塩梅, which can be used in terms of balance/degree of seasoning in cooking can also be used in the context of how a situation is going (like 調子), such as (from my dictionary):
►こういうあんばいで事が運べば if things go at this ┏rate [pace].
►うまいあんばいにいく go well; go all right
・いいあんばいに fortunately; luckily
・いいあんばいに彼がこの町に転勤になった.
Fortunately he's been transferred to (work in) this town.
►この間の試験はどんなあんばいだった.
How did you make out in the last exam?
・今日は暑くもなく寒くもなく, いいあんばいですね.
Today is neither hot nor cold, but just right.
This seems incredibly similar to 具合, as you can say things like うまい具合に ("in a good way" -> luckily).
I am pretty sure you can use 具合 when talking about taste as well, but it seems あんばい is more commonly used there.
These words seem to occupy very similar situations and have a similar array of usage so I wonder where they differ.