Need to be educated re: MC Step-up transformers

I recently purchased the EAR MC-4 Step-up transformer. I was having some noise problems with my analog rig. I spoke with Tim de Paravicini of EAR directly in the UK. He answered all the system matching questions and pronounced the MC-4 a fit with my system. He is very direct, extraordinarily knowledgeable, and seemed very sincere and honest.

I still don't understand the "How" though. Here's what I do understand and relayed to Tim:

1. I use the ClearAudio Stradivari, a MC at 0.7mV output.

2. Currently, my phono stage provides a total of 57 dB of gain: 20 in the MC mode using a JFET and 37 in the MM mode using all tubes. My tube line stage provides 12 dB of gain SE, which is how I run it. So, currently without the MC-4, I have a total of 69 dB gain when running my phono stage in MC mode (20 + 37 + 12).

3. The MC-4 has four taps – I was told by Tim to use the 40 ohm tap which provides a 10x gain in voltage and is compatible with the 32 ohm impedance of my cartridge. This would change the output voltage my phono stage “sees” from 0.7mV to 7.0mV.

4. The phono stage must be run in MM mode, bypassing the JFET in the MC mode.

5. Given all this, then, my phono stage will receive as input a 7.0mV cartridge output from the MC-4. This signal will run through the MM mode and receive 37 dB gain and then another 12 dB gain from the line stage SE for a total of 49 dB gain, down from 69 dB, as we are no longer “gaining” the additional 20 dB from the JFET MC mode.

6. I need to remove the 600 ohm Vishay resistors and get the phono stage back to the stock 47 kohm setting, as the MC-4 will reduce the resistance by the square of the voltage gain or 10^2 or 100: 47,000/100 = 470. That is within the range recommended by Clearaudio of 320 – 900, preferably toward the lower end, though let your ears be your guide.

It was based on this information (which I provided) that the MC-4 was pronounced a fit - I certainly don't doubt that.

Here's my confusion: Am I to understand that 7.0mV of cartridge output from the MC-4 is so much more voltage that all I need is the 49 dB the system provides in its new configuration for low noise and analog bliss?

I just don’t understand the science, I guess. I appreciate the education.

Brent