Missing Fundamental = 7th Chord

I came across a psychoacoustic phenomenon where humans perceive a tone that isn’t really there, called the “Missing Fundamental“. Many musical sounds are comprised of harmonics that are integer multiples of a fundamental frequency.

If you only have all the harmonics without the fundamental, then the brain hears the fundamental.

This gave me the idea of combining notes to achieve this same effect.

Assuming each note is comprised of a harmonic series, then the fundamental of the base note is twice the frequency of the desired “missing” fundamental.

We should be able to add notes at any frequencies where harmonics of the missing note should appear.

Fake Note Harmonics 1 2 3 4 5 6 7 8 9 10
Bass Note (C) 1 2 3 4 5
5th up (G) 1 2 3
10th up (E) 1 2
15th up (B) 1

These higher notes are not exactly the harmonic frequencies in equal temperment, but are close enough. (C, G (+2 cents), E (-14 cents), B (-32 cents)). Many instruments don’t have harmonics at precise multiples of the fundamental, and in Just Temperment the top note is a Bb.

So it is interesting that the C Major 7th, or C Dominant 7th chord could produce a sense of playing a G lower than the lowest note, when using this voicing.

However, the effect is probably better if the volume of the higher notes is reduced so that the amplitudes of the harmonics is more like a real instrument.

This effect is indeed audible if you listen really closely.