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There is an interesting phenomenon in choral (and perhaps also instrumental?) singing in which typically four voices are arranges in such a way that a 'fifth voice' or 'ghost voice' can be heard. It is not terribly well documented, but Barbershop makes use of it fairly often (see here for some explanation and here for some audio example. I've also found some examples of traditional 4-part songs from Sardinia where this phenomenon is used, as thoroughly described here (only in French), including frequency analysis and all.

What examples of the same phenomenon in classical music. Most examples can probably be found in Renaissance music, but I am not sure of this. I found one very good example in a piece by Cipriano da Rore: Mia benigna fortuna (Audio example here). In this piece, at the end of the first phrase, you can clearly hear a voice that isn't actually sung. This is the score:

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I would very much like to hear if people know different examples of the same phenomenon in classical music, perhaps in Renaissance music but maybe also in other styles. Also, is anyone aware of literature on this topic specifically?

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This is a phenomena caused by subharmonics that naturally occurr when waveforms are combined. It's not an answer but you might want to check out Throat singing. Joe satriani uses it in where the opening effect is created by moving the guitar around the room such that it resonates with a different harmonic, changing the sound. – Alexander Troup Sep 2 '13 at 14:33
I think it is important to clarify exactly what is being discussed - subharmonics, "ghost tones" or "implied harmony", combination tones, and just intonation are all different subjects and I think, are being mushed together here in a misguided albeit earnest thought. Alexander Troup - could you explain in specific detail how subharmonics may be in play? I currently do not see the correlation. Also, I listened to the excerpted passage above about a dozen times and was unable to hear the phenomenon described. – jjmusicnotes Sep 2 '13 at 17:54
Good point. The specific phenomenon that I am looking for (regardless of the name you may attach to it) is the one where the harmonics of the notes that are actually sung together produce a sound that 'sounds' as if there were a fifth voice singing (hence the term 'ghost voice'). While experimenting with a choir, we found that it absolutely works best in just intonation (which makes sense), but even with inexperienced choirs the phenomenon can be observed. – Yellow Sep 3 '13 at 9:13
I am studying the traditional chants of Sardinia where there are 4 singers utilising a type of throat singing and also explores varying harmonics, these are some interesting resources.… – user19504 Mar 19 '15 at 18:37

Adding an example to jjmusicnotes' great answer: a ghost "tenor" (that is the third voice from the top) happens in many cases where two flutes or even a flute and a clarinet play a minor third apart in the range near the top of the treble clef staff and create a difference tone of 2*frequency(lower) - frequency(upper) which is also approximately minor third below the lower note, creating the impression of a diminished triad. An acoustics textbook I once read mentioned this as taking place at the end of a flute duet in a symphony by Vaughn Williams. I've heard it very strongly when playing a flute duet by Kuhlau (op. 81, no. 1) on flute and clarinet at m. 114 (1:28 at

; score: -- it's noticeable on the recording but incredibly loud when played with flute and clarinet. Of course the acoustics of the space have a lot to do with whether ghost voices emerge or not; hence why the Sardinians you mention sing very close to each other, facing inwards. (In their music, the fifth voice is called La Quinta or La Quintina -- the little fifth; note the feminine)

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+1 for an example that is not vocal! I'd be interested to find an example of the clarinet + flute version; I haven't been able to find it on YouTube or anything. – Yellow Sep 20 '13 at 10:22

As you mentioned in your question, there is little documentation about this phenomenon. Therefore I will preface my answer by saying that it (my answer) is speculation based from what knowledge I have of acoustics, historical performance practice, and literature.

I am not aware of any piece of music that was conceived with the intention of being constructed with or around the ghost-voice phenomenon. Considering that it is most prominent using just intonation, we could then surmise that musicians during the Renaissance and early Baroque periods most likely experienced ghost-voices since secular musical material consisted dominantly of motets and chansons and Just Intonation was the primary tuning system.

That said, since the tuning system itself was different (and the notation stayed the same, generally speaking,) that would mean that even if Renaissance motets were sung in a contemporary setting, they would be sung and tuned in an Equal-Temperament system. Therefore, to properly experience this phenomenon in the literature, you would have to time travel approximately 500-700 years in the past in order to hear the music in its proper (original) temperament.

Why is this important? Why does it work best with Just Intonation?

The answer to this is two-fold: the overtone series, combination tones, and overtone singing.

Okay, maybe it's three-fold.

In Just Intonation, the emphasis is on tuning perfect octaves and fifths as they are the easiest interval to hear apart from the unison. These intervals were tuned "perfectly" - regardless of their proximity to other, less important intervals.

Okay, so why does that matter? The answer is: Organs.

For their lowest pitches, pipe organs actually make use of their own phenomenon called combination tones in which two pipes of equal length will vibrate at the same pitch adjacent to one another. The additive combination of their frequencies / wavelengths produces a perceived sound an octave lower.

Singing a perfect fifth or a perfect octave in Just Intonation allows combination tones to flourish as they are tuned to small whole integers and not a fractional ratio like Equal Temperament. If you follow the link on combination tones, you'll see that they can even produce multiple perceived pitches as the "sum" or the "difference" between the two pitches.

Therefore, when you experience a "ghost voice" in a piece of music, it is the result of combination tones highlighting upper partials in the overtone series - creating the illusion that more pitches are being produced than are physically being produced.

Other examples of this type of phenomenon may be found in Tuvan Throat / Overtone Singing in which individuals manipulate their vocal folds to reinforce particular harmonics - frequently often able to produce several pitches simultaneously. These are quite a bit different than combination tones, but it is part of their performance practice.

From Tuva, cases may also be made for Tibetan throat singing and perhaps even Russian Orthodox singing technique as well. So, while it is difficult to produce documentation or literature in the Western musical tradition concerning "ghost voices" examples of this phenomenon can be logically considered to have existed in historical practice and in Eastern cultures around the world.

Hope that helps.

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+1 That's all the pieces I would've mentioned, but explained far more coherently than I could've done. :D – luser droog Sep 5 '13 at 4:33
@luserdroog - Thank you, you are kind. Glad to hear my answer made sense, haha. – jjmusicnotes Sep 6 '13 at 0:39
Thank you for your very elaborate answer! You bring up many good points, but I want to recify one thing: I do not agree that when we currently sing Renaissance and/or Baroque music, it is sung in equal temperament. In fact, I know a great many choirs that are trained in using just temperament (and in fact, I think every decent choir should be trained in this), which can be used not only in Renaissance/Baroque, but even in contemporary music. So I don't think we'd have to travel back in time at all: on YouTube there are plenty of performances using just intonation. – Yellow Sep 9 '13 at 13:41
@Yellow - I agree. Unfortunately this practice isn't standard for every contemporary choir, and some would not be able to hear the difference. So, it is important to be aware of this fact when listening to youtube or (God forbid) Naxos recordings. – jjmusicnotes Sep 9 '13 at 20:35
Your description of combination tones for pipe organs is wrong -- it's two pipes at different pitches (usually a note and a fifth above), and thus different lengths, to produce the effect of a lower pitch. – Dave Mar 19 '15 at 19:03

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