A question about feedback mechanisms

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Electric guitar feedback devices, such as the ebow and Sustainiac, aim to produce artificial sustain by using pickups and gain stages to resonate strings. While marketed as capable of "polyphonic sustain," users often find that only one string predominates, similar to natural amplifier feedback. The discussion suggests that sustaining multiple strings simultaneously is feasible only when they are harmonically related, and that the limitations arise from the use of a single transducer and gain stage. The complexity of string interactions and the presence of harmonics complicate the realization of true polyphonic sustain. Ultimately, many marketing claims may exaggerate the capabilities of these devices.
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I'm not sure how many of you are musicians, so i'll preface my post with a bit of background.

There are a number of products on the market for the electric guitar which produce artificial feedback. They basically consist of a pickup, gain stage and magnetic driver. The idea is the device will sustain a string indefinately when activated. They usually come with a harmonic mode switch to sustain the string in a number of different harmonic modes above the fundamental.

The most popular sustainer product (the "ebow") is a small handheld unit which sits over a single string. It is only designed to sustain a single string at a given time.

There are a number of competing products which consist of a pickup that transduces the signal from all of the strings simultaneously and drives all of the strings simultaenously (through a single gain stage).

A similar variant is a device called the "sustainiac" which uses the guitar's output signal to drive a neodymium exciter which is literally clamped to the body of the guitar, causing the strings to resonate by vibrating the body of the guitar.

Most of these devices claim to offer "polyphonic sustain", that is they will allow any number of strings to be sustained simultaneously.

In my experience, however, this doesn't seem to be the case. The same is true for natural feedback that one would obtain from an amplifier turned up very loudly (with loads of preamp gain). If you release the strings, one string will always end up being dominant and will preferentially sustain over the others.

I've found that these sustainer products are capable of sustaining multiple strings simultaneously when they're intimately harmonically related, (for example a string and its higher octave counterpart).

I have been trying to find some insight into why this occurs using control theory, but I haven't had much success. My theory is that if the sustainer product featured six independent transducers (one for each string, commonly referred to as a hexaphonic pickup), six independent gain stages, and six independent drivers, then surely it would be able to sustain six strings simultaneously?

Why is it that a single transducer, single gain stage and single exciter is only capable of resonating at the one frequency.

What's the critical limiting component here?
 
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In theory, it is possible to decompose a complex signal into frequency components. Assuming that each string produces a pure and unique tone, then it should be possible to feed those back.

In practice, it can be very difficult. Srings produce harmonics as well as the fundamental. Strings interact with each other.

So, my guess is that many of the marketing claims you talk about are just puffery. The real devices are imperfect.
 
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