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Binaural recording is so exciting! An environment can be recorded anywhere in the world, and when replayed, it will give a very realistic impression of that environment to someone who has never been there. It is the most accurate form of surround sound.
A basic binaural recording is made by placing microphones in the ears. Two ears, two mics, one in each ear. Each microphone records exactly what sound reaches each ear. If a sound is made very close to the right ear, the right ear will hear it before the left. The time difference isn't much, but its there. Not only that, the head gets in the way of the sound reaching the left ear. The shadowing effect of the head, and the tiny time difference between each ear receiving the same sound (called the inter-aural time difference or ITD), enables our brain to calculate the exact position of a sound.
This may seem like a lot for the brain to do, but all the calculations happen very quickly and those of us lucky enough to hear take it for granted. Although everyone's heads are slightly different it is still very much possible to give great realism to anyone who listens to Binaural recordings.
Binaural stereo is a very little used format and it gives arguably the best true surround sound representation possible. When traditional stereo is played back over loudspeakers, it sounds similar in headphones and gives a very acceptable soundfield. However, binaural is designed for headphone listening only and when it is played back over loudspeakers, it does not give anything close to the same effect as when it is heard in headphones.
Think about it: a sound happens close to the left ear. It reaches the left ear binaural microphone which records the sound slightly earlier and at a much higher level than the right ear binaural microphone.
If this binaural stereo recording is played back over headphones, the left channel will be fed to the left ear of the headphones, so your left ear will receive this sound, slightly earlier and at a much higher level than the right ear, as it happened when the sound was recorded.
If this stereo recording is played back over loudspeakers, both of your ears will hear the sound from the left speaker, and both your ears will also hear it a little later and more quietly from the right speaker. This gives some level of spaciousness but not a patch on listening to the sound through headphones. If you are not convinced, try both methods and see!