Timbre cannot be understood with linear Fourier maps because it is a result of a physical event perceived and directly interpreted by us in our own time domain ...
You do not think as an acoustician but as a dac seller...
You distorted what i intend to say to recover your audio seller pitch...
Your understanding of what is "timbre" is obsolete...
Read this material, not yet in Britannica,and link them all together to have a small idea about what i talk about ...
https://www.nature.com/articles/s41467-024-45812-z
https://www.pnas.org/doi/10.1073/pnas.2308859121
Timbre is always a mystery a problem unsolved in acoustics but we know that it cannot be described by Fourier linear maps computations... WE need something else described in the article of Akpan J. Essien, the last article here above...
And yes Timbre result of the microdynamics vibration of the material components of the sound source then the vibrating object communicating directly to us listener his various qualias... It does not result of your gaze on a electronic dial as a dac seller making his selling pitch...
In a word: there is a physical invariant in the evaluation of Timbre which is directly perceived as a qualia of the vibrating sound sources microdynamics....Timbre is not a mere figure on your electronic dial, it is a bit more complicated ....it is why acoustics is not just engineering but a fundamental multidisciplinary field...
Microdynamics do not create or lead to timbral characteristics — not if you truly understand what you’re talking about.