Significance of higher harmonics I am analyzing a noise signal and have identified the fundamental frequency of a tone and it's higher harmonics. Say for example given the signal below,

The fundamental frequency has a sound pressure level (SPL) of 70.775 dB, and the higher harmonics of 65.13,55.772 and 56.473 dB. Now the overall sound level can be estimated by summing these incoherent sources (as they are of different amplitudes) by
$SPL_{tot} = 10log_{10}(\sum_{i=1}^{n}10^{SPL_i/10})$
However, I would like to parametrize the significance the higher harmonics have in influencing the overall perceived sound pressure level.
While total harmonic distortion compares the ratios of the higher harmonics to the fundamental frequency, is there a standard parameter that can be used to describe the significance of each higher harmonic? Right now I compare the magnitude of each harmonic compared to the overall $SPL_{tot}$.
 A: However interesting, your question is probably too broad. When it comes to perception (so not just simple objective values), this topic is actually not perfectly understood in general. Always remember, that perception of any parameter of the sound is nonlinear and dependent on other parameters (e.g. you need to consider a pitch of the tone, when you approximate its perceived loudness).

We do not perceive the Sound Pressure Level (SPL)
Of course, perceived loudness is related to it, but it's not the same. For that purposes instead of dB we use an unit called Phon with its own scale (in fact that's a corrected SPL). Although, strictly speaking, that's correction made for physiology, but you need a connection to psychology and that's hell tricky.

Some parameters you might find interesting
I think your method is not entirely flawed. Let me just ofer you some more parameters to consider.


*

*Specific Zwicker Loudness. I won't present the whole theory here, just follow the link and maybe read something about barks first.

*Loudness as a RMS (root mean square). Let the c be an amplitude of the k-th harmonic and n the total number of harmonics, then:


$$
RMS = \sqrt{\sum_{k=1}^n c_k^2}
$$
so you can monitor the loudness increase by adding or removing the harmonics.


*

*Brightness of the tone BR. It's not loudness, I know, but the tone should be brighter the more of it's power is in harmonics, so it could be interesting: 


$$
BR = \frac{\sum_{k=1}^n kc_k}{c_0 + \sum_{k=1}^n c_k}
$$

You need to think of all these as of approximations. There always need to be a final check using your own ears (and better more ears than just yours - statistics is the key).

Note that...


*

*You need to consider transient of the tone. Especially the attack part of the tone is really significant in perception of loudness. You need to be sure, that you compare two tones without any unnatural cracks in the beginning (use e.g. fade in) and long enough to be fully perceived (about 1 second).

*You can't completely exclude the phase of harmonics. You've presented just amplitude spectrum and that might not be enough for the perception.

*You should consider some features that may not be easily visible in the spectrum, such as subharmonics (clearly present here!), modulations (beats!!!) or sound masking.

