diff --git a/setclass/setclass.py b/setclass/setclass.py
index dc62532..36946ce 100644
--- a/setclass/setclass.py
+++ b/setclass/setclass.py
@@ -149,6 +149,30 @@ class SetClass(list):
         versions.sort(key=lambda x: x.brightness)
         return versions
 
+    @cache_property
+    def rahn_normal_form(self):
+        """
+        Return the Rahn normal form of the set class; Leonard describes this as "most dispersed from
+        the right". Find the smallest outside interval, and proceed inwards from the right until one
+        result remains. See Rahn (1987), p. 33
+        """
+        # Set class {0,2,4,5,8,9} has four darkest versions:
+        # {0,2,4,5,8,9}   B = 28
+        # {0,1,4,6,8,9}   B = 28
+        # {0,2,3,6,7,10}  B = 28
+        # {0,1,4,5,8,10}  B = 28
+        # {0,3,5,7,8,11}  B = 34
+        # {0,3,4,7,9,11}  B = 34
+        def _most_dispersed(versions, n):
+            return [i for i in versions if i.pitch_classes[-n] == min([i.pitch_classes[-n] for i in versions])]
+
+        versions = self.versions
+        n = 1
+        while len(versions) > 1:
+            versions = _most_dispersed(versions, n)
+            n += 1
+        return versions[0]
+
     @cache_property
     def darkest_form(self):
         """
@@ -241,10 +265,9 @@ class SetClass(list):
             return chain.from_iterable(combinations(seq, r) for r in range(len(seq) + 1))
 
         if tonality < cardinality:
-            return ValueError("Set classes of cardinality {cardinality} are not possible in a {tonality}-tone octave.")
+            raise ValueError("Set classes of cardinality {cardinality} are not possible in a {tonality}-tone octave.")
 
-        a = set(SetClass(*i, tonality=tonality) for i in _powerset(range(tonality)) if len(i) == cardinality and 0 in i)
-        return a
+        return set(SetClass(*i, tonality=tonality) for i in _powerset(range(tonality)) if len(i) == cardinality and 0 in i)
 
     def darkest_of_cardinality(cardinality: int, tonality: int = 12, prime: bool = False) -> set:
         """
@@ -253,8 +276,13 @@ class SetClass(list):
         Warning: high values of tonality can take a long time to calculate (T=24 takes about a
         minute on an Intel i7-13700H CPU).
         """
-        if tonality < cardinality:
-            return ValueError("Set classes of cardinality {cardinality} are not possible in a {tonality}-tone octave.")
+        return set(i.darkest_form for i in SetClass.all_of_cardinality(cardinality, tonality))
 
-        a = set(i.darkest_form for i in SetClass.all_of_cardinality(cardinality, tonality))
-        return a
+    def normal_of_cardinality(cardinality: int, tonality: int = 12, prime: bool = False) -> set:
+        """
+        Returns all set classes of a given cardinality, in their (darkest) Rahn normal forms (ignore
+        rotations). Tonality can be specified, default is 12.
+        Warning: high values of tonality can take a long time to calculate (T=24 takes about a
+        minute on an Intel i7-13700H CPU).
+        """
+        return set(i.rahn_normal_form for i in SetClass.all_of_cardinality(cardinality, tonality))
diff --git a/setclass/tests/test_cardinalities.py b/setclass/tests/test_cardinalities.py
index c9c5e79..1c2a751 100644
--- a/setclass/tests/test_cardinalities.py
+++ b/setclass/tests/test_cardinalities.py
@@ -1,3 +1,4 @@
+import pytest
 from setclass.setclass import SetClass
 
 
@@ -13,6 +14,30 @@ def test_darkest_of_cardinality_set_lengths():
     assert [len(s) for s in sets] == [1, 6, 22, 55, 66, 127, 66, 55, 22, 6, 1, 1]
 
 
+def test_normal_of_cardinality_set_lengths():
+    "Confirm expected lengths of the sets of set classes, for cardinality 1 through 12"
+    sets = [SetClass.normal_of_cardinality(i + 1) for i in range(12)]
+    assert [len(s) for s in sets] == [1, 6, 19, 43, 66, 80, 66, 43, 19, 6, 1, 1]
+
+
+def test_all_of_cardinality_error():
+    "Set cardinality ≤ tonality"
+    with pytest.raises(ValueError):
+        SetClass.normal_of_cardinality(13)
+
+
+def test_darkest_of_cardinality_error():
+    "Set cardinality ≤ tonality"
+    with pytest.raises(ValueError):
+        SetClass.normal_of_cardinality(13)
+
+
+def test_normal_of_cardinality_error():
+    "Set cardinality ≤ tonality"
+    with pytest.raises(ValueError):
+        SetClass.normal_of_cardinality(13)
+
+
 def test_all_of_cardinality():
     s3 = SetClass.all_of_cardinality(3)
     s6 = SetClass.all_of_cardinality(6)
diff --git a/setclass/tests/test_setclass.py b/setclass/tests/test_setclass.py
index 8f8b4f7..f16c957 100644
--- a/setclass/tests/test_setclass.py
+++ b/setclass/tests/test_setclass.py
@@ -116,6 +116,20 @@ def test_darkest_form():
     assert d.leonard_notation == '[0₁1₂3₄7₁8₄]⁽¹⁹⁾'
 
 
+def test_rahn_normal_form():
+    r = f520.rahn_normal_form
+    assert r in f520.versions
+    assert r == SetClass(0, 1, 5, 6, 8)
+
+
+def test_inversion():
+    i = f520.inversion
+    assert i not in f520.versions
+    assert i not in f520.complement.versions
+    assert i not in f520.complement.inversion.versions
+    assert i == SetClass(0, 4, 6, 7, 11)
+
+
 def test_leonard_notation():
     assert f520.leonard_notation == '[0₁1₄5₁6₂8₄]⁽²⁰⁾'
 
@@ -152,6 +166,20 @@ def test_complement_versions():
     assert len(f520.complement.versions) == 7
 
 
+def test_complement_rahn_normal_form():
+    r = f520.complement.rahn_normal_form
+    assert r in f520.complement.versions
+    assert r == SetClass(0, 2, 3, 4, 7, 8, 9)
+
+
+def test_complement_inversion():
+    i = f520.complement.inversion
+    assert i not in f520.versions
+    assert i not in f520.inversion.versions
+    assert i not in f520.complement.versions
+    assert i == SetClass(0, 3, 4, 5, 7, 10, 11)
+
+
 def test_complement_brightest_form():
     b = f520.complement.brightest_form
     assert b in f520.complement.versions