diff --git a/pandas/tests/arrays/interval/test_interval.py b/pandas/tests/arrays/interval/test_interval.py
index 024721896cc58..be4b2c3e7e74c 100644
--- a/pandas/tests/arrays/interval/test_interval.py
+++ b/pandas/tests/arrays/interval/test_interval.py
@@ -229,178 +229,3 @@ def test_min_max(self, left_right_dtypes, index_or_series_or_array):
         res = arr_na.max(skipna=True)
         assert res == MAX
         assert type(res) == type(MAX)
-
-
-# ----------------------------------------------------------------------------
-# Arrow interaction
-
-
-def test_arrow_extension_type():
-    pa = pytest.importorskip("pyarrow")
-
-    from pandas.core.arrays.arrow.extension_types import ArrowIntervalType
-
-    p1 = ArrowIntervalType(pa.int64(), "left")
-    p2 = ArrowIntervalType(pa.int64(), "left")
-    p3 = ArrowIntervalType(pa.int64(), "right")
-
-    assert p1.closed == "left"
-    assert p1 == p2
-    assert p1 != p3
-    assert hash(p1) == hash(p2)
-    assert hash(p1) != hash(p3)
-
-
-def test_arrow_array():
-    pa = pytest.importorskip("pyarrow")
-
-    from pandas.core.arrays.arrow.extension_types import ArrowIntervalType
-
-    intervals = pd.interval_range(1, 5, freq=1).array
-
-    result = pa.array(intervals)
-    assert isinstance(result.type, ArrowIntervalType)
-    assert result.type.closed == intervals.closed
-    assert result.type.subtype == pa.int64()
-    assert result.storage.field("left").equals(pa.array([1, 2, 3, 4], type="int64"))
-    assert result.storage.field("right").equals(pa.array([2, 3, 4, 5], type="int64"))
-
-    expected = pa.array([{"left": i, "right": i + 1} for i in range(1, 5)])
-    assert result.storage.equals(expected)
-
-    # convert to its storage type
-    result = pa.array(intervals, type=expected.type)
-    assert result.equals(expected)
-
-    # unsupported conversions
-    with pytest.raises(TypeError, match="Not supported to convert IntervalArray"):
-        pa.array(intervals, type="float64")
-
-    with pytest.raises(TypeError, match="Not supported to convert IntervalArray"):
-        pa.array(intervals, type=ArrowIntervalType(pa.float64(), "left"))
-
-
-def test_arrow_array_missing():
-    pa = pytest.importorskip("pyarrow")
-
-    from pandas.core.arrays.arrow.extension_types import ArrowIntervalType
-
-    arr = IntervalArray.from_breaks([0.0, 1.0, 2.0, 3.0])
-    arr[1] = None
-
-    result = pa.array(arr)
-    assert isinstance(result.type, ArrowIntervalType)
-    assert result.type.closed == arr.closed
-    assert result.type.subtype == pa.float64()
-
-    # fields have missing values (not NaN)
-    left = pa.array([0.0, None, 2.0], type="float64")
-    right = pa.array([1.0, None, 3.0], type="float64")
-    assert result.storage.field("left").equals(left)
-    assert result.storage.field("right").equals(right)
-
-    # structarray itself also has missing values on the array level
-    vals = [
-        {"left": 0.0, "right": 1.0},
-        {"left": None, "right": None},
-        {"left": 2.0, "right": 3.0},
-    ]
-    expected = pa.StructArray.from_pandas(vals, mask=np.array([False, True, False]))
-    assert result.storage.equals(expected)
-
-
-@pytest.mark.filterwarnings(
-    "ignore:Passing a BlockManager to DataFrame:DeprecationWarning"
-)
-@pytest.mark.parametrize(
-    "breaks",
-    [[0.0, 1.0, 2.0, 3.0], date_range("2017", periods=4, freq="D")],
-    ids=["float", "datetime64[ns]"],
-)
-def test_arrow_table_roundtrip(breaks):
-    pa = pytest.importorskip("pyarrow")
-
-    from pandas.core.arrays.arrow.extension_types import ArrowIntervalType
-
-    arr = IntervalArray.from_breaks(breaks)
-    arr[1] = None
-    df = pd.DataFrame({"a": arr})
-
-    table = pa.table(df)
-    assert isinstance(table.field("a").type, ArrowIntervalType)
-    result = table.to_pandas()
-    assert isinstance(result["a"].dtype, pd.IntervalDtype)
-    tm.assert_frame_equal(result, df)
-
-    table2 = pa.concat_tables([table, table])
-    result = table2.to_pandas()
-    expected = pd.concat([df, df], ignore_index=True)
-    tm.assert_frame_equal(result, expected)
-
-    # GH-41040
-    table = pa.table(
-        [pa.chunked_array([], type=table.column(0).type)], schema=table.schema
-    )
-    result = table.to_pandas()
-    tm.assert_frame_equal(result, expected[0:0])
-
-
-@pytest.mark.filterwarnings(
-    "ignore:Passing a BlockManager to DataFrame:DeprecationWarning"
-)
-@pytest.mark.parametrize(
-    "breaks",
-    [[0.0, 1.0, 2.0, 3.0], date_range("2017", periods=4, freq="D")],
-    ids=["float", "datetime64[ns]"],
-)
-def test_arrow_table_roundtrip_without_metadata(breaks):
-    pa = pytest.importorskip("pyarrow")
-
-    arr = IntervalArray.from_breaks(breaks)
-    arr[1] = None
-    df = pd.DataFrame({"a": arr})
-
-    table = pa.table(df)
-    # remove the metadata
-    table = table.replace_schema_metadata()
-    assert table.schema.metadata is None
-
-    result = table.to_pandas()
-    assert isinstance(result["a"].dtype, pd.IntervalDtype)
-    tm.assert_frame_equal(result, df)
-
-
-def test_from_arrow_from_raw_struct_array():
-    # in case pyarrow lost the Interval extension type (eg on parquet roundtrip
-    # with datetime64[ns] subtype, see GH-45881), still allow conversion
-    # from arrow to IntervalArray
-    pa = pytest.importorskip("pyarrow")
-
-    arr = pa.array([{"left": 0, "right": 1}, {"left": 1, "right": 2}])
-    dtype = pd.IntervalDtype(np.dtype("int64"), closed="neither")
-
-    result = dtype.__from_arrow__(arr)
-    expected = IntervalArray.from_breaks(
-        np.array([0, 1, 2], dtype="int64"), closed="neither"
-    )
-    tm.assert_extension_array_equal(result, expected)
-
-    result = dtype.__from_arrow__(pa.chunked_array([arr]))
-    tm.assert_extension_array_equal(result, expected)
-
-
-@pytest.mark.parametrize("timezone", ["UTC", "US/Pacific", "GMT"])
-def test_interval_index_subtype(timezone, inclusive_endpoints_fixture):
-    # GH 46999
-    dates = date_range("2022", periods=3, tz=timezone)
-    dtype = f"interval[datetime64[ns, {timezone}], {inclusive_endpoints_fixture}]"
-    result = IntervalIndex.from_arrays(
-        ["2022-01-01", "2022-01-02"],
-        ["2022-01-02", "2022-01-03"],
-        closed=inclusive_endpoints_fixture,
-        dtype=dtype,
-    )
-    expected = IntervalIndex.from_arrays(
-        dates[:-1], dates[1:], closed=inclusive_endpoints_fixture
-    )
-    tm.assert_index_equal(result, expected)
diff --git a/pandas/tests/arrays/interval/test_interval_pyarrow.py b/pandas/tests/arrays/interval/test_interval_pyarrow.py
new file mode 100644
index 0000000000000..ef8701be81e2b
--- /dev/null
+++ b/pandas/tests/arrays/interval/test_interval_pyarrow.py
@@ -0,0 +1,160 @@
+import numpy as np
+import pytest
+
+import pandas as pd
+import pandas._testing as tm
+from pandas.core.arrays import IntervalArray
+
+
+def test_arrow_extension_type():
+    pa = pytest.importorskip("pyarrow")
+
+    from pandas.core.arrays.arrow.extension_types import ArrowIntervalType
+
+    p1 = ArrowIntervalType(pa.int64(), "left")
+    p2 = ArrowIntervalType(pa.int64(), "left")
+    p3 = ArrowIntervalType(pa.int64(), "right")
+
+    assert p1.closed == "left"
+    assert p1 == p2
+    assert p1 != p3
+    assert hash(p1) == hash(p2)
+    assert hash(p1) != hash(p3)
+
+
+def test_arrow_array():
+    pa = pytest.importorskip("pyarrow")
+
+    from pandas.core.arrays.arrow.extension_types import ArrowIntervalType
+
+    intervals = pd.interval_range(1, 5, freq=1).array
+
+    result = pa.array(intervals)
+    assert isinstance(result.type, ArrowIntervalType)
+    assert result.type.closed == intervals.closed
+    assert result.type.subtype == pa.int64()
+    assert result.storage.field("left").equals(pa.array([1, 2, 3, 4], type="int64"))
+    assert result.storage.field("right").equals(pa.array([2, 3, 4, 5], type="int64"))
+
+    expected = pa.array([{"left": i, "right": i + 1} for i in range(1, 5)])
+    assert result.storage.equals(expected)
+
+    # convert to its storage type
+    result = pa.array(intervals, type=expected.type)
+    assert result.equals(expected)
+
+    # unsupported conversions
+    with pytest.raises(TypeError, match="Not supported to convert IntervalArray"):
+        pa.array(intervals, type="float64")
+
+    with pytest.raises(TypeError, match="Not supported to convert IntervalArray"):
+        pa.array(intervals, type=ArrowIntervalType(pa.float64(), "left"))
+
+
+def test_arrow_array_missing():
+    pa = pytest.importorskip("pyarrow")
+
+    from pandas.core.arrays.arrow.extension_types import ArrowIntervalType
+
+    arr = IntervalArray.from_breaks([0.0, 1.0, 2.0, 3.0])
+    arr[1] = None
+
+    result = pa.array(arr)
+    assert isinstance(result.type, ArrowIntervalType)
+    assert result.type.closed == arr.closed
+    assert result.type.subtype == pa.float64()
+
+    # fields have missing values (not NaN)
+    left = pa.array([0.0, None, 2.0], type="float64")
+    right = pa.array([1.0, None, 3.0], type="float64")
+    assert result.storage.field("left").equals(left)
+    assert result.storage.field("right").equals(right)
+
+    # structarray itself also has missing values on the array level
+    vals = [
+        {"left": 0.0, "right": 1.0},
+        {"left": None, "right": None},
+        {"left": 2.0, "right": 3.0},
+    ]
+    expected = pa.StructArray.from_pandas(vals, mask=np.array([False, True, False]))
+    assert result.storage.equals(expected)
+
+
+@pytest.mark.filterwarnings(
+    "ignore:Passing a BlockManager to DataFrame:DeprecationWarning"
+)
+@pytest.mark.parametrize(
+    "breaks",
+    [[0.0, 1.0, 2.0, 3.0], pd.date_range("2017", periods=4, freq="D")],
+    ids=["float", "datetime64[ns]"],
+)
+def test_arrow_table_roundtrip(breaks):
+    pa = pytest.importorskip("pyarrow")
+
+    from pandas.core.arrays.arrow.extension_types import ArrowIntervalType
+
+    arr = IntervalArray.from_breaks(breaks)
+    arr[1] = None
+    df = pd.DataFrame({"a": arr})
+
+    table = pa.table(df)
+    assert isinstance(table.field("a").type, ArrowIntervalType)
+    result = table.to_pandas()
+    assert isinstance(result["a"].dtype, pd.IntervalDtype)
+    tm.assert_frame_equal(result, df)
+
+    table2 = pa.concat_tables([table, table])
+    result = table2.to_pandas()
+    expected = pd.concat([df, df], ignore_index=True)
+    tm.assert_frame_equal(result, expected)
+
+    # GH#41040
+    table = pa.table(
+        [pa.chunked_array([], type=table.column(0).type)], schema=table.schema
+    )
+    result = table.to_pandas()
+    tm.assert_frame_equal(result, expected[0:0])
+
+
+@pytest.mark.filterwarnings(
+    "ignore:Passing a BlockManager to DataFrame:DeprecationWarning"
+)
+@pytest.mark.parametrize(
+    "breaks",
+    [[0.0, 1.0, 2.0, 3.0], pd.date_range("2017", periods=4, freq="D")],
+    ids=["float", "datetime64[ns]"],
+)
+def test_arrow_table_roundtrip_without_metadata(breaks):
+    pa = pytest.importorskip("pyarrow")
+
+    arr = IntervalArray.from_breaks(breaks)
+    arr[1] = None
+    df = pd.DataFrame({"a": arr})
+
+    table = pa.table(df)
+    # remove the metadata
+    table = table.replace_schema_metadata()
+    assert table.schema.metadata is None
+
+    result = table.to_pandas()
+    assert isinstance(result["a"].dtype, pd.IntervalDtype)
+    tm.assert_frame_equal(result, df)
+
+
+def test_from_arrow_from_raw_struct_array():
+    # in case pyarrow lost the Interval extension type (eg on parquet roundtrip
+    # with datetime64[ns] subtype, see GH-45881), still allow conversion
+    # from arrow to IntervalArray
+    pa = pytest.importorskip("pyarrow")
+
+    arr = pa.array([{"left": 0, "right": 1}, {"left": 1, "right": 2}])
+    dtype = pd.IntervalDtype(np.dtype("int64"), closed="neither")
+
+    result = dtype.__from_arrow__(arr)
+    expected = IntervalArray.from_breaks(
+        np.array([0, 1, 2], dtype="int64"), closed="neither"
+    )
+    tm.assert_extension_array_equal(result, expected)
+
+    result = dtype.__from_arrow__(pa.chunked_array([arr]))
+    tm.assert_extension_array_equal(result, expected)
diff --git a/pandas/tests/indexes/interval/test_base.py b/pandas/tests/indexes/interval/test_base.py
deleted file mode 100644
index e0155a13481ac..0000000000000
--- a/pandas/tests/indexes/interval/test_base.py
+++ /dev/null
@@ -1,56 +0,0 @@
-import numpy as np
-import pytest
-
-from pandas import IntervalIndex
-import pandas._testing as tm
-
-
-class TestInterval:
-    """
-    Tests specific to the shared common index tests; unrelated tests should be placed
-    in test_interval.py or the specific test file (e.g. test_astype.py)
-    """
-
-    @pytest.fixture
-    def simple_index(self) -> IntervalIndex:
-        return IntervalIndex.from_breaks(range(11), closed="right")
-
-    @pytest.fixture
-    def index(self):
-        return tm.makeIntervalIndex(10)
-
-    def test_take(self, closed):
-        index = IntervalIndex.from_breaks(range(11), closed=closed)
-
-        result = index.take(range(10))
-        tm.assert_index_equal(result, index)
-
-        result = index.take([0, 0, 1])
-        expected = IntervalIndex.from_arrays([0, 0, 1], [1, 1, 2], closed=closed)
-        tm.assert_index_equal(result, expected)
-
-    def test_where(self, simple_index, listlike_box):
-        klass = listlike_box
-
-        idx = simple_index
-        cond = [True] * len(idx)
-        expected = idx
-        result = expected.where(klass(cond))
-        tm.assert_index_equal(result, expected)
-
-        cond = [False] + [True] * len(idx[1:])
-        expected = IntervalIndex([np.nan] + idx[1:].tolist())
-        result = idx.where(klass(cond))
-        tm.assert_index_equal(result, expected)
-
-    def test_getitem_2d_deprecated(self, simple_index):
-        # GH#30588 multi-dim indexing is deprecated, but raising is also acceptable
-        idx = simple_index
-        with pytest.raises(ValueError, match="multi-dimensional indexing not allowed"):
-            idx[:, None]
-        with pytest.raises(ValueError, match="multi-dimensional indexing not allowed"):
-            # GH#44051
-            idx[True]
-        with pytest.raises(ValueError, match="multi-dimensional indexing not allowed"):
-            # GH#44051
-            idx[False]
diff --git a/pandas/tests/indexes/interval/test_constructors.py b/pandas/tests/indexes/interval/test_constructors.py
index 1efe5ff980f6c..078a0e06e0ed7 100644
--- a/pandas/tests/indexes/interval/test_constructors.py
+++ b/pandas/tests/indexes/interval/test_constructors.py
@@ -488,6 +488,23 @@ def test_index_mixed_closed(self):
         tm.assert_index_equal(result, expected)
 
 
+@pytest.mark.parametrize("timezone", ["UTC", "US/Pacific", "GMT"])
+def test_interval_index_subtype(timezone, inclusive_endpoints_fixture):
+    # GH#46999
+    dates = date_range("2022", periods=3, tz=timezone)
+    dtype = f"interval[datetime64[ns, {timezone}], {inclusive_endpoints_fixture}]"
+    result = IntervalIndex.from_arrays(
+        ["2022-01-01", "2022-01-02"],
+        ["2022-01-02", "2022-01-03"],
+        closed=inclusive_endpoints_fixture,
+        dtype=dtype,
+    )
+    expected = IntervalIndex.from_arrays(
+        dates[:-1], dates[1:], closed=inclusive_endpoints_fixture
+    )
+    tm.assert_index_equal(result, expected)
+
+
 def test_dtype_closed_mismatch():
     # GH#38394 closed specified in both dtype and IntervalIndex constructor
 
diff --git a/pandas/tests/indexes/interval/test_indexing.py b/pandas/tests/indexes/interval/test_indexing.py
index db8f697b95cd8..2007a793843c9 100644
--- a/pandas/tests/indexes/interval/test_indexing.py
+++ b/pandas/tests/indexes/interval/test_indexing.py
@@ -19,12 +19,75 @@
     array,
     date_range,
     interval_range,
+    isna,
     period_range,
     timedelta_range,
 )
 import pandas._testing as tm
 
 
+class TestGetItem:
+    def test_getitem(self, closed):
+        idx = IntervalIndex.from_arrays((0, 1, np.nan), (1, 2, np.nan), closed=closed)
+        assert idx[0] == Interval(0.0, 1.0, closed=closed)
+        assert idx[1] == Interval(1.0, 2.0, closed=closed)
+        assert isna(idx[2])
+
+        result = idx[0:1]
+        expected = IntervalIndex.from_arrays((0.0,), (1.0,), closed=closed)
+        tm.assert_index_equal(result, expected)
+
+        result = idx[0:2]
+        expected = IntervalIndex.from_arrays((0.0, 1), (1.0, 2.0), closed=closed)
+        tm.assert_index_equal(result, expected)
+
+        result = idx[1:3]
+        expected = IntervalIndex.from_arrays(
+            (1.0, np.nan), (2.0, np.nan), closed=closed
+        )
+        tm.assert_index_equal(result, expected)
+
+    def test_getitem_2d_deprecated(self):
+        # GH#30588 multi-dim indexing is deprecated, but raising is also acceptable
+        idx = IntervalIndex.from_breaks(range(11), closed="right")
+        with pytest.raises(ValueError, match="multi-dimensional indexing not allowed"):
+            idx[:, None]
+        with pytest.raises(ValueError, match="multi-dimensional indexing not allowed"):
+            # GH#44051
+            idx[True]
+        with pytest.raises(ValueError, match="multi-dimensional indexing not allowed"):
+            # GH#44051
+            idx[False]
+
+
+class TestWhere:
+    def test_where(self, listlike_box):
+        klass = listlike_box
+
+        idx = IntervalIndex.from_breaks(range(11), closed="right")
+        cond = [True] * len(idx)
+        expected = idx
+        result = expected.where(klass(cond))
+        tm.assert_index_equal(result, expected)
+
+        cond = [False] + [True] * len(idx[1:])
+        expected = IntervalIndex([np.nan] + idx[1:].tolist())
+        result = idx.where(klass(cond))
+        tm.assert_index_equal(result, expected)
+
+
+class TestTake:
+    def test_take(self, closed):
+        index = IntervalIndex.from_breaks(range(11), closed=closed)
+
+        result = index.take(range(10))
+        tm.assert_index_equal(result, index)
+
+        result = index.take([0, 0, 1])
+        expected = IntervalIndex.from_arrays([0, 0, 1], [1, 1, 2], closed=closed)
+        tm.assert_index_equal(result, expected)
+
+
 class TestGetLoc:
     @pytest.mark.parametrize("side", ["right", "left", "both", "neither"])
     def test_get_loc_interval(self, closed, side):
diff --git a/pandas/tests/indexes/interval/test_interval.py b/pandas/tests/indexes/interval/test_interval.py
index dea40eff8d2ac..e19b1700236f5 100644
--- a/pandas/tests/indexes/interval/test_interval.py
+++ b/pandas/tests/indexes/interval/test_interval.py
@@ -341,26 +341,6 @@ def test_is_monotonic_with_nans(self):
         assert not index._is_strictly_monotonic_decreasing
         assert not index.is_monotonic_decreasing
 
-    def test_get_item(self, closed):
-        i = IntervalIndex.from_arrays((0, 1, np.nan), (1, 2, np.nan), closed=closed)
-        assert i[0] == Interval(0.0, 1.0, closed=closed)
-        assert i[1] == Interval(1.0, 2.0, closed=closed)
-        assert isna(i[2])
-
-        result = i[0:1]
-        expected = IntervalIndex.from_arrays((0.0,), (1.0,), closed=closed)
-        tm.assert_index_equal(result, expected)
-
-        result = i[0:2]
-        expected = IntervalIndex.from_arrays((0.0, 1), (1.0, 2.0), closed=closed)
-        tm.assert_index_equal(result, expected)
-
-        result = i[1:3]
-        expected = IntervalIndex.from_arrays(
-            (1.0, np.nan), (2.0, np.nan), closed=closed
-        )
-        tm.assert_index_equal(result, expected)
-
     @pytest.mark.parametrize(
         "breaks",
         [
diff --git a/pandas/tests/scalar/interval/test_arithmetic.py b/pandas/tests/scalar/interval/test_arithmetic.py
index 863446c64de42..603763227cb88 100644
--- a/pandas/tests/scalar/interval/test_arithmetic.py
+++ b/pandas/tests/scalar/interval/test_arithmetic.py
@@ -8,56 +8,185 @@
     Timedelta,
     Timestamp,
 )
+import pandas._testing as tm
 
 
-@pytest.mark.parametrize("method", ["__add__", "__sub__"])
-@pytest.mark.parametrize(
-    "interval",
-    [
-        Interval(Timestamp("2017-01-01 00:00:00"), Timestamp("2018-01-01 00:00:00")),
-        Interval(Timedelta(days=7), Timedelta(days=14)),
-    ],
-)
-@pytest.mark.parametrize(
-    "delta", [Timedelta(days=7), timedelta(7), np.timedelta64(7, "D")]
-)
-def test_time_interval_add_subtract_timedelta(interval, delta, method):
-    # https://github.com/pandas-dev/pandas/issues/32023
-    result = getattr(interval, method)(delta)
-    left = getattr(interval.left, method)(delta)
-    right = getattr(interval.right, method)(delta)
-    expected = Interval(left, right)
+class TestIntervalArithmetic:
+    def test_interval_add(self, closed):
+        interval = Interval(0, 1, closed=closed)
+        expected = Interval(1, 2, closed=closed)
 
-    assert result == expected
+        result = interval + 1
+        assert result == expected
 
+        result = 1 + interval
+        assert result == expected
 
-@pytest.mark.parametrize("interval", [Interval(1, 2), Interval(1.0, 2.0)])
-@pytest.mark.parametrize(
-    "delta", [Timedelta(days=7), timedelta(7), np.timedelta64(7, "D")]
-)
-def test_numeric_interval_add_timedelta_raises(interval, delta):
-    # https://github.com/pandas-dev/pandas/issues/32023
-    msg = "|".join(
+        result = interval
+        result += 1
+        assert result == expected
+
+        msg = r"unsupported operand type\(s\) for \+"
+        with pytest.raises(TypeError, match=msg):
+            interval + interval
+
+        with pytest.raises(TypeError, match=msg):
+            interval + "foo"
+
+    def test_interval_sub(self, closed):
+        interval = Interval(0, 1, closed=closed)
+        expected = Interval(-1, 0, closed=closed)
+
+        result = interval - 1
+        assert result == expected
+
+        result = interval
+        result -= 1
+        assert result == expected
+
+        msg = r"unsupported operand type\(s\) for -"
+        with pytest.raises(TypeError, match=msg):
+            interval - interval
+
+        with pytest.raises(TypeError, match=msg):
+            interval - "foo"
+
+    def test_interval_mult(self, closed):
+        interval = Interval(0, 1, closed=closed)
+        expected = Interval(0, 2, closed=closed)
+
+        result = interval * 2
+        assert result == expected
+
+        result = 2 * interval
+        assert result == expected
+
+        result = interval
+        result *= 2
+        assert result == expected
+
+        msg = r"unsupported operand type\(s\) for \*"
+        with pytest.raises(TypeError, match=msg):
+            interval * interval
+
+        msg = r"can\'t multiply sequence by non-int"
+        with pytest.raises(TypeError, match=msg):
+            interval * "foo"
+
+    def test_interval_div(self, closed):
+        interval = Interval(0, 1, closed=closed)
+        expected = Interval(0, 0.5, closed=closed)
+
+        result = interval / 2.0
+        assert result == expected
+
+        result = interval
+        result /= 2.0
+        assert result == expected
+
+        msg = r"unsupported operand type\(s\) for /"
+        with pytest.raises(TypeError, match=msg):
+            interval / interval
+
+        with pytest.raises(TypeError, match=msg):
+            interval / "foo"
+
+    def test_interval_floordiv(self, closed):
+        interval = Interval(1, 2, closed=closed)
+        expected = Interval(0, 1, closed=closed)
+
+        result = interval // 2
+        assert result == expected
+
+        result = interval
+        result //= 2
+        assert result == expected
+
+        msg = r"unsupported operand type\(s\) for //"
+        with pytest.raises(TypeError, match=msg):
+            interval // interval
+
+        with pytest.raises(TypeError, match=msg):
+            interval // "foo"
+
+    @pytest.mark.parametrize("method", ["__add__", "__sub__"])
+    @pytest.mark.parametrize(
+        "interval",
         [
-            "unsupported operand",
-            "cannot use operands",
-            "Only numeric, Timestamp and Timedelta endpoints are allowed",
-        ]
+            Interval(
+                Timestamp("2017-01-01 00:00:00"), Timestamp("2018-01-01 00:00:00")
+            ),
+            Interval(Timedelta(days=7), Timedelta(days=14)),
+        ],
     )
-    with pytest.raises((TypeError, ValueError), match=msg):
-        interval + delta
+    @pytest.mark.parametrize(
+        "delta", [Timedelta(days=7), timedelta(7), np.timedelta64(7, "D")]
+    )
+    def test_time_interval_add_subtract_timedelta(self, interval, delta, method):
+        # https://github.com/pandas-dev/pandas/issues/32023
+        result = getattr(interval, method)(delta)
+        left = getattr(interval.left, method)(delta)
+        right = getattr(interval.right, method)(delta)
+        expected = Interval(left, right)
+
+        assert result == expected
+
+    @pytest.mark.parametrize("interval", [Interval(1, 2), Interval(1.0, 2.0)])
+    @pytest.mark.parametrize(
+        "delta", [Timedelta(days=7), timedelta(7), np.timedelta64(7, "D")]
+    )
+    def test_numeric_interval_add_timedelta_raises(self, interval, delta):
+        # https://github.com/pandas-dev/pandas/issues/32023
+        msg = "|".join(
+            [
+                "unsupported operand",
+                "cannot use operands",
+                "Only numeric, Timestamp and Timedelta endpoints are allowed",
+            ]
+        )
+        with pytest.raises((TypeError, ValueError), match=msg):
+            interval + delta
+
+        with pytest.raises((TypeError, ValueError), match=msg):
+            delta + interval
+
+    @pytest.mark.parametrize("klass", [timedelta, np.timedelta64, Timedelta])
+    def test_timedelta_add_timestamp_interval(self, klass):
+        delta = klass(0)
+        expected = Interval(Timestamp("2020-01-01"), Timestamp("2020-02-01"))
+
+        result = delta + expected
+        assert result == expected
+
+        result = expected + delta
+        assert result == expected
 
-    with pytest.raises((TypeError, ValueError), match=msg):
-        delta + interval
 
+class TestIntervalComparisons:
+    def test_interval_equal(self):
+        assert Interval(0, 1) == Interval(0, 1, closed="right")
+        assert Interval(0, 1) != Interval(0, 1, closed="left")
+        assert Interval(0, 1) != 0
 
-@pytest.mark.parametrize("klass", [timedelta, np.timedelta64, Timedelta])
-def test_timedelta_add_timestamp_interval(klass):
-    delta = klass(0)
-    expected = Interval(Timestamp("2020-01-01"), Timestamp("2020-02-01"))
+    def test_interval_comparison(self):
+        msg = (
+            "'<' not supported between instances of "
+            "'pandas._libs.interval.Interval' and 'int'"
+        )
+        with pytest.raises(TypeError, match=msg):
+            Interval(0, 1) < 2
 
-    result = delta + expected
-    assert result == expected
+        assert Interval(0, 1) < Interval(1, 2)
+        assert Interval(0, 1) < Interval(0, 2)
+        assert Interval(0, 1) < Interval(0.5, 1.5)
+        assert Interval(0, 1) <= Interval(0, 1)
+        assert Interval(0, 1) > Interval(-1, 2)
+        assert Interval(0, 1) >= Interval(0, 1)
 
-    result = expected + delta
-    assert result == expected
+    def test_equality_comparison_broadcasts_over_array(self):
+        # https://github.com/pandas-dev/pandas/issues/35931
+        interval = Interval(0, 1)
+        arr = np.array([interval, interval])
+        result = interval == arr
+        expected = np.array([True, True])
+        tm.assert_numpy_array_equal(result, expected)
diff --git a/pandas/tests/scalar/interval/test_constructors.py b/pandas/tests/scalar/interval/test_constructors.py
new file mode 100644
index 0000000000000..a4bc00b923434
--- /dev/null
+++ b/pandas/tests/scalar/interval/test_constructors.py
@@ -0,0 +1,51 @@
+import pytest
+
+from pandas import (
+    Interval,
+    Period,
+    Timestamp,
+)
+
+
+class TestIntervalConstructors:
+    @pytest.mark.parametrize(
+        "left, right",
+        [
+            ("a", "z"),
+            (("a", "b"), ("c", "d")),
+            (list("AB"), list("ab")),
+            (Interval(0, 1), Interval(1, 2)),
+            (Period("2018Q1", freq="Q"), Period("2018Q1", freq="Q")),
+        ],
+    )
+    def test_construct_errors(self, left, right):
+        # GH#23013
+        msg = "Only numeric, Timestamp and Timedelta endpoints are allowed"
+        with pytest.raises(ValueError, match=msg):
+            Interval(left, right)
+
+    def test_constructor_errors(self):
+        msg = "invalid option for 'closed': foo"
+        with pytest.raises(ValueError, match=msg):
+            Interval(0, 1, closed="foo")
+
+        msg = "left side of interval must be <= right side"
+        with pytest.raises(ValueError, match=msg):
+            Interval(1, 0)
+
+    @pytest.mark.parametrize(
+        "tz_left, tz_right", [(None, "UTC"), ("UTC", None), ("UTC", "US/Eastern")]
+    )
+    def test_constructor_errors_tz(self, tz_left, tz_right):
+        # GH#18538
+        left = Timestamp("2017-01-01", tz=tz_left)
+        right = Timestamp("2017-01-02", tz=tz_right)
+
+        if tz_left is None or tz_right is None:
+            error = TypeError
+            msg = "Cannot compare tz-naive and tz-aware timestamps"
+        else:
+            error = ValueError
+            msg = "left and right must have the same time zone"
+        with pytest.raises(error, match=msg):
+            Interval(left, right)
diff --git a/pandas/tests/scalar/interval/test_contains.py b/pandas/tests/scalar/interval/test_contains.py
new file mode 100644
index 0000000000000..8dfca117a658b
--- /dev/null
+++ b/pandas/tests/scalar/interval/test_contains.py
@@ -0,0 +1,73 @@
+import pytest
+
+from pandas import (
+    Interval,
+    Timedelta,
+    Timestamp,
+)
+
+
+class TestContains:
+    def test_contains(self):
+        interval = Interval(0, 1)
+        assert 0.5 in interval
+        assert 1 in interval
+        assert 0 not in interval
+
+        interval_both = Interval(0, 1, "both")
+        assert 0 in interval_both
+        assert 1 in interval_both
+
+        interval_neither = Interval(0, 1, closed="neither")
+        assert 0 not in interval_neither
+        assert 0.5 in interval_neither
+        assert 1 not in interval_neither
+
+    def test_contains_interval(self, inclusive_endpoints_fixture):
+        interval1 = Interval(0, 1, "both")
+        interval2 = Interval(0, 1, inclusive_endpoints_fixture)
+        assert interval1 in interval1
+        assert interval2 in interval2
+        assert interval2 in interval1
+        assert interval1 not in interval2 or inclusive_endpoints_fixture == "both"
+
+    def test_contains_infinite_length(self):
+        interval1 = Interval(0, 1, "both")
+        interval2 = Interval(float("-inf"), float("inf"), "neither")
+        assert interval1 in interval2
+        assert interval2 not in interval1
+
+    def test_contains_zero_length(self):
+        interval1 = Interval(0, 1, "both")
+        interval2 = Interval(-1, -1, "both")
+        interval3 = Interval(0.5, 0.5, "both")
+        assert interval2 not in interval1
+        assert interval3 in interval1
+        assert interval2 not in interval3 and interval3 not in interval2
+        assert interval1 not in interval2 and interval1 not in interval3
+
+    @pytest.mark.parametrize(
+        "type1",
+        [
+            (0, 1),
+            (Timestamp(2000, 1, 1, 0), Timestamp(2000, 1, 1, 1)),
+            (Timedelta("0h"), Timedelta("1h")),
+        ],
+    )
+    @pytest.mark.parametrize(
+        "type2",
+        [
+            (0, 1),
+            (Timestamp(2000, 1, 1, 0), Timestamp(2000, 1, 1, 1)),
+            (Timedelta("0h"), Timedelta("1h")),
+        ],
+    )
+    def test_contains_mixed_types(self, type1, type2):
+        interval1 = Interval(*type1)
+        interval2 = Interval(*type2)
+        if type1 == type2:
+            assert interval1 in interval2
+        else:
+            msg = "^'<=' not supported between instances of"
+            with pytest.raises(TypeError, match=msg):
+                interval1 in interval2
diff --git a/pandas/tests/scalar/interval/test_formats.py b/pandas/tests/scalar/interval/test_formats.py
new file mode 100644
index 0000000000000..6bf7aa91df3ce
--- /dev/null
+++ b/pandas/tests/scalar/interval/test_formats.py
@@ -0,0 +1,11 @@
+from pandas import Interval
+
+
+def test_interval_repr():
+    interval = Interval(0, 1)
+    assert repr(interval) == "Interval(0, 1, closed='right')"
+    assert str(interval) == "(0, 1]"
+
+    interval_left = Interval(0, 1, closed="left")
+    assert repr(interval_left) == "Interval(0, 1, closed='left')"
+    assert str(interval_left) == "[0, 1)"
diff --git a/pandas/tests/scalar/interval/test_interval.py b/pandas/tests/scalar/interval/test_interval.py
index 4841c488a5768..91b31e82f9c52 100644
--- a/pandas/tests/scalar/interval/test_interval.py
+++ b/pandas/tests/scalar/interval/test_interval.py
@@ -3,12 +3,9 @@
 
 from pandas import (
     Interval,
-    Period,
     Timedelta,
     Timestamp,
 )
-import pandas._testing as tm
-import pandas.core.common as com
 
 
 @pytest.fixture
@@ -23,48 +20,6 @@ def test_properties(self, interval):
         assert interval.right == 1
         assert interval.mid == 0.5
 
-    def test_repr(self, interval):
-        assert repr(interval) == "Interval(0, 1, closed='right')"
-        assert str(interval) == "(0, 1]"
-
-        interval_left = Interval(0, 1, closed="left")
-        assert repr(interval_left) == "Interval(0, 1, closed='left')"
-        assert str(interval_left) == "[0, 1)"
-
-    def test_contains(self, interval):
-        assert 0.5 in interval
-        assert 1 in interval
-        assert 0 not in interval
-
-        interval_both = Interval(0, 1, "both")
-        assert 0 in interval_both
-        assert 1 in interval_both
-
-        interval_neither = Interval(0, 1, closed="neither")
-        assert 0 not in interval_neither
-        assert 0.5 in interval_neither
-        assert 1 not in interval_neither
-
-    def test_equal(self):
-        assert Interval(0, 1) == Interval(0, 1, closed="right")
-        assert Interval(0, 1) != Interval(0, 1, closed="left")
-        assert Interval(0, 1) != 0
-
-    def test_comparison(self):
-        msg = (
-            "'<' not supported between instances of "
-            "'pandas._libs.interval.Interval' and 'int'"
-        )
-        with pytest.raises(TypeError, match=msg):
-            Interval(0, 1) < 2
-
-        assert Interval(0, 1) < Interval(1, 2)
-        assert Interval(0, 1) < Interval(0, 2)
-        assert Interval(0, 1) < Interval(0.5, 1.5)
-        assert Interval(0, 1) <= Interval(0, 1)
-        assert Interval(0, 1) > Interval(-1, 2)
-        assert Interval(0, 1) >= Interval(0, 1)
-
     def test_hash(self, interval):
         # should not raise
         hash(interval)
@@ -130,150 +85,3 @@ def test_is_empty(self, left, right, closed):
         result = iv.is_empty
         expected = closed != "both"
         assert result is expected
-
-    @pytest.mark.parametrize(
-        "left, right",
-        [
-            ("a", "z"),
-            (("a", "b"), ("c", "d")),
-            (list("AB"), list("ab")),
-            (Interval(0, 1), Interval(1, 2)),
-            (Period("2018Q1", freq="Q"), Period("2018Q1", freq="Q")),
-        ],
-    )
-    def test_construct_errors(self, left, right):
-        # GH 23013
-        msg = "Only numeric, Timestamp and Timedelta endpoints are allowed"
-        with pytest.raises(ValueError, match=msg):
-            Interval(left, right)
-
-    def test_math_add(self, closed):
-        interval = Interval(0, 1, closed=closed)
-        expected = Interval(1, 2, closed=closed)
-
-        result = interval + 1
-        assert result == expected
-
-        result = 1 + interval
-        assert result == expected
-
-        result = interval
-        result += 1
-        assert result == expected
-
-        msg = r"unsupported operand type\(s\) for \+"
-        with pytest.raises(TypeError, match=msg):
-            interval + interval
-
-        with pytest.raises(TypeError, match=msg):
-            interval + "foo"
-
-    def test_math_sub(self, closed):
-        interval = Interval(0, 1, closed=closed)
-        expected = Interval(-1, 0, closed=closed)
-
-        result = interval - 1
-        assert result == expected
-
-        result = interval
-        result -= 1
-        assert result == expected
-
-        msg = r"unsupported operand type\(s\) for -"
-        with pytest.raises(TypeError, match=msg):
-            interval - interval
-
-        with pytest.raises(TypeError, match=msg):
-            interval - "foo"
-
-    def test_math_mult(self, closed):
-        interval = Interval(0, 1, closed=closed)
-        expected = Interval(0, 2, closed=closed)
-
-        result = interval * 2
-        assert result == expected
-
-        result = 2 * interval
-        assert result == expected
-
-        result = interval
-        result *= 2
-        assert result == expected
-
-        msg = r"unsupported operand type\(s\) for \*"
-        with pytest.raises(TypeError, match=msg):
-            interval * interval
-
-        msg = r"can\'t multiply sequence by non-int"
-        with pytest.raises(TypeError, match=msg):
-            interval * "foo"
-
-    def test_math_div(self, closed):
-        interval = Interval(0, 1, closed=closed)
-        expected = Interval(0, 0.5, closed=closed)
-
-        result = interval / 2.0
-        assert result == expected
-
-        result = interval
-        result /= 2.0
-        assert result == expected
-
-        msg = r"unsupported operand type\(s\) for /"
-        with pytest.raises(TypeError, match=msg):
-            interval / interval
-
-        with pytest.raises(TypeError, match=msg):
-            interval / "foo"
-
-    def test_math_floordiv(self, closed):
-        interval = Interval(1, 2, closed=closed)
-        expected = Interval(0, 1, closed=closed)
-
-        result = interval // 2
-        assert result == expected
-
-        result = interval
-        result //= 2
-        assert result == expected
-
-        msg = r"unsupported operand type\(s\) for //"
-        with pytest.raises(TypeError, match=msg):
-            interval // interval
-
-        with pytest.raises(TypeError, match=msg):
-            interval // "foo"
-
-    def test_constructor_errors(self):
-        msg = "invalid option for 'closed': foo"
-        with pytest.raises(ValueError, match=msg):
-            Interval(0, 1, closed="foo")
-
-        msg = "left side of interval must be <= right side"
-        with pytest.raises(ValueError, match=msg):
-            Interval(1, 0)
-
-    @pytest.mark.parametrize(
-        "tz_left, tz_right", [(None, "UTC"), ("UTC", None), ("UTC", "US/Eastern")]
-    )
-    def test_constructor_errors_tz(self, tz_left, tz_right):
-        # GH 18538
-        left = Timestamp("2017-01-01", tz=tz_left)
-        right = Timestamp("2017-01-02", tz=tz_right)
-
-        if com.any_none(tz_left, tz_right):
-            error = TypeError
-            msg = "Cannot compare tz-naive and tz-aware timestamps"
-        else:
-            error = ValueError
-            msg = "left and right must have the same time zone"
-        with pytest.raises(error, match=msg):
-            Interval(left, right)
-
-    def test_equality_comparison_broadcasts_over_array(self):
-        # https://github.com/pandas-dev/pandas/issues/35931
-        interval = Interval(0, 1)
-        arr = np.array([interval, interval])
-        result = interval == arr
-        expected = np.array([True, True])
-        tm.assert_numpy_array_equal(result, expected)
diff --git a/pandas/tests/scalar/interval/test_ops.py b/pandas/tests/scalar/interval/test_overlaps.py
similarity index 54%
rename from pandas/tests/scalar/interval/test_ops.py
rename to pandas/tests/scalar/interval/test_overlaps.py
index 92db6ac772830..7fcf59d7bb4af 100644
--- a/pandas/tests/scalar/interval/test_ops.py
+++ b/pandas/tests/scalar/interval/test_overlaps.py
@@ -1,4 +1,3 @@
-"""Tests for Interval-Interval operations, such as overlaps, contains, etc."""
 import pytest
 
 from pandas import (
@@ -66,54 +65,3 @@ def test_overlaps_invalid_type(self, other):
         msg = f"`other` must be an Interval, got {type(other).__name__}"
         with pytest.raises(TypeError, match=msg):
             interval.overlaps(other)
-
-
-class TestContains:
-    def test_contains_interval(self, inclusive_endpoints_fixture):
-        interval1 = Interval(0, 1, "both")
-        interval2 = Interval(0, 1, inclusive_endpoints_fixture)
-        assert interval1 in interval1
-        assert interval2 in interval2
-        assert interval2 in interval1
-        assert interval1 not in interval2 or inclusive_endpoints_fixture == "both"
-
-    def test_contains_infinite_length(self):
-        interval1 = Interval(0, 1, "both")
-        interval2 = Interval(float("-inf"), float("inf"), "neither")
-        assert interval1 in interval2
-        assert interval2 not in interval1
-
-    def test_contains_zero_length(self):
-        interval1 = Interval(0, 1, "both")
-        interval2 = Interval(-1, -1, "both")
-        interval3 = Interval(0.5, 0.5, "both")
-        assert interval2 not in interval1
-        assert interval3 in interval1
-        assert interval2 not in interval3 and interval3 not in interval2
-        assert interval1 not in interval2 and interval1 not in interval3
-
-    @pytest.mark.parametrize(
-        "type1",
-        [
-            (0, 1),
-            (Timestamp(2000, 1, 1, 0), Timestamp(2000, 1, 1, 1)),
-            (Timedelta("0h"), Timedelta("1h")),
-        ],
-    )
-    @pytest.mark.parametrize(
-        "type2",
-        [
-            (0, 1),
-            (Timestamp(2000, 1, 1, 0), Timestamp(2000, 1, 1, 1)),
-            (Timedelta("0h"), Timedelta("1h")),
-        ],
-    )
-    def test_contains_mixed_types(self, type1, type2):
-        interval1 = Interval(*type1)
-        interval2 = Interval(*type2)
-        if type1 == type2:
-            assert interval1 in interval2
-        else:
-            msg = "^'<=' not supported between instances of"
-            with pytest.raises(TypeError, match=msg):
-                interval1 in interval2