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Wood Weights

Alder is typically lighter than Ash... but not as light as Balsa.

Keep in mind that extremely light woods don't have a dense grain.

Dense grain helps to stiffen the wood. Stiff wood helps to return energy to the strings. Returning energy to the strings has an impact on the resonance of the strings. The resonance of the strings affects the signals that are generated by the pickups.

There are a few exceptions; woods that are relatively light AND have good "tone" qualities due to their ability to return energy to the strings. Alder is one of those woods.

Balsa would probably suck the life out of your strings.

(I'm just using that as an example.)
 
Swamp ash varies greatly from piece to piece as swamp ash does not refer to a specific species. Swamp ash is southern US ash graded and selected for weight. Some pieces are stupidly lightweight. Alder is much more consistent board for board.

Specific gravity of alder is .53 on average.
White or green ash .66 on average.
Black ash .56 on average.

Swamp ash is generally unusually light weight black ash.