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Double Bass Tube Pre for no-amp-gigs

It's just distortion- both clipping (distortion of the amplitude range) and harmonic distortion (distortion of the frequency range). All amplification circuits introduce some distortion, but solid-state circuits are generally designed for the minimum amount possible within budget, while tube designs are often designed to take advantage of the way they distort, which is typically thought of as "musically pleasing". Different types of amplification circuit introduce different types of distortion. It is entirely possible (and common amongst audiophiles) to design a tube amp that has less distortion than a typical solid-state amp.

Note that "distortion" in this context means "any alteration of the signal", it does not necessarily mean a grindy/buzzy noise.

Well, not exactly. The "warm and fuzzy" is usually the result of the transfer function and not distortion. In English, the transfer function yields the frequency response. Distortion is not typically "any alteration of the signal" as that would include mere changes in amplitude. Frequency response anomalies (changes in relative amplitude as a function of frequency) are not considered distortion. Distortion usually refers to circuit non-linearities that produce new frequencies (e.g., harmonic distortion, intermodulation distortion, transient intermodulation distortion). Harmonic distortion is not "distortion of the frequency range." It is as much an alteration of the time waveform as is clipping. In fact, harmonic distortion results from types of non-linearity that causes the addition of frequency components that are harmonics of the original signal. The profile of the harmonics produced can differ across tube and solid-state circuits.

As I wrote in an earlier post:
...The advantages of tubes in sound reinforcement stem from their overload characteristics. Many guitar players prefer them for the characteristic nature of the distortion products they produce. It's part of the "the sound." When most of us amplify our DBs, we aren't looking to push the amplifier into overload.

On the other hand, some would argue that because some tube circuits distort more "gracefully" in that they produce largely even-order harmonics, they are preferred. Given a properly designed and used modern solid-state amplifier, however, this should not be an issue. That, coupled with the fact that tube-based amps are more delicate and potentially less reliable gives them, IMO, no advantage.

Now, sometimes, pushing a tube circuit well beyond its near-linear range is quite intentional in which case it it part of the sound. It is also the case that typical tube circuits operating within their normal limits produce greater amounts of distortion than do solid-state circuits. The issue then is one of audibility and tolerance. How much distortion is too much? The truth is that it depends on the type. Even-order harmonic distortion (produced by some tube circuits) is less aversive than is the odd-order distortion typical of solid-state circuits. It is the case, however, that typical solid-state amps when not pushed into overload produce vanishingly small amounts of distortion. In the audiophile world, I don't think you'll find ANY tube circuit from the 1940s on up to today that actually produces less distortion than a good modern solid-state amp. In fact, some of the most expensive modern tube amps actually produce amounts of distortion that are orders of magnitude greater than typical solid-state amps and much greater than the most linear of the best tube designs from decades ago. So, no, it is not at all common among audiophiles to have tube circuits with distortion less than modern solid-state amps. They essentially do not exist. (The possible exceptions are "laboratory" tube amps. I know these well and have used them in my research). Of course, there are other parameters that are important in amplifier design but I won't go there now.

Now back to the warm and fuzzy. To the extent that exists, it is often related to the frequency response anomalies of the transformer-coupled tube circuit. It is quite possible and, in fact, rather easy to build that transfer function into a solid-state amp. Many manufacturers do exactly that.
 
Distortion is not typically "any alteration of the signal" as that would include mere changes in amplitude.
I can see how perfect amplification with no other alteration of the wave other than scale would not be considered distortion, but so far my engineering teachers have insisted that any change to the shape of the wave is distortion. Perhaps in your field the definition is more specific, or perhaps my classes have not gotten to the point of needing more specificity.
Harmonic distortion is not "distortion of the frequency range." It is as much an alteration of the time waveform as is clipping.
Captain obvious here, the frequency range is the time waveform. ;) However I'm just a first year engineering student, so I'm not really trying to one-up or anything like that- I'm open to being corrected. Just making conversation. :)
 
I can see how perfect amplification with no other alteration of the wave other than scale would not be considered distortion, but so far my engineering teachers have insisted that any change to the shape of the wave is distortion. Perhaps in your field the definition is more specific, or perhaps my classes have not gotten to the point of needing more specificity.

I am specifically discussing the engineering field and communication engineering in particular. Now that I'm at my office, I pulled out the IEEE Dictionary. This is the "bible." Here's the definition of distortion:

An undesired change in waveform. The principal sources of distortion are: (1) A nonlinear relation between input and output at a given frequency, (2) Nonuniform transmission at different frequencies, and (3) Phase shift not proportional to frequency.

Indeed, definition #2 would include anything but a flat "frequency response." It is the case, however, that in the practical engineering world one does not typically speak of non-uniform frequency response as distortion. A prime example is the technical specification of amplifying devices. They include distortion specs (harmonic, intermodulation, TIM) and then the deviations from uniformity of the frequency response and its bandwidth. That is, frequency response anomalies (changes in relative amplitude across frequency) are not included in calculations of percentages of and specifications of distortion. One would not say to a colleague, "Man, that amplifier has massive distortion" when referring only to frequency response anomalies. One might say, "Man, the transfer function is a problem." :) By the way, if we wanted to split hairs on the definition, an amplitude change at a single frequency often is "undesired." Essentially no one refers to that as "distortion."

Captain obvious here, the frequency range is the time waveform. ;) However I'm just a first year engineering student, so I'm not really trying to one-up or anything like that- I'm open to being corrected. Just making conversation. :)

Yup-- I specifically chose not to bring up the principle of "time-domain/frequency domain duality." Any alteration of the time-waveform manifests itself in the frequency domain and vice versa. You, however, chose to identify clipping with "distortion of the amplitude range" harmonic distortion with "alteration of the frequency range." Both are both! That is, both can be viewed in terms of the alterations they produce to the time waveform or the spectrum. It is true that clipping is more intuitively understood in the time domain as harmonic distortion is in the frequency domain but neither, as you know, are exclusive to those domains.

Hey, good luck with those engineering classes. Been a while since I sat in those. As you might suspect, I'm now on the other side of that fence.