Help me understand compliance!

@yeti42, good for you. Measuring is the only way to go. There is enough variability in cartridges and tonearms that the predicted resonance frequency can be a good deal different than the measured one as you noticed. You are not seeing the vertical resonance because it is being well dampened. 8 Hz is perfect, what I shoot for. You can see the vertical resonance if you use a more sensitive measurement device like an oscilloscope. You can put a seismometer app on your phone and place it on your speaker or subwoofer and you might be able to see it. I have not tried it yet but I will once I get my system set up again. 

I find the Korf Audio blog post linked above to be very interesting and am surprised nobody makes note of the fact that he seems to call out the "way everyone does it" as flawed.  I have tried to back out the actual compliance from other know parameters and found like korf that something else dominates this equation.  Below are his conclusions from post IV

http://korfaudio.com/blog70http://

1 Carlson's formula of a low frequency resonance does not describe the measured low frequency behaviour of the cartridge/tonearm interaction

2 Modern cartridges (meaning all those built in the last 60 years or so) have too much suspension damping and non-linearity for the resonances to dominate

3 The frequency of the observed motion is determined largely by the frequency of the excitation

4 The cartridge/tonearm system acts as a lowpass filter for vibrations picked up by the stylus

5 Too low an effective mass for a given compliance (or too low a compliance for a given effective mass) results in low frequency attenuation and excessive tonearm motion.6Too high an effective mass for a given compliance (or too high a compliance for a given effective mass) results in "ringing"—a small resonant peak—that is largely benign
and barely registers in the measurements

Oddly enough he also provides a compliance calculator that gives results that are in direct contrast to his measured experiments.

dave

In Korf’s #5, too low a compliance for a given effective mass is the same condition as #6, too high an effective mass for a given compliance, etc, yet he posits very different outcomes in #5 vs #6. Same for the converse conditions he describes.

I think the difference between #5 and #6  is that #5 refers to a mismatch of a low compliance cart to a low mass arm and #6 refers to the mismatch of a high compliance cart to a high mass arm.

Either way... the big thing that is overlooked by everyone thus far is he drastically altered one of the factors (compliance) in the traditionally used formula and kept the other two constant.  His results did not show the expected shift in resonant frequency but did show a decided effect on the damping of the frequency peaks.  I believe his compliance calculator goes more to showing the possible magnitude of the unwanted behaviors resultant from a mismatch and I think situation #5 is problematic and #6 may be quite benign.

As you have heard,  I use a really high compliance cartridge in an insanely high mass tonearm with no apparent ill results.  Even though it breaks just about every matching rule known to man and incites endless lectures on my ignorance,  I have found it to be a sublimely musical combo.

Einstein one said...  “If the facts don't fit the theory, change the theory".  Sadly, in this case I don't see that ever happening.

@intactaudio , I can't be sure what you mean. What to you is an insanely high mass arm (in effective mass please)?  and what is a really high compliance cartridge? It sounds fine to you but, I would like to know what is happening where it does not sound, below 8 Hz. If the tonearm is massive enough some very unhappy things are going to manifest and no cartridge I know of (excluding the Decca) has enough damping to deal with it. Hook your phone stage up to an oscilloscope. 
As I said before, I do not use formula or rely on theory. I measure. Unless you measure one has no idea what is going on. "Sounds good" is a hopelessly inaccurate way of describing the situation where the needle hits the groove. T

This is for certain. If you add mass the resonance frequency is going to drop. If you remove mass the resonance frequency is going up. If you can't see or hear the resonance point with a good test record it is because the system is dampening it out. In which case it is not a problem. If you want to increase your resolution hook up an oscilloscope to your phono stage (assuming it goes down that low) and you will probably see it along with some other scary looking stuff.