User Guide: Harmonic Series Viewer

The Harmonic Series Legatto is an interactive tool that allows you to break down the physical phenomenon that occurs when a string vibrates. It is fundamental to understanding why instruments sound the way they do (timbre) and how musical intervals are constructed from nature.

1. What is this tool used for?

In nature, a sound is never a single pure frequency, but a combination of many. This tool allows you to:

• Visualizing the vibration of a string: See how a string is physically divided to produce different harmonics.

• Understanding the Timbre: See how the sum of different harmonics creates complex waves.

• Studying Proportions: Understanding the mathematical relationship between the fundamental frequency and its harmonics (2x, 3x, 4x, etc.).

2. How to use the application (Step by step)

The tool features a simulation of vibrating strings with dynamic controls.

Step 1: Configure the String (String Settings)

In the top panel, you can select the rope you want to work on. By default, you'll see the "String 1"You can interact with the following controls:

• Harmonic (Numeric selector): Change the number of the harmonic you want to visualize.

  • Harmonic 1: It is the fundamental frequency (the string vibrates completely).

  • Harmonic 2: The string splits in two (one octave higher).

  • Harmonic 3: The string is divided into three (a perfect fifth above the octave), and so on.

Step 2: Observe the 3D Vibration

In the center of the screen you will see the rope in motion.

• Nodes and Antinodes: Observe the points where the string does not move (nodes) and where the amplitude is maximum.

• Interaction: As with Legatto's other tools, you can rotate and zoom in the 3D view to analyze the vibration pattern from any angle.

Step 3: The 2D Oscilloscope

Below the 3D visualization, you will find a real-time oscilloscope.

• This graph shows the waveform resulting from the vibration.

• As you go up the harmonic series, you will notice how the wave becomes faster and more complex, reflecting the change in pitch and brightness of the sound.

Step 4: MIDI Connection (Hardware)

Like Scale Studio, this tool is compatible with USB MIDI controllers:

• Connect your keyboard and press a note.

• The tool will react to your playing, allowing you to "play" the harmonic series and see how the string geometry changes according to the selected note and harmonic.