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Reproducible Example

per1 = pd.Period("2016Q1", freq="Q")
per2 = per1.asfreq("M")

>>> per1 < per2
pandas._libs.tslibs.period.IncompatibleFrequency: Input has different freq=M from Period(freq=Q-DEC)

idx = pd.Index([per1, per2])
idx2 = pd.Index([per1, "foo"])

>>> idx.is_monotonic_increasing
pandas._libs.tslibs.period.IncompatibleFrequency: Input has different freq=Q-DEC from Period(freq=M)

>>> idx2.is_monotonic_increasing
False

Issue Description

In general the exception you get from mismatched comparisons should be a TypeError (xref #54847). ATM IncompatibleFrequency subclasses ValueError. Might be worth changing that in 3.0.

Expected Behavior

NA

Installed Versions