THD will usually track level with respect to the stimulus.

However, consider a brief, incomplete and overly simplified discussion of auditory masking and the basilar membrane. I'm going to reference Equivalent Rectangular Bandwidth (ERB), Critical Bands (CB), and the Bark scale.

Some information on ERB here:

https://ccrma.stanford.edu/~jos/bbt/Equivalent_Rectangular_Bandwidth.html
Referring to equation 28 in that paper

ERB(f) = 0.108f + 24.7

at 1000 Hz ERB(1KHz) = 132.7 Hz for moderate sound levels. Not the entire 20 Hz to 20 KHz audio band.

Now consider a Bark scale chart describing critical bands for some pre-determined frequencies. In reality the CB are continuous and not discrete, but the discrete chart allows a simplified discussion,

https://ccrma.stanford.edu/courses/120-fall-2003/lecture-5.html
Using a Bark scale approximation (look at last graph on page)

For 1000 Hz

2nd harmonic is approximately 4 critical bands higher

3rd harmonic is approximately 7 critical bands higher

4th harmonic is approximately 9 critical bands higher

The basilar membrane treats signals outside a stimulated critical band differently than inside. Outside may be detected in presence of a masker inside a given critical band.

In dense, complex musical passages with many maskers present, then detection may not occur. If presented with sparse or less complex signals, say a bell or triangle, piano in solo or nearly solo role, as examples, then the harmonics may not be masked and detection possible. 2nd and 3rd harmonics are musically related so they are likely to be enjoyed as described in the OP, but 4th harmonic is not musically related and can appear to be that something slightly sour about those sparse passages.

Again, be careful. One must sum the levels in all the FFT bins to obtain residual noise level. Summation is not direct but through the following equation:

FFT size process gain:

http://www.analog.com/media/en/training-seminars/tutorials/MT-001.pdf
https://www.designnews.com/aerospace/where-does-fft-process-gain-come/100022666833951
For post #1 tutorial above FFT size is 128K (131072). For M = FFT size

FFT process gain = 10*log(M/2)

In the tutorial examples, process gain calculates to 48.16 dB

Now looking at the average of the FFT baseline noise floor for BS-6, estimate -125 dBu.

-125 dBu + 48 dB process gain = -77 dBu.

-77 dBu from our reference of 132 dB at 0 dBu given for the Andromeda IEMs results in 55 dB SPL.

This will be audible hiss.

Another example would be Focal Clear with sensitivity of 104 dB/mW and 55R nominal impedance. Running the calculations results in 33 dB SPL for the same BS-1, 5 and 6 hum, buzz, or hiss.

33 dB SPL may or may not be audible depending on ambient environment of the listener. Fan noise is likely to mask. Quiet rural bedroom the residual noise between tracks, if not using track overlap fades, may be annoying.

If you were located near my lab I could demonstrate this, audibly, as I have done for many of my colleagues. My lab space often achieves 22 dBA and 28 ~ 30 dBC SPL ambient. Hum, buzz and hiss annoy me personally, others may not be bothered.

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