BUG: Add frequency to DatetimeArray/TimedeltaArray take

doc/source/whatsnew/v3.0.0.rst

@@ -556,6 +556,7 @@ MultiIndex
 - :func:`DataFrame.loc` with ``axis=0``  and :class:`MultiIndex` when setting a value adds extra columns (:issue:`58116`)
 - :meth:`DataFrame.melt` would not accept multiple names in ``var_name`` when the columns were a :class:`MultiIndex` (:issue:`58033`)
 - :meth:`MultiIndex.insert` would not insert NA value correctly at unified location of index -1 (:issue:`59003`)
+- :func:`MultiIndex.get_level_values` accessing a :class:`DatetimeIndex` does not carry the frequency attribute along (:issue:`58327`, :issue:`57949`)
 -
 
 I/O

pandas/core/arrays/datetimelike.py

@@ -65,6 +65,7 @@
     ScalarIndexer,
     Self,
     SequenceIndexer,
+    TakeIndexer,
     TimeAmbiguous,
     TimeNonexistent,
     npt,
@@ -2340,6 +2341,27 @@ def interpolate(
             return self
         return type(self)._simple_new(out_data, dtype=self.dtype)
 
+    def take(
+        self,
+        indices: TakeIndexer,
+        *,
+        allow_fill: bool = False,
+        fill_value: Any = None,
+        axis: AxisInt = 0,
+    ) -> Self:
+        result = super().take(
+            indices=indices, allow_fill=allow_fill, fill_value=fill_value, axis=axis
+        )
+
+        indices = np.asarray(indices, dtype=np.intp)
+        maybe_slice = lib.maybe_indices_to_slice(indices, len(self))
+
+        if isinstance(maybe_slice, slice):
+            freq = self._get_getitem_freq(maybe_slice)
+            result._freq = freq
+
+        return result
+
     # --------------------------------------------------------------
     # Unsorted
 

pandas/tests/indexes/multi/test_get_level_values.py

@@ -122,3 +122,12 @@ def test_values_loses_freq_of_underlying_index():
     midx.values
     assert idx.freq is not None
     tm.assert_index_equal(idx, expected)
+
+
+def test_get_level_values_gets_frequency_correctly():
+    # GH#57949 GH#58327
+    datetime_index = date_range(start=pd.to_datetime("1/1/2018"), periods=4, freq="YS")
+    other_index = ["A"]
+    multi_index = MultiIndex.from_product([datetime_index, other_index])
+
+    assert multi_index.get_level_values(0).freq == datetime_index.freq