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   I don't have any extra tubes to try at the moment.  It takes 5 tubes - a combo of (2) 12AX7 with (3) 12AT7 or you can use (4) 12AX7 and just one 12AT7 to get the extra 5dB of gain.  Keith uses all EH tubes for this model so at least they are pretty cheap.
Tubes can be noisy and microphonic, they can also be expired, they do not last forever. As for the 12AT7 i would recommend NOS Sylvania Gold Brand with Gold Pins - this is amazing tube with moderate price for a NOS. A tube phono stage owner must have a bunch of backup tubes, an issue like this is one of the reason i would never use a tube phono stage myself. But when i’ve been using a tube amp i quickly realized than some nice NOS tubes (like those Telefunken, Sylvania, Matsushita) are always better than any new tubes, the difference is sound is huge. So it’s always an open question, endless tube rolling.
Both my phono-pres have 4 amplification stages. Basis Exclusive
max. is 71 dB, Klyne 3,5 ; 67 dB. The ''sense'' of 4 amplification 
stages is to use the lowest possible for a given cart because the
''higher amplification the higher distortions'' (hi Raul). 
Herron, according to uberwaltz , produces ''2 flavours'' instead
( 64 and 69 dB).  ''Hiss'' may be other expression for distortion?

Three, go here   http://www.tubeaudiostore.com/tubes.html.
Some tubes are much better than others. Roger sifts through hundreds of tubes and categorizes them as regular, low noise and super low noise.
I changed the three 6922's in my ARC phono amp for Roger's Super Low Noise tubes and my noise level dropped at least 6 dB. Very impressive. The tubes are now 6 years old and still going strong. 

Mike


@mijostyn   Thanks for the link on tubeaudiostore.  I've never ordered tubes from him but those Super Low Noise tubes sound compelling.  Although super low noise certainly comes at a price!