Technical doubt on stereo vinyl recording (for mathematicians / physicists)

A thing came to my mind, since recently I found an album (2LPs) which is pressed incredibly well (perfectly flat, no pops, no crackle, no defects) but which has more "hiss" on the left channel than on the right.

We know that a stereo sound on vinyl is recorded by modulating the groove horizontally (L+R) and vertically (L-R).

Left channel = H + V
Right channel = H - V

So far so good, right?

Let's suppose that the surface noise (not pops, crackle, etc., just the plain high frequency hiss generated by friction of the stylus against the groove) is of the same amount on the horizontal and on the vertical modulation.

So we can consider the horizontal component to be H + NH (where NH is perfectly gaussian white noise), and the vertical component V + NV.

NV and NH have very similar amplitude theoretically, and also in reality in a well pressed record in which only the friction of the stylus matters (and no debris, dirt, etc, which would affect H more than V or viceversa).

Since the left channel is the sum of H + V and the right channel is the difference, taking noise into consideration we have:

L = H + NH + V + NV = H + V + the SUM of both gaussian noises
R = H + NH - V - NV = H - V + the DIFFERENCE of both gaussian noises


My mathematical/physical mind says that if both NH and NV are truly gaussian (which in reality is only an approximation), the left channel should always be MORE noisy than the right one. And by "more noisy" I mean simply "more hissy", without taking into account all other vinyl imperfections.


And, curiously, this is what I hear on this otherwise fantastically pressed album. And it happens on all three of my cartridges (AT 440 MLa, Ortofon 2m Black, Nagaoka MP-500). And on no other of my other 1000 LPs (which, on the other hand, being often of the used kind, showcase some crackle and noise of other kinds).


Does my mathematical/physical way of thought make sense? To me it's obvious that the left channel should be more "hissy" than the right, and the more the record is well pressed and clean and the better the cartridge is aligned... the more it should be so (=noise components approaching the purely gaussian distribution). It seems to be inherent in how the L and R channels are derived from groove info, in how the stereo recording on vinyl was designed.


Feel free to comment!

 

No way

The equations you wrote are valid only for 100% correlation between NH and NV, where they actually are independent from each other. The noise is the same in each channel, because both summing or subtracting two gaussian variables gives the same variance on the result, i.e. the square root of the sum of the squares of the two original variances.

 

What he said.

 

No, I mean: what? he said.

 

Good points!

But then my theory would apply if NH and NV were not exactly gaussian (as real life noise would probably be)... Right?

 

Don't you need a sample size greater than one here (I assume you are referring to a 2 LP set)? It is not as if you have a perfectly calibrated test object which varies only on the factor of interest. You are testing an ordinary stock record which could have idiosyncratic reasons for more hiss in one channel than the other.