What's the difference between たびに, ごとに and おきに?


I can't wrap my head around the difference between たびに, ごとに and おきに. I have
already looked up at the answers already posted in two previous posts and on
the internet, but I still don't get it.

I understand that たびに means that every time something happens the result is
always the same; whereas, ごとに has basically the same meaning, but it also has
the nuance of "more" as in this sentence

> "君と会う **ごとに** 不満が増してゆく"

However, there are sentences as

> "彼は会う **たびに** 好きになる" and "私の孫は会う **たびに** 、前より大きくなっている"

where たびに also bears the meaning of "more" and, thus, it can be replaced by
ごとに. So what is the difference?

Moreover, I have the same problem with ごとに and おきに. They both mean "every",
but they are not always interchangeable or they do not always bear the same
meaning, as in

> "この電車は二駅 **おきに** 止まる"

and in

> "この電車は二駅 **ごとに** 止まる"

If I got it right

> "この電車は二駅 **おきに** 止まる"

means that "the train stops every tree stops", while

> "この電車は二駅 **ごとに** 止まる"

means that "the train stops every two stops".

On the other hand, in this sentence

> "私は二日 **ごとに** 花子と会っている"

ごとに and おきに are interchangeable and bear the same meaning. Can somebody help
me to figure it out?




おきに is different from the other two because it always implies intervals. `X
おきに` always implies `with an interval of X`. You can't use it if there aren't
any predictable intervals. The emphasis is on describing what happens at what
interval.

This is different from たびに、ごとに because they can be used without an "interval":

> 見るたびに、見るごとに美しくなっていく

When used this way, the focus is on describing the correlation (when A
happens, B happens). They do have slightly different nuances - ごとに implies
accumulation if used where some sort of accumulation can happen. E.g.:

> 会うたびに重い 会うごとに重い

The above sentences have a similar meaning, but the first implies "it's
emotionally taxing every time we meet", where the second implies "it's getting
more emotionally taxing every time we meet".ごとに also sounds a tad archaic.

Another difference is that ごとに can be used on nouns, while たびに can't.

> 二日ごとに温度を測る、家ごとに水をためる ← OK  
>  二日たびに温度を測る、家たびに水をためる ← NOT GOOD

Note that おきに refers to the interval (what's in between), unlike ごとに. E.g.:

> 二日おきに温度を測る ← Measure every 3rd day  
>  二日ごとに温度を測る ← Measure every 2nd day  
>  家おきに水をためる ← Every second home saves water  
>  家ごとに水をためる ← Every home saves water

