According to the JB website calculations, this is my current floor status, with actual 21" o.c., old strong 2x8, probably douglas fir:

For joists that are SYP or Douglas Fir, in good condition, 7.25 inches tall, 1.5 inches wide, 20 inches on center, and 9.5 feet long between supports, the deflection calculated is 0.262 inches.

This translates to a deflection of L / 435.

Since the maximum deflection for tile is L / 360, and for natural stone is L / 720, your floor is rated for Ceramic tile, Congratulations!

If I add joist between these existing joist I can bring the floor up to:

For joists that are SYP or Douglas Fir, in good condition, 7.25 inches tall, 1.5 inches wide, 10 inches on center, and 9.5 feet long between supports, the deflection calculated is 0.131 inches.

This translates to a deflection of L / 871.

Since the maximum deflection for tile is L / 360, and for natural stone is L / 720, your floor is rated for Ceramic tile or Natural stone, Congratulations!

I want to get my floor to L/720 minimum, as recommended by this calculation, to install my 12x12 slate tile.

The floors are level and the existing joist are straight and level. The total area is about 6.5'x9.5' in the room. The crawl space has the joist running 9.5' with about 6 or so inches setting on a ledge at the far end of the room. The near end was toenailed into the ledger. Since the floor was level and the joist were level, using a 4' long level, we just installed joist hangers on the near end to maintain integrity of the existing joist. My subfloor is 3/4"x6" (or 8") diagonal. The flooring is 3/4"x3" T&G fir.

I got lots of good information from a post that I placed last fall. I will post a link below. What I didn't get straight was how to actually install the joist to the existing subfloor. I am thinking that one would toenail in the new joist into the bottom layer of the flooring only. My DH thought that we would just nail down into the joist from above going through the fir flooring and through the diagonal subfloor. This would be very easy to do but I don't know which is best for structure and safety of new stone tile.

My tile install over the existing fir floor and subfloor is planned, and is as follows:

3/8 exterior grade SYP plywood screwed 6" spacing throughout into the fir floor.

SLC primer

Electric floor warming system (cables not matt)

SLC

unmodified thinset (as per Schluter Ditra handbook, over concrete, since I wont be going directly over wood. Otherwise modified thinset is used over wood)

Ditra

unmodified thin set

Slate 12x12 tile

Questions:
How do I fasten the new 2x8 filler joist into place?
What fasteners to use, screws, nails?
If screws, hardened or not?

What about that idea?

Here is #1 joist being installed by DH, #2 is waiting for tomorrow:

New joist on the far right, it is the same size as the rest, it is just bolder:) :

Anyone out there to help me figure out if it is ok to just nail down through both old floors from the top side down into the new joist? Or should I have it screwed down. I will be adding a 3/8" ply underlayment that I will not be fastening to the joist and will not be having the edges join over the joist. Screw down 6"o.c. throughout. Ditra will be my decoupling membrane before the tile goes down.