1/3 is not the same order of magnitude in base-3 or less, I tend to think in base-2 at least as much as base-10 when considering order of magnitude issues.
Put another way, if I coded something where the performance delta was 1/3 or 3x, I would certainly be complaining or bragging about an order of magnitude change.
Order of magnitude without any base specified is commonly understood as being base 10, and it is extremely confusing to use other bases, as no one else uses them as 'orders of magnitude'.
You can talk about logarithmic scales without risk of confusion.
Put another way, if I coded something where the performance delta was 1/3 or 3x, I would certainly be complaining or bragging about an order of magnitude change.