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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:

enter image description here

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?

  • 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 youtube.com/watch?v=SINl5JY7LhI 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
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    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
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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: http://erato.uvt.nl/files/imglnks/usimg/c/cd/IMSLP15021-3_Brilliant_Duos__Op_81__2_Flutes_.pdf) -- 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)

  • If two pitches are a minor 3rd apart, the third pitch you mention is a major, not a minor, 3rd below the lower. The three pitches' frequencies are in the ratio 6:5:4. The difference pitch more likely to be heard, I think, is the one whose frequency is f(upper)-f(lower). This is 2 octaves below the pitch you describe. – Rosie F Oct 8 '18 at 9:08
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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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    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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    @ Dave Thank you for the source - it was an interesting read. Apparently, we are both mistaken, according to the article combination (or "resultant") tones do not exist. – jjmusicnotes Mar 22 '15 at 16:04
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I am not an authority on the subject of ghost/fifth voice -- but I do sing in choir and in a Barbershop Chorus / quartet. the latter of which intentionally seeks to produce the Fifth voice quite often in songs.

It is my understanding that the fifth Voice is achieved when the vibratory frequency of the 4 part vocalizations blend together in a precise way. You hear the phenomena mainly with voices like those heard in barbershop.

The equal temperament tuning of modern instruments (A-440), prevents the necessary original frequencies of vibrations from occurring. However, the human voice is not restricted in the way that a piano keyboard is restricted. The human voice can sing all the frequencies between the notes on the keyboard.

At one point in the past -- it was decided that there were advantages to having more range /notes on the piano keyboard, but it wasn't as simple as just adding notes to the left and right of middle C. This was because the further you went out to the left or right the more the notes tended to become unpleasant when combined with other instruments.

To get the wider range of notes, it was decided it would be best to make ALL the notes "equally out of tune" (The notes at the extremes sounded better but it left the other notes slightly less pure). The difference between the new notes vs original notes was hardly perceptible to the average listener.

The human voice (and some instruments) can can shift frequency away from the standard modern tuning to achieve fifth /ghost voice.

This may be oversimplistic so I welcome corrections from others if they need to be made.

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