Originally Posted By: Gordon Scott

The main place where we view things differently is in how/where colouration and distortion overlap.
I look at this (like many things in life) as being on a spectrum. Where does "coloration" end and "distortion" begin. Ask a bunch of musicians and you'll probably get a bunch of different answers. That's why I gave Rain On Me as an example of what I consider fat, distortion-free bass.

You mention FFTs, so you'll understand well spectral data. Even-order harmonics tend to sound like part of the intended sound ... complementary; sawtooth-like waves. Odd harmonics are those that sound harsh; square-like waves, and the ones it's clear you definitely don't want. Worse still by far are intermodulation products.

Yes, I am well aquainted with FFT (Fast Fourier Transform). Here is a copy of a couple pages out of one of my engineering handbooks. I apologize for the poor quality, my handbook refused to sit flat on the scanner glass. What I have labelled "A" is a time-domain measurement with duration less than 250 ms. The Y-axis is acceleration, but could easily be velocity, displacement, force, electrical current, strain, pressure or other engineering quantity. So this transient signal could be the electrical current generated by a bass guitar pickup as a result of a sting being plucked. Of course, this signal (perhaps converted to voltage) is then sent to the amplifier to be shaped and amplified. Pickup design and amplifier design could fill many books, just like the required steps to process vibration data could fill many books.

What I have labeled "B" is the result of an FFT algorithm being fed the data from "A" and is in the frequency-domain. The peaks are of great interest to the engineer involved in interpreting this plot. So is the fact there is no significant energy beyond 2 kHz. Studio One and many other DAWs have this capability and the screenshot in the original post is such an example.

As Team Lead on the Boeing project I previously described, it was my responsibility to oversee the processing of the multi-giga byte, tri-axial accelerometer data set collected during the flight test. Before the flight test I needed to learn the mathematics behind the FFT algorithm so that I could write a custom program to process the data we would collect. It took me a couple of months of 12 hour days to understand the math, write and debug the code and finally validate my program against well-understood test cases. Then I assembled a small group of data processors (4 and a half junior engineers) that I could train to use my code and to do the actual processing. The end result was a set of laboratory-ready, broadband random vibration PSD spectra/profiles from 20 to 3200 Hz that when applied to our product would simulate (in the lab) an entire lifetime's worth (measured in years) of mechanical fatigue and other damage. The time required to do this lab simulation on our military-grade shake table was measured in days. This allowed us to quickly identify and fix the flaw in our design. To tell you the truth, I miss this stuff, but equally true is I'm fascinated by music and the side of my brain that music lights up smile

I don't know if +++ this chart +++ this chart helps explain why odd-order, notably the higher ones, (clipping) harmonics can sound so bad. Even heavily distorted guitars try to avoid the worst of the upper harmonics. A small amount of some can help.

There's a good Sound-On-Sound article +++ here +++ that may or may not help you in getting the sound you want and may better explain than me what I've been trying to say.
Thanks for the web links, they're good background info.

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For me there’s no better place in the band than to have one leg in the harmony world and the other in the percussive. Thank you Paul Tutmarc and Leo Fender.