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How do I achieve this weird tuning? D2, G2, C3, F3

I'll spare you the long story that lead me to wanting to do this. I'll just say that I basically want a four string bass strung starting at the top two strings and continuing on. or, I suppose, the top three strings of a 6 string with an additional F string (which would be the 7th string).

So it would be strung like D2, G2, C3, and then... F3?

My bass is string with 45-105s and I would like the keep the same feel. I looked at a 6 string set and the C is a 30. What would be the best gauge to be the high string and where would I be able to get it?
 
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I'm considering if I way over thought this though when I would just string it with piccolo strings...

Basically you're taking the EADG Piccolo tuning and down-tuning it one whole step.

Using the GHS Boomers just as an example, here's how the tension numbers work out...

F - .020 - 35.5 lbs. (NOTE: This one is wound like the other three.)
C - .030 - 37.2 lbs.
G - .040 - 33.5 lbs.
D - .055 - 35.3 lbs.
 
Could you just get a set of piccolo bass strings and tune them down a step? Daddario and GHS both make them, amongst others.

Edit: You said you were hoping for a similar feel...not sure if that is possible, honestly.
 
Octave-up EADG piccolo sets always have a plain steel G3, because the maximum pitch for roundwounds on 34"/35" is approximately F3.
You might not like the tone or surface texture of a plain steel string.
The G3 is often a plain .020 which is stiff and therefore rather inharmonic, too stiff and inharmonic for me. A plain .018 is better.

Because you want to tune to F3, you will be able to find roundwounds that can reach this pitch. So you might prefer to build a set from singles .065 .045 .030 plus a purpose-designed .020 or .022 F3. Conklin Guitars sell them by mail order from their website.

Thin roundwounds have thin cores so are near their tension limit at F3, so this might need to be a purpose-designed bass guitar wound high F string to be strong enough.
 
Octave-up EADG piccolo sets always have a plain steel G3, because the maximum pitch for roundwounds on 34"/35" is approximately F3.
You might not like the tone or surface texture of a plain steel string.
The G3 is often a plain .020 which is stiff and therefore rather inharmonic, too stiff and inharmonic for me. A plain .018 is better.

Because you want to tune to F3, you will be able to find roundwounds that can reach this pitch. So you might prefer to build a set from singles .065 .045 .030 plus a purpose-designed .020 or .022 F3. Conklin Guitars sell them by mail order from their website.

Thin roundwounds have thin cores so are near their tension limit at F3, so this might need to be a purpose-designed bass guitar wound high F string to be strong enough.

I'll keep this in mind. I'm going to grab a pack of piccolo strings to toy around with but the more I think about it the more I like the idea of DGCF which could be put in CFBE drop tuning which I think sits nicely (or, at least, interestingly) in between a bass and a guitar. And keeping that high round would be a plus
 
20200123_162159.jpg

A set of S.I.T. Conklin PowerSteel PSR18135 stainless.
The .018 plain steel is an F.
 
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I think sits nicely in between a bass and a guitar. And keeping that high round would be a plus
Hi, thats what i´m doing right now.

i run a 5String with A-D-G-B-E = 075-060-045-030-020* (i prefer here the guitar tuning cause of the perfect fit with open strings when playing in E )
For my first test set of Strings (that i´m still on) i used Pyramid single strings.
( those, since they are available as single Strings from Thomann)
* the plan was to use a 025 for the high E, but i broke two Strings immediately.
But i could have been one octave to high, who knows, ......since i´m just freshly back to play Bass again

from my feel do i indeed wish a thicker String for the high E.
and my 030 that i use for B feels inharmonicly thin, not shure if i mixpuzzled here something ? If not, will i try thicker Strings later, when i had again the oportunity to order something at thomann.
If this would work, would i even like to try a 075-060-050-040-030 setting. Or maybe even a 070 for the low A

For what i´m doing its the perfect setup !....playing at home over 5" Studio speakers, or even mostly unconnected. I totally enjoy it. And if i had a guess free, would i say this will become a upcoming thing ( beeing on a 34" Bass right now)