Speedskater
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For different but related example, in a large orchestral texture, the melody may be played at unison by strings, flutes, oboes, clarinets. The conductor halts the rehearsal and says "2nd clarinet, you're not blending in at the 3rd bar, please match the tone of the 1st chair there."
The engineers cannot parse the 2nd clarinet's sound out of the mixdown signal (obviously they could if every part was separately miked). The conductor's brain can take the binaural signal arriving at his/her ears and distinguish every characteristic of every part. The engineer may be able to run stats and see a slightly different spectrum, different peaks, maybe a vanishingly small RMS amplitude difference--but they can neither measure nor point to the difference that the conductor hears, the one s/he cares about.
This happens at virtually every orchestra rehearsal (with a decent conductor) everywhere. It's not quite the same as "measuring"; probably this should be called "decoding the signal". Your brain can separate the components of the sound in ways that are not available via hardware or software.
If you were to place binaural microphones (sort of like headphones) on that conductor's head and make a recording.
See:
Stereo Recording & Rendering - 101
http://www.linkwitzlab.com/Recording/AS_creation.htm
Then another equally skilled conductor could hear the same problem when listening to the playback.