Things are much clearer now the only thing is the FFT bins that are a little difficult to totally comprehend(your math of minusing 36 is enough for now to see the noise level with Amir's measurements and compare which I have understood well) but I don't think that is of paramount importance to understand the overall concept. I do have a few more questions though, simple ones that will clear a few things up, if you don't mind.
I am afraid you may get a lot of maybe and might be answers here. These are all very good questions you ask.
1. Amir's test is a 1khz tone. So is performing the test only at this frequency representantive of the whole bandwidth when it comes to distortion?
1 khz is something of a standard to test. The first few harmonics occur where our hearing is most sensitive. Our hearing is less sensitive to distortion at low frequencies, and at higher frequencies the harmonics are too high to hear. Good devices don't change distortion over frequency very much, but not all devices are good. So sometimes distortion rises at higher frequencies.
2. You mention that everything under about 100db is generally inaudible. I understand that is very technical and open for debate but is the this the general consensus with noise and distortion?(at least what we agree here on ASR)
Another gray area. Some might prefer -110 db, some might say you can get away with even -80 db. One reason for these gray areas is we can come up with particular listening tests where we can probe the limits of hearing distortion or noise. When we are listening to more complex sounds from music our ability to hear it is much reduced. 1% distortion on music is likely fine and it might not matter until more like 3% with some music. 1% is merely -40 db.
Noise is a little clearer to answer. If you turn your system up as loud as you'll ever listen do you hear noise? If not you are okay. Depending upon how quiet your room is, how sensitive your speakers, that might be -80 db or it might be -100 db. If you get noise down around -100 db you are very unlikely to hear it, and if you barely did in quiet portions almost any music at all would mask it.
Also remember noise can be things like hum. 60,120, 180 hz from power supply hum doesn't have to be very loud until it ruins quieter portions of music.
3. You also mentioned a few times that noise is worse than distortion depending on the distortion, especially if the distortion is the 3rd harmonic and if under 100db? Again, is that the general consensus that noise with a similar result is more audible and more worrying than distortion?
Harmonic distortion only occurs during a signal to be distorted. So it can be masked by that signal. Especially 2nd and 3rd harmonics. Noise on the other hand can be constant and therefore isn't only going to occur when there is other signal to mask it. Without a signal it is simply there to be heard. Portions of music will cover it, but quiet parts of recordings or in between there is nothing to mask constant noise.
4. Lastly, as the harmonics continue say 2nd, 3rd, 4th are they less important than the previous? So 2nd harmonics is the most audible and the one we should be looking out for.
All the harmonics depends upon levels. Typically after the 3rd higher harmonic distortion is at lower and lower levels. There are exceptions, and upper harmonics can be more noticeable if they aren't low because being further from the main signal they are masked less.
Reading this wikipedia entry on masking is probably worthwhile.
https://en.wikipedia.org/wiki/Auditory_masking
Masking can be rather complex with forward and backward masking which varies with level and frequency and how long it lasts. Generally you'd strive to keep all harmonic distortion so low it doesn't need any masking to be inaudible.
All these are debatable areas. If you wanted a near indisputable set of guidelines, you want all noise, all distortion and all spurious noise to be -120 db below full output or lower. That would be right up against state of the art (SOTA) limits of what is physically possible. OTOH, most of the time, nearly all of the time, some specifications can be loosened and have no consequences you can hear. If it is inaudible, making it more inaudible doesn't make any difference. There is a big price difference in a 100% blameless audio system and one that is effectively so 98% of the time.
Transducers are the bottleneck to performance. On the playback end we are talking speakers and headphones. The frequency response and distortion levels put a limit on how good the sound can be in terms of fidelity.