Yields on city tile

[Persipnei]

Is there some overview how yields on a city tile are calculated?

If I settle a grassland (2F), the tile becomes (3F, 1P)
but if I settle a plains hill (2P), the tile become (2F, 2P)

I didn't play CIV 5 in a while, but can't remember it working like this?

 

[Persipnei]

I just settled another grassland (2F), the tile became (2F,1P,1G)

Que?

 

[Rekk]

City is always 2F, 1P

Settle near fresh water, gain +1 food.
Otherwise, settle on a hill, gain +1 production.
Otherwise, settle anywhere, gain +1 gold.

 

[Persipnei]

I see, thank you very much, sir

 

[Omen of Peace]

I think it's Hill > Fresh Water > else because a fresh water hill is 2F 2P.

Also if you settle on a tile with more than 2F 1P, you keep the extra yield. This is the case for resource tiles: for instance a marble hill is 3P, if you settle on it it would be 2F 3P.