feat(frequency): ✨ add harmonics related methods (#268)

lib/src/note/frequency.dart

@@ -80,6 +80,40 @@ class Frequency implements Comparable<Frequency> {
     );
   }
 
+  /// Returns the harmonic at [index] from this [Frequency], including negative
+  /// values as part of the [undertone series](https://en.wikipedia.org/wiki/Undertone_series).
+  ///
+  /// Example:
+  /// ```dart
+  /// const Frequency(220).harmonic(1) == const Frequency(440)
+  /// const Frequency(880).harmonic(-3) == const Frequency(220)
+  ///
+  /// Note.c.inOctave(1).equalTemperamentFrequency().harmonic(3)
+  ///   .closestPositionedNote().$1 == Note.e.inOctave(3)
+  /// ```
+  Frequency harmonic(int index) =>
+      index.isNegative ? this / (index.abs() + 1) : this * (index + 1);
+
+  /// Returns a [Set] of the [harmonics series](https://en.wikipedia.org/wiki/Harmonic_series_(music))
+  /// [upToIndex] from this [Frequency].
+  ///
+  /// Example:
+  /// ```dart
+  /// Note.a.inOctave(3).equalTemperamentFrequency().harmonics(upTo: 2)
+  ///   == {const Frequency(220), const Frequency(440), const Frequency(660)}
+  ///
+  /// Note.a.inOctave(5).equalTemperamentFrequency().harmonics(upTo: -2)
+  ///   == {const Frequency(880), const Frequency(440), const Frequency(293.33)}
+  ///
+  /// Note.c.inOctave(1).equalTemperamentFrequency().harmonics(upTo: 4)
+  ///   .map((frequency) => frequency.closestPositionedNote().$1).toSet()
+  ///   == {Note.c.inOctave(1), Note.c.inOctave(2), Note.g.inOctave(2),
+  ///       Note.c.inOctave(3), Note.e.inOctave(3)}
+  /// ```
+  Set<Frequency> harmonics({required int upToIndex}) => {
+        for (var i = 0; i <= upToIndex.abs(); i++) harmonic(i * upToIndex.sign),
+      };
+
   /// Adds [other] to this [Frequency].
   ///
   /// Example:

test/src/note/frequency_test.dart

@@ -82,6 +82,79 @@ void main() {
       });
     });
 
+    group('.harmonic()', () {
+      test('should return the harmonic at index from this Frequency', () {
+        expect(const Frequency(880).harmonic(-3), const Frequency(220));
+        expect(const Frequency(440).harmonic(-1), const Frequency(220));
+        expect(const Frequency(110).harmonic(0), const Frequency(110));
+        expect(const Frequency(256).harmonic(1), const Frequency(512));
+        expect(const Frequency(32).harmonic(4), const Frequency(160));
+      });
+    });
+
+    group('.harmonics()', () {
+      test(
+        'should return a Set of the harmonic series up to index from this '
+        'Frequency',
+        () {
+          expect(
+            const Frequency(512).harmonics(upToIndex: -15),
+            {
+              const Frequency(512),
+              const Frequency(256),
+              const Frequency(170.66666666666666),
+              const Frequency(128),
+              const Frequency(102.4),
+              const Frequency(85.33333333333333),
+              const Frequency(73.14285714285714),
+              const Frequency(64),
+              const Frequency(56.888888888888886),
+              const Frequency(51.2),
+              const Frequency(46.54545454545455),
+              const Frequency(42.666666666666664),
+              const Frequency(39.38461538461539),
+              const Frequency(36.57142857142857),
+              const Frequency(34.13333333333333),
+              const Frequency(32),
+            },
+          );
+          expect(
+            const Frequency(400).harmonics(upToIndex: -1),
+            {const Frequency(400), const Frequency(200)},
+          );
+          expect(
+            const Frequency(220).harmonics(upToIndex: 0),
+            {const Frequency(220)},
+          );
+          expect(
+            const Frequency(110).harmonics(upToIndex: 1),
+            {const Frequency(110), const Frequency(220)},
+          );
+          expect(
+            const Frequency(32).harmonics(upToIndex: 15),
+            {
+              const Frequency(32),
+              const Frequency(64),
+              const Frequency(96),
+              const Frequency(128),
+              const Frequency(160),
+              const Frequency(192),
+              const Frequency(224),
+              const Frequency(256),
+              const Frequency(288),
+              const Frequency(320),
+              const Frequency(352),
+              const Frequency(384),
+              const Frequency(416),
+              const Frequency(448),
+              const Frequency(480),
+              const Frequency(512),
+            },
+          );
+        },
+      );
+    });
+
     group('operator +()', () {
       test('should add other to this Frequency', () {
         expect(