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Visualize Two Note Harmonies with Lissajous Diagrams

Visualize Two Note Harmonies with Lissajous Diagrams
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2018-07-21 01:40
TrigonometryCoordinate GeometryParametric Equation
This example uses Lissajous diagrams to visualize the harmony between two notes. It involves core concepts of trigonometry and coordinate geometry. Users can adjust the frequency, phase, and amplitude of the notes using GeoGebra commands like Segment, CurveCartesian, and Textfield, observing the changes in the Lissajous diagram. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(A, C) → f
  2. Segment(B, C) → g
  3. CurveCartesian(((Amplitude_x * sin((((2 * π) * frequency2) * s) + Phase2)) * ℯ^(If[b, ((-damping_x) * s), 0])), ((Amplitude_y * sin((((2 * π) * frequency1) * s) + Phase1)) * ℯ^(If[b, ((-damping_y) * s), 0])), s, 0, maxt) → a
  4. Segment((0, 1), (0, 3)) → h
  5. Segment((1, 0), (3, 0)) → i
  6. Textfield(freq2) → InputBox2
  7. Textfield(freq1) → InputBox1