diff --git a/masque/ref.py b/masque/ref.py
index f3241e4..a40776a 100644
--- a/masque/ref.py
+++ b/masque/ref.py
@@ -44,7 +44,7 @@ class Ref(
     __slots__ = (
         '_mirrored',
         # inherited
-        '_offset', '_rotation', 'scale', '_repetition', '_annotations',
+        '_offset', '_rotation', '_scale', '_repetition', '_annotations',
         )
 
     _mirrored: bool
diff --git a/masque/test/test_ref.py b/masque/test/test_ref.py
index e2d266b..c1dbf26 100644
--- a/masque/test/test_ref.py
+++ b/masque/test/test_ref.py
@@ -1,7 +1,9 @@
 from typing import cast, TYPE_CHECKING
+import pytest
 from numpy.testing import assert_equal, assert_allclose
 from numpy import pi
 
+from ..error import MasqueError
 from ..pattern import Pattern
 from ..ref import Ref
 from ..repetition import Grid
@@ -70,3 +72,18 @@ def test_ref_copy() -> None:
 
     ref2.offset[0] = 100
     assert ref1.offset[0] == 1
+
+
+def test_ref_rejects_nonpositive_scale() -> None:
+    with pytest.raises(MasqueError, match='Scale must be positive'):
+        Ref(scale=0)
+
+    with pytest.raises(MasqueError, match='Scale must be positive'):
+        Ref(scale=-1)
+
+
+def test_ref_scale_by_rejects_nonpositive_scale() -> None:
+    ref = Ref(scale=2.0)
+
+    with pytest.raises(MasqueError, match='Scale must be positive'):
+        ref.scale_by(-1)