Continuing with the theme of auditory illusions, combination tones (or resultant tones), when heard in the presence of two audible pitches, can be quite startling. It’s as if there is a third pitch there. This ‘third’ frequency, however, is not actually present in terms of measurable frequencies or volume. It cannot be detected or measured on any spectrum analysis device. It is only the human ear which detects this phenomenon. If two singers each produce pure sine wave- like tones in different pitches, they can move these around, creating different interval relationships, producing the effect of a siren-like sweep of combination tones. The resulting siren effect depends on the relationship between the two changing frequencies produced by the singers, and by the direction they are moving (closer together, or further apart).
The ability of the listener to detect combination tones depends upon certain physiological, experiential and sensory factors. It seems to be related to a function of the brain to focus and categorize the experience. Singers skilled in overtone singing seem to be particularly adept at perceiving these tones.
The imagined frequency can be much lower than the original two. This is due to it being the difference in vibration between the two original pitches. These are known as differential tones.
It can also be higher than the original pitches, corresponding to the sum of their vibrations. In this case, the tones may be referred to as summational tones.
The effect may be especially pronounced given ideal acoustical properties of the space they are in. This is curious, since the differential tones themselves cannot be recorded or measured, yet the very architecture may enhance our ‘perception’ of sound.
The best experience I had in hearing these tones (both listening to other singers and participating in the singing), was in a modern ‘castle’ in the Czech Republic, which had a very unusual ceiling with vaulted areas that produced a very surreal ‘bonus’ acoustic effect.
I highly recommend experimenting with this phenomenon (with a friend), as it is sure to increase your listening sensitivity, and heighten your ability to hear the partials in your own voice.
Check out the Titchener Test for combination tones. It is an excellent self- study program for finding and expanding your level of intuitive listening (as opposed to ‘analytical’ listening). I would call it an ideal companion to the study of perfect and/ or relative pitch, and by extension, the study of overtone singing.
CommentThe seemingly never ending descending or ascending of pitches is an auditory illusion that can be reproduced with synthesized tones, superb acoustic orchestration or human voices. Albeit the human voice version of this experiment is a bit more tricky.
The vocal version requires a choir of at least 8-12 with full ranges, who is very skilled at overtone singing, to the point where they have great control over their dynamics. The reason for this is stated below:
My colleague and voice researcher Wolfgang Saus, explains:
“The effect is based on Jean-Claude Risset’s acoustic illusion. The formants are either fixed on /ɔ/ or alike, with first formant high, or second formant should rise continuously while the fundamental decreases. Towards the lower end of the glide the volume decreases and the voice starts softly with a high pitch again, each time ending a bit lower. The loudest part is always in the middle section of a glide.”
I will add to that, saying that collectively, the singers stagger their entries (seemingly at random) at the top end of the glide. This is what allows the illusion of the constantly descending pitch. Also, singers choose their own overtone to use each time, moving down in a parallel way, keeping the same overtone all the way down. Thus, each new entry may add a different ‘vowel’ sound to it. This further adds to the complexity of the harmonic texture of the sound overall.
In this piece of music, Arc Descents, composed by David Hykes, you will hear this effect starting at the 2:30 mark.
For a detailed explanation of what exactly occurs in a standard ‘Shepard tone’ sequence, please refer to the following Wikipedia pages: (Here you can also listen to audio examples)
Jean-Claude Risset on Wikipedia
For a splendid example of orchestration illustrating this effect, have a listen to Arvo Part’s Cantus in memoriam of Benjamin Britten
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