SR Specials 4-string – Can I get the single H tone from the HH model?

SR Specials 4-string – Can I get the single H tone from the HH model?

I could be mistaken but have this memory that older HH SR’s would not sound the same as a single H model assuming the neck pup was off.

Can I get the exact H tone with a HH model in the Special series?
Looks to be better availability of HH models in my area.
TIA

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