Phono Cart Impedance Question


I have a little bit of hiss through my 6 ohm, 0.28mV cart but only at a volume pushing the upper end of my listening volume...and it's only audible before I drop the needle, and even then not from the listening position.  I realize I therefore likely have a "non problem"!  

But I still have a generic question on to the sensitivity of producing hiss as it relates to cartridge impedance alone.  If one kept all other cart specs identical (including output of course) would you expect hiss to go up or down at the same volume and system gain if I used an 8 ohm or 12 ohm cart instead?  It seems like the hiss would likely go up just like moving to a higher impedance speaker under the same gain setup but perhaps I'm looking at this incorrectly? I realize moving to a slightly output cart could very well reduce the hiss.

Thoughts?   Sorry if this is a ridiculously obvious question and answer.

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@uberwaltz  Agreed.

What do you guys think...if I wanted to perhaps try just a couple of the SLN tubes to see if they start to lower noise where would be the best place to start?  As follows:

1st gain stage (pair)
2nd gain stage (pair)
output stage (single)

It would be nice to just dip my toe in the water to check for improvement w/o making a financial commitment for all 5 SLN tubes at $95/ea.  Where would the biggest improvement most likely be heard?
Whatever you decide, keep in mind that all tubes change noise characteristics as they age, and the curve for increasing noise as tubes go from SLN to not so SLN is not predictable from tube to tube. So SLN tubes are a crap shoot wherein the game is rigged against you. No aspersions on RAM tubes are intended; it just is what it is.
If you really want to learn more about tubes you’d better read Tube Assylum forum, some folks like are crazy about tubes and tried almost everything and they are not sellers. I spent a year on this forum just reading and making notes. If you’re in America then vintage Sylvania Gold Brand (Gold Pins) 12at7WA is superb even compared to my Telefunken ecc801s.

The best tubes are NOS Military Grade, they last much longer, they are stable, low microphonic and very quiet. None of the new 12AT7 or 12AX7 can beat them. Tube rolling is fun, but very expensive.

Look for NOS tubes, save for NOS tubes.

I don’t know much about 12AX7, used Soviet tubes in my Luxman amp for a short time, but 12AT7 was in my WLM Minueta amp for many years and i’ve been looking for cheaper alternative of Telefunken ecc801 (very expensive), i found Sylvania 12at7WA and Matsushita 12at7WA (gold pins) amazingly good.
I have the vtph-2a and with needle off, volume cranked, ear a foot away from speaker, I certainly hear white noise. When I drop the needle nothing except some very loud tunes and some extra clicks and pops. At volumes I typically listen at, nothing with my ear next to the speaker. With a tube phono pre and tube integrated, I'd expect some noise when the gain cranked and needle is up. I think you are gtg..  My tube rolling experiences with the Herron is - I prefer Keith's tubes every time! 
... if I wanted to perhaps try just a couple of the SLN tubes to see if they start to lower noise where would be the best place to start? As follows:

1st gain stage (pair)
2nd gain stage (pair)
output stage (single)

While I'm not familiar with the internal design of the VTPH-2 or 2A, and I've never taken the cover off of my VTPH-2 (having seen a number of past comments which like Jmolsberg's comment above have described finding tube rolling to not provide much if any benefit to Keith's phono stages), my guess is that if you want to give it a try the first gain stage would be where to start. Especially if that is where the 12AX7s are used.  (I don't know if the 12AX7s are used in the first stage or the second stage).  

Since signal level is presumably lowest in that first stage any noise generated by that stage will degrade signal-to-noise ratio more than it would be degraded by a similar amount of noise generated further downstream. Also, it may be relevant that the 12AX7 has a higher intrinsic gain than the 12AT7. 

Good luck. Regards,
-- Al