The OP never stated that his water supply uses chlorine. In fact, some areas of the US have as high as 4 ppm chlorine and/or chloramine in their supply lines, at least where levels are recorded by the local municipality. IMO chlorine/chloramine exposure is a far greater risk than a shift in pH, and typically when pH values shift it is the change in TDS that kills the fish, not a change in pH. Not nit picking, just sayin ....
I posted the following a few yrs ago ......
Both chlorine &/or chloramine can cause long term damage & even death to fish, in some cases even at low levels, especially young fish which are typically the most sensitive to these substances. Free chlorine can cause acute necrosis of gill tissue in fish, the younger the fish the worse it can be. In short chlorine is an oxidizer, that can burn a fishes gills & kill cell tissue, sometimes even at low levels.
The amount of chlorine and or chloramine can vary greatly from one municipality to another, as well as from one tap to another, and can also vary greatly throughout the season. There is no way that anyone on a public forum can possibly attempt to tell you what a "safe" amount is in your case unless they have the specs on your local tap water at your user end. Water temp, pH values, etc can also determine how 'safe' certain levels of known toxic substances such as chlorine/chloramine can be on fish.
According to Edward Noga, a professor at NC State that is considered an expert in the disease & health of fish, chlorine levels as low as 0.10 mg/l (which is very common in many tap water levels) can be acutely fatal in aquaria that has low levels of organics. (as in a new set up) Others have found residual chlorine levels as low as 0.05 mg/l to be toxic to certain species of fish. Many areas of the USA contain 2-4 mg/l of either chlorine, or chloramine.
There has been a TON of work done in this area over the past few decades, by a number of researchers, such as Tompkins & Tsai (1976) for anyone that is interested in understanding just how toxic both chlorine & chloramine can be in a closed system that contains fish.