Fundamental Frequency Harmonics Calculator

The Frequency Harmonics Calculator is a tool designed to help you visualise and calculate the harmonics of a fundamental frequency. You can switch between frequency mode and note mode to input your desired fundamental frequency. You can also click and drag the yellow dot to change the fundamental frequency.

How to use the Frequency Harmonics Calculator

Use the toggle switch to switch between “Hz” (frequency mode) and “Notes” (note mode).
Hz Mode: Allows you to input a frequency value in Hertz.
Notes Mode: Allows you to select a musical note from a dropdown list.

Input your note or frequency – In either mode you can click and drag the fundamental note/frequency.
Frequency Mode: Enter a frequency value between 20 Hz and 20,000 Hz in the input box.
Note Mode: Select a musical note from the dropdown list.

The graph and table will update automatically to show the harmonics of the entered frequency.

Just need to convert Hz to Notes? Check out the Hz to Note Converter.

Understanding the results

The graph displays the harmonics of the fundamental frequency on a logarithmic scale.
Each harmonic is represented by a green dot, and the fundamental frequency is highlighted.
The green line connects all harmonics, showing the frequency response curve.
The table below the graph lists the harmonics, showing their frequency and amplitude in decibels (dB).

Click and drag the fundamental frequency to adjust it.
In frequency mode, the frequency value will update in real-time.
In note mode, it will snap to the closest note.

What are 1st, 2nd, and 3rd harmonics?

The 1st, 2nd, and 3rd harmonics refer to the fundamental frequency and its integer multiples in a harmonic series.

1st Harmonic (Fundamental Frequency)
This is the lowest frequency in a harmonic series and is perceived as the pitch of the sound.
It determines the base frequency from which all harmonics are derived.

2nd Harmonic (First Overtone)
This is twice the fundamental frequency (2×f).
It contributes to the overall tone but does not change the perceived pitch.
Often, it reinforces the fundamental, making the sound fuller.

3rd Harmonic (Second Overtone)
This is three times the fundamental frequency (3×f).
It adds complexity to the timbre, influencing the richness of the sound.
In musical instruments, it plays a role in tone colouration.

What Are Fundamental Frequency Harmonics?

Frequency harmonics are integer multiples of a fundamental frequency. When a sound is produced, it typically consists of a fundamental frequency (the lowest frequency) and a series of frequency harmonics that are higher frequencies.

The Fundamental Frequency is the lowest frequency of a sound wave and is perceived as the pitch of the sound. It is the first frequency harmonic.

Overtones are the frequency harmonics above the fundamental frequency. The first overtone is the second frequency harmonic, the second overtone is the third frequency harmonic, and so on.

The frequency harmonic series is a sequence of frequencies that are integer multiples of the fundamental frequency. For example, if the fundamental frequency is f, the frequency harmonics are 2f, 3f, 4f, etc.

Frequency harmonics naturally occur in musical instruments and the human voice, contributing to the timbre or colour of the sound.

Importance of frequency harmonics in Music

The presence and relative strength of frequency harmonics determine the timbre of a sound, which is why a piano and a violin sound different even when playing the same note.

Frequency harmonics are the basis for musical harmony and tuning systems. They influence how chords and intervals are perceived.

Frequency harmonics in Audio Engineering

Understanding frequency harmonics is essential for sound design as it allows engineers to shape the tonal quality of sounds.

Audio engineers use knowledge of frequency harmonics to adjust the frequency balance of recordings, enhancing clarity and presence when providing professional mixing services and mastering.

Frequency harmonics are studied in acoustics to understand how sound waves interact with environments and materials and in speech science, frequency harmonics are analysed to understand vocal production and perception in hearing.

Visualising Frequency Harmonics

Tools like spectrograms and frequency harmonics calculators visualise frequency harmonics, showing how they contribute to the overall sound. Frequency harmonics are integral to the nature of sound, influencing everything from musical expression to audio technology. They provide insight into the complex structure of sound waves and are essential for various applications in music, engineering, and science.

Use cases for the Frequency Harmonics Calculator

The Frequency Harmonics Calculator provides a visual representation of frequency harmonics, helping users understand how different frequencies and notes produce harmonic overtones. This is particularly useful for students and educators in music and acoustics. By allowing users to switch between frequency and note modes, the Frequency Harmonics Calculator offers an interactive way to explore the relationship between musical notes and their corresponding frequencies.

Audio engineers and sound designers can use the Frequency Harmonics Calculator to understand the harmonic content of sounds, which is crucial for tasks like equalisation, mixing, and mastering. The Frequency Harmonics Calculator can help identify problematic frequencies in a mix by visualising frequency harmonics, allowing engineers to make informed decisions about frequency adjustments.

Researchers in acoustics can use the Frequency Harmonics Calculator to study the harmonic properties of sound waves, contributing to fields such as architectural acoustics and audio technology development. The Frequency Harmonics Calculator’s graph provides a clear view of the frequency response of a fundamental tone, which is valuable for analysing the acoustic characteristics of different environments and materials.

Examples

Understanding Harmonics of a Musical Note

Enter 440 Hz (A4) into the Frequency Harmonics Calculator.
The tool will display harmonics at 880 Hz, 1320 Hz, 1760 Hz, etc.
This visualisation helps understand why instruments with the same fundamental frequency can sound different due to varying harmonic content.

Identifying Problematic Frequencies in a Mix

If you hear an unwanted resonance in your mix, enter that problematic frequency into the calculator.
The tool will display harmonics that could be causing masking issues.
This helps in making better EQ decisions to clean up the mix.