levels of two probe tones tuned near the 2nd order IMD tone at 200 Hz and the 3rd order IMD tone at 700 Hz. Toggle switches labeled P2 and P3 turn these probe tones on or off. I generally enable only one at a time, while setting the Probe fader to that level that maximizes the beat note.

You can control the degree of detuning by +/-15 Hz with the Detune fader. In conjunction with the attenuator switches you should set the Probe fader to maximum beat note amplitude. To help you judge this use some attenuation on and off. For small amounts of attenuation you should hear good strong beats at both settings.

The Probe2 tone is more forgiving of slight errors than the Probe3 tone simply because the Probe2 attenuates at 2x while the Probe3 tone attenuates at 3x. You probably won't be able to achieve good solid beating on the Probe3 tone for attenuations beyond 3 dB (!Atten1 + !Atten2).

The reason for this, as you will begin to see, is that our nonlinearity is itself nonlinear. At low input levels, I am seeing exponent values around 0.8 with this Sound, diminishing at higher !Amp settings to around 0.5. What that means is that your nonlinear response to loudness levels becomes more nonlinear at higher sound levels than at low sound levels. Smaller values of the exponent Alpha mean more nonlinear behavior than larger values. Reasonable values for Alpha lie between 0 and 1. If Alpha ever reaches 1 then you have linear hearing (doubtful!).

Now many of us realize, as musicians, that loud sounds are flatter sounding that soft sounds. Violinists naturally play sharp because they hear the loud sound near their ears as detuned toward flat tones. Hence they unwittingly compensate by playing sharper. And an untrained violinist sounds horribly sharp to a distant observer.

I have a question for you all... I haven't tried this yet. But are the IMD product tones also flattened at higher loudness levels? If so, are they flattened only in proportion to their own loudness level, or by some multiple of the detuning of the parent tones? Using this Sound and a simple stopwatch you should be able to answer this question. Set the detune for, say, 1 Hz and you should hear 1 pulse per second of beatnote at low input levels. Now boost the Amp to a much louder level, but keep it tolerable, and then adjust the probe tones to maximize beating again and time the beats. Do this for, say 10, beats overall timing. Are these timings the same at both amplitude settings? Are they the same for Probe2 and Probe3?

For many of you, just hearing beats at these non-existent frequencies of 200 Hz and 700 Hz will be an eye-opener for you. There is little doubt that they are there and quite prominent as shown by the strength of the beats against the probe tones. But normally you are unaware of their presence. This alone is a remarkable demonstration of the nonlinearity of human hearing.

This probe tone technique was first described to me by Dr. Arthur Benade. He might have learned it from another master, who knows... Helmholtz used wine glasses cupped to his ear to detect harmonics of piano tones. No doubt something like this probe tone technique was known even back in his time.

Cheers,

posted 27 March 2002 16:42            

Putting these results into Kyma makes the Crescendo sound even more delicious than before!

So once again, Kyma has permitted us to find a result that probably would have eluded all of us for much longer. The discovery of a non-constant loudness exponent was an important find. Previous investigators with widely different values for alpha all appear to have been correct over limited loudness ranges.

Kyma is a truly incredible instrument in so many ways!!!

posted 28 March 2002 12:49            

imd_tests.kym

The idea is that you set your parent tones, the IMD locations are computed for you for one 2nd order tone and 1 3rd order tone. Set the detune slider to about 1 Hz and turn on one of the probe tones. Adjust its amplitude fader until you hear good beats. Now set the detune to 0, and adjust phase for minimum signal. Finally, make fine adjustments to the probe amplitude fader until silence remains at the IMD tone frequency.

Repeat for the other IMD tone, and then the Alpha box shows your estimated exponent value for that amplitude setting on the parent tones.

By changing the parent amplitudes and repeating this nulling process, you can map out the variation of your exponent with input parent amplitude.

This idea was first suggested by Julius Goldstein of the Harvard Psychoacoustics Lab. It works quite well, quite a bit better even, than attempting to maximize the beat tone.

When I use this variation, I still get the trend of high exponents, around 0.8, for input levels at -24 dBFS and lower. And when the parent tones are increased to -16 dBFS I get around 0.6 for the exponent. So the variability remains confirmed. Our hearing gets ever more nonlinear at higher sound levels. But -16 dBFS is only -6 dBVU and so this amplitude corresponds to comfortable music listening levels.

Having auditioned many hours of CD listening with the graded exponent hearing model, I can certainly attest to the improvements it makes. A little less compression and a little more makeup gain. The results are tantalizing.