“You keep using that word. I do not think it means what you think it means.” Inigo Montoya in The Princess Bride.
I get a kick out of that statement as it aptly demonstrates how a word can have different meanings to different people and in different contexts. Certainly that is true of the word "distortion." Here are some thoughts that may shed some light on the subject of distortion as it applies to virtual organ systems.
What do we mean by distortion? There are several possibilities, all of which can and do apply to sound reproduction:
1. Source distortion. In the simplest sense, any audio waveform other than a pure sine wave is the product of distortion. A pure sine wave (think of the 60 or 50 cycle hum caused by a ground loop) is incredibly boring. If you doubt this, just cue up any pure sine wave (such as the Virtual Minirator found at this link: http://realtraps.com/info.htm) and see how long you can tolerate having it drone on. It is, in fact, distortion (or nonlinearities, if you prefer) applied to a basic sine wave that make a sound potentially interesting and even musical.
The process occurs when a pure sine wave is distorted (by applying filters and modulation to an electronic signal, or using different shapes, sizes, materials, etc. for physical instruments) and thereby creates overtones that change the fundamental nature of the waveform and produces the essential character of its tone. Qualities such as attack, decay, compression, etc. are also forms of distortion that affect the nature of the tone. (For an excellent discussion of these concepts, see Everett Truette's Organ Registration available at this and other links across the Web: http://imslp.org/wiki/Organ_Registration_(Truette,_Everett_Ellsworth).)
As an aside, whenever discussing overtones or the harmonic series, it is helpful to keep in mind the relationship between the two, i.e., the first overtone is equal to the second harmonic, etc. (see here, for instance: http://www.sengpielaudio.com/calculator-harmonics.htm).
2. Amplification/Audio Interface Distortion. The types of distortion we most frequently hear about are harmonic distortion (including total harmonic distortion or THD) and intermodulation distortion (IMD). Both of these kinds of distortion are created by nonlinearities in the amplification/audio interface circuitry that further change the input waveform (or signal) in potentially desirable or undesirable ways.
A quality tube amp, for instance, adds a certain amount of lower-order even harmonic distortion that is generally considered desirable even when not pushed into an overdriven state (such as high-quality hi-fi tube amps like these: http://www.manley.com/hifi_power_amplifiers.php). A solid state amplifier, on the other hand, if overdriven will add unpleasant-sounding high-order and odd harmonics to the sound. By the same token, amplifiers designed to have the least effect on the input waveform or signal will nearly always be solid state.
So, just as certain distortions and nonlinearities combine to create a certain tone in the first instance, the amplification/audio interface circuitry used can leave unchanged, detract or add to that input signal or tone depending upon how much and of what quality distortion is injected into the audio chain.
It is important to keep in mind that numbers cited for THD and IMD are often misleading and potentially useless. A seemingly helpful resource (based upon the viewable pages online) is the book "Rethinking Distortion: Towards a Theory of 'Sonic Signatures'" by Bernd Gottinger, New York University, 2007 (a sampling of pages from the book is viewable at this link: https://books.google.com/books?id=G3vkSkvTf-cC&pg=PA37&dq=rethinking+distortion+intermodulation&hl=en&sa=X&ei=flKDVYG6CY-vogSCh4a4Dw&ved=0CB4Q6AEwAA#v=onepage&q=rethinking%20distortion%20intermodulation&f=false).
Gottinger notes, for instance, at the bottom of page 36 that a particular THD number can be "misleading because it does not reveal the spectral pattern, or distribution of the energy over the multitude of harmonics." Thus, just as two organ pipes with the same overall volume can have dramatically different tones from one another, amplifier circuits with the same THD numbers may just as well have very different effects on the input signal, with some being more desirable than others (such as the tube amp example given above).
Gottinger's discussion of IMD beginning at page 37 is also quite useful. While harmonic distortion is always seen as integer multiples of the fundamental (just as the harmonic series of an organ pipe consists of the fundamental and its integer multiples; see Truette cited above), IMD "deals with summation- and difference tones between two input tones." Of particular concern to us is that "IMD is considered a more serious degradation of the audio signal, because unlike harmonic distortion, intermodulation products are NOT musically related to the fundamentals, therefore effectively creating additional dissonant overtones." Gottinger also notes that intermodulation products are difficult to measure for a variety of reasons.
Concerning the audible affects of IMD, on p. 38 Gottinger quotes Newell describing IMD as "a little like trying to listen to a good hi-fi system whilst somebody is just outside the window using a chain saw, whose noise production is dependent on the level and spectral density of the music, though not directly proportional to either."
Perhaps even most importantly for our purposes is Gottinger's assertion that the distortion percentage figures provided in the spec sheets for audio equipment (for THD or IMD) are not of great practical value without some type of metric that determines "perceptual relevance." In other words, without knowing if and how distortion is actually perceived by the person listening to the final output, the quoted numbers are of potentially little to no value. As Gottinger observes (beginning at the bottom of p. 34), despite repeated calls for a perceptual weighting of distortion measurements, most audio equipment manufacturers continue to publish THD and IMD numbers "that are essentially meaningless perceptually."
That published distortion figures are of essentially no practical value further reinforces the conclusion that many of us have drawn that there is simply no substitute for actually hearing what a specific system sounds like in its installed space.
3. Reproduction Distortion. So far, I have only talked about IMD as it relates to the amplification/audio interface portion of the system. However, IMD can also be a product of the physical reproduction portions of the system as well. Other forms of distortion that can also affect the physical reproduction side include comb filtering, standing waves, early reflections and so forth. As stated earlier, essentially anything that further modifies the original sound is a form of distortion or nonlinearity. A bad room (or faulty speaker placement in a room) can produce audible distortions such as comb filtering or standing waves that are far more unpleasantly noticeable than a bit of intermodulation distortion.
Where IMD is perhaps most noticeable in a virtual organ system is when playing a group of notes and ranks simultaneously through the same driver. While with a pipe organ each pipe is in effect its own driver and therefore perfectly capable of producing its own distinctive voice with integrity regardless of what other pipes may also be sounding (assuming the wind system is sufficient), in a virtual system, the driver is having to deal with several notes and ranks being played through it at the same time with IMD resulting from the non-harmonic interactions between the harmonic series of various of the individual notes (i.e., the harmonic series of one note may not coincide with the harmonic series of other notes, thus causing the non-harmonic intermodulation products that comprise IMD). And because only a single driver is reproducing those multiple notes, the effects of IMD in that situation can be quite pronounced.
Various ways in which virtual organ designers attempt to get around the problem of IMD at the driver level is to cycle notes and ranks in such a way as to avoid having the individual notes of a minor second sounding simultaneously through the same driver (known as C/C# cycling), octave cycling, etc. This was an important enough consideration in the early days of electronic organs that Baldwin Co held a patent issued in 1967 titled "Multiple speaker sound output system for reducing intermodulation distortion." The abstract of patent is a fascinating read and includes a succinct discussion of the effects of IMD on electronic organ tone: http://www.google.com/patents/US3327043. Of course, with the patent protection having long since expired, now that and other systems for reducing IMD at the driver level are readily available and easily implemented in programs like Hauptwerk.
Dealing with other forms of distortion at the reproduction end (such as standing waves, comb filtering, etc.) is a whole other area of discussion that requires attention in order to achieve the best-sounding virtual organ system. For a wealth of information on these sorts of issues, see the various resources available at Ethan Winer's RealTraps website, including this one: http://realtraps.com/art_basics.htm. One observation I would make based upon my experience and research is that more is not necessarily better. Indeed, the more drivers involved with a sound reproduction system, the more likely it is that undesirable artifacts such as comb filtering or low frequency cancellation/reinforcement will be an issue.
4. Hearing Distortion. Philip Newell in his book "Recording Studio Design," 3d Edition, Focal Press 2011, cites to the research concerning how the physical shapes of individual ears, heads, etc. play a role in how sound is perceived. Suffice it to say that we all hear things a bit differently because our individual physiologies as they affect hearing and sound perception differ from one another.
5. Other Distortions. I have purposely avoided discussing other types of distortion such as digital clipping (source overdrive), analog clipping (amp/preamp overdrive), speaker overload, etc. because those kinds of distortion are entirely avoidable and would perhaps be better addressed in a discussion of how to properly gain-stage the audio chain or adequately specify amps and drivers (much of the discussion in this thread has already addressed the latter).