diff --git a/pandas/_libs/tslibs/period.pyi b/pandas/_libs/tslibs/period.pyi
index 846d238beadbd..df6ce675b07fc 100644
--- a/pandas/_libs/tslibs/period.pyi
+++ b/pandas/_libs/tslibs/period.pyi
@@ -63,7 +63,7 @@ class PeriodMixin:
     def end_time(self) -> Timestamp: ...
     @property
     def start_time(self) -> Timestamp: ...
-    def _require_matching_freq(self, other, base: bool = ...) -> None: ...
+    def _require_matching_freq(self, other: BaseOffset, base: bool = ...) -> None: ...
 
 class Period(PeriodMixin):
     ordinal: int  # int64_t
diff --git a/pandas/_libs/tslibs/period.pyx b/pandas/_libs/tslibs/period.pyx
index 22f96f8f6c3fa..6b105f5974f9b 100644
--- a/pandas/_libs/tslibs/period.pyx
+++ b/pandas/_libs/tslibs/period.pyx
@@ -1714,21 +1714,16 @@ cdef class PeriodMixin:
         """
         return self.to_timestamp(how="end")
 
-    def _require_matching_freq(self, other, base=False):
+    def _require_matching_freq(self, other: BaseOffset, bint base=False):
         # See also arrays.period.raise_on_incompatible
-        if is_offset_object(other):
-            other_freq = other
-        else:
-            other_freq = other.freq
-
         if base:
-            condition = self.freq.base != other_freq.base
+            condition = self.freq.base != other.base
         else:
-            condition = self.freq != other_freq
+            condition = self.freq != other
 
         if condition:
             freqstr = freq_to_period_freqstr(self.freq.n, self.freq.name)
-            other_freqstr = freq_to_period_freqstr(other_freq.n, other_freq.name)
+            other_freqstr = freq_to_period_freqstr(other.n, other.name)
             msg = DIFFERENT_FREQ.format(
                 cls=type(self).__name__,
                 own_freq=freqstr,
@@ -1803,7 +1798,7 @@ cdef class _Period(PeriodMixin):
                     return False
                 elif op == Py_NE:
                     return True
-                self._require_matching_freq(other)
+                self._require_matching_freq(other.freq)
             return PyObject_RichCompareBool(self.ordinal, other.ordinal, op)
         elif other is NaT:
             return op == Py_NE
@@ -1893,7 +1888,7 @@ cdef class _Period(PeriodMixin):
         ):
             return self + (-other)
         elif is_period_object(other):
-            self._require_matching_freq(other)
+            self._require_matching_freq(other.freq)
             # GH 23915 - mul by base freq since __add__ is agnostic of n
             return (self.ordinal - other.ordinal) * self.freq.base
         elif other is NaT:
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index a8c21cfbb6e2f..5f267a9f816e7 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -370,10 +370,15 @@ def _unbox_scalar(  # type: ignore[override]
     def _scalar_from_string(self, value: str) -> Period:
         return Period(value, freq=self.freq)
 
-    def _check_compatible_with(self, other) -> None:
+    # error: Argument 1 of "_check_compatible_with" is incompatible with
+    # supertype "DatetimeLikeArrayMixin"; supertype defines the argument type
+    # as "Period | Timestamp | Timedelta | NaTType"
+    def _check_compatible_with(self, other: Period | NaTType | PeriodArray) -> None:  # type: ignore[override]
         if other is NaT:
             return
-        self._require_matching_freq(other)
+        # error: Item "NaTType" of "Period | NaTType | PeriodArray" has no
+        # attribute "freq"
+        self._require_matching_freq(other.freq)  # type: ignore[union-attr]
 
     # --------------------------------------------------------------------
     # Data / Attributes