Hi mwseriff,
I do not take issue with your conclusions. If the end result is music, #1 the judgment is going to be personal, and #2 looking at a waveform doesn't tell you as much as you'd like to know about how it will ultimately sound. So the fingers and ears have to be the final judge.
I'm an engineer first and a musician second, so I do look at musical electronics from an analytical perspective. I also readily acknowledge that to the extent I studied audio electronics, the focus was on creating amplifiers with low distortion and flat frequency response - for "hi-fi". So, almost nothing I learned is relevant to creating guitar-oriented musical audio devices. I also did not study tubes in school although one chapter of my semiconductor electronics textbook (written in 1966) does deign to talk about vacuum tube circuit models.
My comparison of these two circuits was triggered by Joe's statement along the lines of "I'm tired of op-amp and diode distortions". I took a look at some (clone) schematics online, and although the Klon and TS are both op-amp and diode distortions, at their core, the way they generate distortion is quite different. You could, for example, take the heart of the TS and drop it into a Klon circuit (or vice versa), and what would happen? Would it sound more like a Klon, or a TS? I don't know. Who wants to try? I think the TS circuit is pretty clever, but it's also certainly not how any tube amp I am aware of actually operates.
I've noticed that almost every diode distortion circuit I've seen uses identical diodes, so the distortion thus created will favor odd rather than even harmonics. This effect has a pretty strong correlation between what the waveform looks like, what the spectrum looks like, and what it sounds like. Once you know the difference between the SOUND of even vs. odd harmonics, then you can make choices in your own experiments. Maybe you want one, the other, a switch or maybe a continuous blend between them. My suggestion to anyone who wants to build a diode-based distortion is to at least put a switch in there so you can unbalance it. If you don't like that sound, OK - leave it out. But maybe that was just what you were looking for.
For people who want to go beyond paint-by-numbers DIY, I think some understanding of how things really work is important. For example, power amp distortion from a single ended tube amp sounds different from a push-pull amp, and furthermore that may also depend on the type of phase invertor circuit you are using. No amount of analysis will tell you which one you will prefer, if any of them. However, once you identify something you like, knowing why it works can only be helpful as you continue your pursuit to recreate it and make it better.
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