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Q. What made me hear a phantom low note when singing in a choir?

By Hugh Robjohns & Mike Senior

I recently attended a choir workshop in a large, square, empty church. The space had incredible acoustics and we measured around six seconds of reverb, even with 40 people in the room. At one point, the tutor had us all stand in a circle and sing particular notes of a scale increasing in pitch at the following intervals: 1, 5, 1, 3, 5, flat 7, 1 and 2, starting an octave below middle C. We all just held an ‘ah’ sound at our given note and, very quickly, a tone two octaves below middle C was clearly audible, appearing to come from different parts of the room — it sounded like there was an invisible nine–foot man singing in the middle of us! What on earth was going on, and can it be achieved with other instruments? Can it be used in any practical way in music–making?

Ellen Maltby

SOS Technical Editor Hugh Robjohns replies: This sounds amazing! I suspect that the note intervals generated an interference beat–tone which resonated as a standing wave within the hall — the standing wave bit seems certain given your comment about it being audible at specific places within the room. I imagine the same would be possible with anything that generated suitably sustained tones of the right pitch — relatively pure–toned instruments, rather than very harmonically complex ones.

A ‘missing fundamental’  (dotted line) can sometimes be ‘heard’ if enough of its harmonics are present.A ‘missing fundamental’ (dotted line) can sometimes be ‘heard’ if enough of its harmonics are present.Could it be practical for music-making? If it’s related to standing waves, then it will be totally building specific, in which case it might be useful for a piece that will only ever be performed in the one place, but it would fail if performed elsewhere (assuming it didn’t match the precise dimensions). I have in the back of my mind that some monastic choral music only works in the monasteries where it was written — and that may be for similar reasons... or that might just be the random regurgitations of a befuddled mind!

SOS contributor Mike Senior adds: I’d agree with Hugh that acoustic interference effects almost certainly play an important part in creating the ‘phantom bass singer’ you heard. In other words, the frequency differences between note fundamentals are creating interference ‘beats’ at frequencies in the audible spectrum — in your specific case at a frequency of around 65.5Hz for C2 (two octaves below middle C). The chord you mention provides maximum opportunity for this, because it neatly arrays the fundamental of each note 65.5Hz apart from both its neighbours — assuming, that is, that the choir are singing unaccompanied and tuning amongst themselves by ear, using what we call ‘just’ intonation rather than the equal–tempered intonation used by most keyboard instruments.

However, the acoustic aspect of this effect was probably only part of what you heard. A very similar phenomenon has been demonstrated to occur within the physiological apparatus of the inner ear (so it doesn’t rely on tones mixing in the air), as well as entirely as a perceptual illusion (difference tones can be created even between sounds fed independently to separate ears over headphones — fairly freaky if you think too hard about it!).

But why do you hear this added tone as forming part of the choir, rather than as some kind of separate note? I think this has something to do with the ‘missing fundamental’ effect, whereby we judge the pitch of a note according to its fundamental frequency, regardless of whether we can actually hear the fundamental. In other words, we’re very adept at perceptually extrapolating what a note’s fundamental should be even when we’re only presented with the upper partials of that note’s harmonic series. A common audio–engineering ramification of this is that we can still recognise low–pitched notes when they’re coming through a small speaker that could never produce their fundamental frequencies.In your situation, I reckon that your brain is (incorrectly) identifying the presence of a C2 note within the choir texture, simply because so many of the important frequency components of that note’s harmonic series are present. Your perception is filling in the missing fundamental, making it appear as if there’s someone in the choir channelling the spirit of Barry White!

So what can we use this effect for? Not much, to be honest, simply because you need a stack of quite pure tones in ‘just’ intonation to create appreciable difference–tone levels, and the appeal of that kind of chordal texture is fairly limited, not least because most Western music is based around the deliberate tuning impurities of the equal–tempered scale. Plus, the relationship between musical intervals and the difference tones they generate is rather counter–intuitive from a musical perspective — whereas a C3–G3 interval produces a difference tone at C2, the C3–F3 and C3–A3 intervals give, respectively, difference tones a fifth below (F1) and a fourth above (F2). In practice, this pretty much rules out using difference tones creatively for most musicians, unless your music–making tends to involve burning a lot of incense. In fact, the most practical application of the idea I’ve discovered is where some church organs use difference tones (termed ‘resultant tones’) to mimic the effects of deep–pitched pipes that would be physically too long to install.

Published February 2015