Relationship of cartridge output to perceived volume

I’m in the process of replacing my MC cartridge but wondering how cartridge output voltage will affect perceived volume.

So for example, if one cartridge has an output of 0.4mV how much quieter will it be than one with an output of 0.5mV.

I realise that there’s some complicated maths involved and that actual volume depends on the performance of every component in the chain between the needle and the ear.

But in general, assuming identical components in each case, is the relationship linear? Or exponential?

In that example, assuming the output rating of each was measured in the same manner, and the ratio between the two is constant across the audio spectrum, and all replay settings, volume control, listening position etc constant, music from the lower output one will be 2dB quieter than from the other. (If you increase the volume to compensate, any electronic or induced noise from the phono stage, signal wire and preamp input stages will also become 2 dB louder.)

If you want to do the calculation for any others, based on voltage the difference in sound level is given by taking the ratio 0.4/0.5=0.8, find the log10 of that = -0.0969, then multiply by 20 = -1.938dB. As the values of the voltages are probably not precisely as quoted, there being some tolerance, round to the nearest whole decibel.

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It’s an interesting, though purely academic question.

I’d have assumed the relationship was strong and before I had a turntable was under the impression I’d have to crank my amp up from 9 O’clock to 12 O’clock when switching to vinyl from my NDX. But I have an unusually low output 0.25mv MM cartridge and yet through a normal Stageline the volume difference is obvious but not massive. 9 O’clock becomes 10 O’clock. A jump but nothing major. My more standard 0.5mv output MM doesn’t seem to be significantly different.

A more inquisitive mind might ask why since it doesn’t make sense initially. I just shrug and put another record on.

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Difference between 0.25 and 0.5mV is 6dB. Whilst that corresponds to 4x the power, which seems huge, it is the same difference as moving from your normal listening position halfway to the speakers or back again.

But that doesn’t sounds more like the output from MC rather than MM cartridges, latter usually more like 10x this?

You are correct. I put the decimal in the wrong place. 5mv against 2.5mv.