Add interval vector calculations, tests

setclass/setclass.py

@@ -48,7 +48,7 @@ class SetClass(list):
 
     def __repr__(self) -> str:
         """Return the Python instance string representation."""
-        return f"SetClass{self.pitch_classes}".replace(' ', '')
+        return f"SetClass{set(self.pitch_classes) or '{}'}".replace(' ', '')
 
     def __hash__(self) -> int:
         return sum([hash(i) for i in self.pitch_classes])
@@ -89,6 +89,38 @@ class SetClass(list):
         intervals.append(self.tonality - prev)
         return intervals
 
+    @cache_property
+    def interval_vector(self):
+        """
+        An ordered tuple containing the multiplicities of each interval class in the set class.
+        Denoted in angle-brackets, e.g.
+        The interval vector of {0,2,4,5,7,9,11} is ⟨2,5,4,3,6,1⟩
+        — Rahn (1987), p. 100
+        """
+        from itertools import combinations
+        iv = [0 for i in range(1, int(self.tonality / 2) + 1)]
+        for (a, b) in combinations(self.pitch_classes, 2):
+            ic = SetClass.unordered_interval(a, b)
+            iv[ic - 1] += 1
+        return iv
+
+    def ordered_interval(a: int, b: int) -> int:
+        """
+        The ordered interval or "directed interval" (Babbitt) of two pitch classes is determined by
+        the difference of the pitch class values, modulo 12:
+        i⟨a,b⟩ = b-a mod 12  — Rahn (1987), p. 25
+        """
+        return (b % 12 - a % 12) % 12
+
+    def unordered_interval(a: int, b: int) -> int:
+        """
+        The unordered interval (also "interval distance", "interval class", "ic", or "undirected
+        interval") of two pitch classes is the smaller of the two possible ordered intervals
+        (differences in pitch class value):
+        i(a,b) = min: i⟨a,b⟩, i⟨b,a⟩  — Rahn (1987), p. 28
+        """
+        return min(SetClass.ordered_interval(a, b), SetClass.ordered_interval(b, a))
+
     @cache_property
     def versions(self):
         """

setclass/tests/test_setclass.py

@@ -38,6 +38,31 @@ def test_repeat_intervals():
     assert a == SetClass(12, 1, -11, 15, -9)
 
 
+def test_interval_vector():
+    test = [
+        # pairs of set class, expected interval vector
+        (SetClass(0, 3, 4, 7, 8, 11), [3, 0, 3, 6, 3, 0]),
+        (SetClass(0, 1, 3, 5, 6, 8, 10), [2, 5, 4, 3, 6, 1]),
+    ]
+    for (sc, iv) in test:
+        assert sc.interval_vector == iv
+
+
+def test_interval_vector_invarance():
+    test = [
+        SetClass(0, 1, 3, 5, 6, 8, 10),
+        SetClass(0, 1, 3, 5, 7, 8, 10),
+        SetClass(0, 2, 3, 5, 7, 8, 10),
+        SetClass(0, 2, 3, 5, 7, 9, 10),
+        SetClass(0, 2, 4, 5, 7, 9, 10),
+        SetClass(0, 2, 4, 5, 7, 9, 11),
+        SetClass(0, 2, 4, 6, 7, 9, 11),
+    ]
+    iv = [2, 5, 4, 3, 6, 1]
+    for sc in test:
+        assert sc.interval_vector == iv
+
+
 # ----------------------------------------------------------------------------
 # Example Forte 5-20 set class
 f520 = SetClass(0, 1, 5, 6, 8)
@@ -180,11 +205,11 @@ def test_empty_bright_dark_forms_equal():
 
 
 def test_empty_duodecimal_notation():
-    assert empty.duodecimal_notation == 'SetClass[]'
+    assert empty.duodecimal_notation == 'SetClass{}'
 
 
 def test_empty_dozenal_notation():
-    assert empty.dozenal_notation == 'SetClass[]'
+    assert empty.dozenal_notation == 'SetClass{}'
 
 
 def test_empty_leonard_notation():
@@ -192,7 +217,7 @@ def test_empty_leonard_notation():
 
 
 # ----------------------------------------------------------------------------
-# Forte 12-1, the complement of empty (full set class)
+# Forte 12-1, the complement of empty is the "aggregate" set class
 f121 = empty.complement
 
 
@@ -239,11 +264,11 @@ def test_empty_complement_bright_dark_forms_equal():
 
 
 def test_empty_complement_duodecimal_notation():
-    assert f121.duodecimal_notation == 'SetClass[0,1,2,3,4,5,6,7,8,9,T,E]'
+    assert f121.duodecimal_notation == 'SetClass{0,1,2,3,4,5,6,7,8,9,T,E}'
 
 
 def test_empty_complement_dozenal_notation():
-    assert f121.dozenal_notation == 'SetClass[0,1,2,3,4,5,6,7,8,9,↊,↋]'
+    assert f121.dozenal_notation == 'SetClass{0,1,2,3,4,5,6,7,8,9,↊,↋}'
 
 
 def test_empty_complement_leonard_notation():