Occam's Razor: The Signal to Noise Ratio

A timbre experience is a subjective perception which come from a multidimensional set of interacting parameters and cannot be reduced to SNR concept and to a physical waveform...

Audio is not so much about the gear but about psychoacoustics...

«At this point, the signal can be regarded as having a very high acoustic SNR since there is no acoustic noise (distorted waveform) yet associated with the signal/waveform. (This may be the reason headphones are enjoyed by many.) Once it leaves the speaker, this waveform, the original signal, makes a beeline to our ears but it also travels to every corner of our room, where it is reflected and after a while, makes it to our ears as well. If these waveform reflections that are relatively loud hit our ears within the window during which we cannot distinguish their arrival time from the incoming original waveform, they become the noise that competes with the original signal/waveform and consequently lowers the signal to noise ratio. Reducing these competing waveforms in number or amplitude through absorption or diffusion will increase your SNR. You do want to retain some reflections for a sense of space and ambiance so pure absorption is not indicated. You just want fewer or softer competing waveforms (noise) so the original waveform (signal) predominates.»

All timbre information is contained within the original waveform.

From Britannica.com: "timbre, quality of auditory sensations produced by the tone of a sound wave."  

From DSP Guide.com: "The perception of a continuous sound, such as a note from a musical instrument, is often divided into three parts: loudness, pitch, and timbre (pronounced "timber").  Loudness is a measure of sound wave intensity, as previously described.  Pitch is the frequency of the fundamental component in the sound, that is, the frequency with which the waveform repeats itself. While there are subtle effects in both these perceptions, they are a straightforward match with easily characterized physical quantities.Timbre is more complicated, being determined by the harmonic content of the signal." 

"Harmonic content of the signal."  I don't know where harmonic content would reside other than in the waveform.

Again, it's all about the waveform and its purity. Psychoacoustics doesn't start until the waveforms have hit your eardrum. By then, damage done.

All timbre information is contained within the original waveform.

You forgot to observe the way our ears-brain-room will modify a recorded timbre and will transform it in an experienced timbre in a specific way for each different room and ears/brain.

Timbre is not reducible to a SNR analysis...

From Britannica.com: "timbre, quality of auditory sensations produced by the tone of a sound wave."

From DSP Guide.com: "The perception of a continuous sound, such as a note from a musical instrument, is often divided into three parts: loudness, pitch, and timbre (pronounced "timber"). Loudness is a measure of sound wave intensity, as previously described. Pitch is the frequency of the fundamental component in the sound, that is, the frequency with which the waveform repeats itself. While there are subtle effects in both these perceptions, they are a straightforward match with easily characterized physical quantities.Timbre is more complicated, being determined by the harmonic content of the signal."

Instead of these too simplistic definition read the article i suggested on psychoacoustics

http://acousticslab.org/psychoacoustics/PMFiles/Module06.htm

Timbre is not only determined by the harmonic content of the waveforms but by his time envelope and timing dimensions of the room also by the dynamic of the sound...

1. signal time variance (envelope)

2. degree of attack and decay synchrony of the sine components;

3. presence or absence of high-frequency inharmonic energy in the attack portion of a signal;

4. spectral energy distribution (frequency, amplitude and phase values of the sine components of a complex signal - may change with changes in intensity and register, even for a given instrument); and

5. spectral energy distribution time-variance (spectral flux or "jitter").

Your sentence here resume all your misunderstanding:

Again, it’s all about the waveform and its purity. Psychoacoustics doesn’t start until the waveforms have hit your eardrum. By then, damage done.

For sure you are right ...But the physical waveform in the room is an acoustic translation of the recorded waveform not a mere deformation or a perturbation or a mere loss from a so called pure signal but an acoustic positive-negative trade-off transformation which cannot be explained by only a SNR metaphor... For example crosstalk effect result in a loss of spatial information in all stereo system and had no direct relation to only measured SNR of the gear but resulted from physical stereo disposition and physiological conditions.

Then you are not wrong you forgot half of the story... Timbre is experienced in a room and with some ears... Then it is not only about electronic reproduction it is about acoustic translation ...Then it is more than just SNR meassures...

Psychoacoustics begins before the waveform has hit your eardrums. 😁It begins in the design of the gear itself , for example in the Dr. Choueiri design of his filters to erase the effect of crosstalk . This is way more than SNR physical measures, it is psychoacoustics design .

Psychoacoustics is the root and the canopy of the audio tree...Gear design resulted from this science at the end. It is way more than just SNR measures...Your are not even wrong and this is my point... I added only the part of the acoustic story you inconsciously  put under the SNR rug metaphor...

Audiophile experience is more than buying gear design with good measured SNR, it is also acoustics and psychoacoustics varying parameters in the TRANSLATION of acoustic recorded waveform for your room/ears/brain in another perceived experience which will differ from the recorded waveform by acoustic definition..

No audio system is perfect high fidelity reproduction ... They all translate in a relative way some experience, timbre and spatial acoustic qualities, which are not reducible at all to signal noise ratio on a line

The title of your link is “Perceptual attributes of acoustic waves – Timbre”. I believe you make my point right there but I will expand further.

You cite the following factors:

1. signal time variance (envelope) 
2. degree of attack and decay synchrony of the sine components;
3. presence or absence of high-frequency inharmonic energy in the attack portion of a signal;
4. spectral energy distribution (frequency, amplitude and phase values of the sine components of a complex signal - may change with changes in intensity and register, even for a given instrument); and 
5. spectral energy distribution time-variance (spectral flux or "jitter").

Where in the article does it refer to something other than a waveform?

a. The “signal” is a waveform

b. “Sine components” are only found in a wave

c. “inharmonic energy” refers to waves

d. “Frequency amplitude and phase changes of the sine components” refer to waves

e.  and from the article itself: “Helmholtz was the first scholar to link timbre (a perceptual aspect of sound waves) to spectral distribution (a physical aspect of sound waves). He specifically focused on the spectral distribution of the steady state portion of sound signals (defined below). This approach overlooked several acoustical aspects of sound signals, such as attack (onset transients) and signal/spectral time variance, both of which have been proven important to timbre perception.” 

Where do you think onset transients or signal/spectral time variances are found, if not during the delivery of waves? These are not created in one’s head. 

Regarding crosstalk, it is defined by Wikipedia as “usually caused by undesired capacitive, inductive, or conductive coupling from one circuit or channel to another.”

Meaning that the electromagnetic waves created in one wire impact the electromagnetic waves in an adjacent wire, thereby making it different from the original signal. Crosstalk is an example of electromagnetic interference.  Waves again.

Referring to psychoacoustics, Ansys.com states: “Psychoacoustics is the study of how humans perceive sound. It’s a relatively young field that began in the late 1800s to help aid in the development of communications. Psychoacoustics combines the physiology of sound — how our bodies receive sound — with the psychology of sound, or how our brains interpret sound.”

Our stereo systems can only address what sounds (waveforms/signals) our body receives. As I said earlier, once it hits the brain, the damage is done. Your brain cannot repair what was missing from or added to the original signal. It can interpret it, but it cannot change it.  That has to happen before it gets to the eardrum.

You finish with: “No audio system is perfect high fidelity reproduction ... They all translate in a relative way some experience, timbre and spatial acoustic qualities, which are not reducible at all to signal noise ratio on a line”.

First of all, they are reducible, but only in part. The other influence is the speaker’s interaction with the room and that is why I continue to emphasize that to get the best signal/waveform to your ears, you need to address the signal in the room as well as in your electronics. What happens to the signals in your head is your problem and yours alone.