Music Interval Calculator in Hz

Understanding musical intervals in Hz helps musicians, composers, and audio engineers work with precise frequencies. This calculator helps you determine the frequency of any musical interval based on a reference note.

What is a Music Interval?

A musical interval is the distance between two pitches. In Western music, intervals are typically measured in semitones, with each semitone representing a specific frequency ratio. The most common tuning system is the 12-tone equal temperament system, where each semitone has a frequency ratio of 2^(1/12).

The frequency ratio between two notes separated by an interval is calculated using the formula: f₂ = f₁ × 2^(n/12), where n is the number of semitones between the two notes.

Intervals can be classified as perfect, major, minor, augmented, or diminished, depending on their size and quality. For example, a perfect fifth is 7 semitones apart, while a major third is 4 semitones apart.

How to Calculate Intervals in Hz

To calculate the frequency of a note that forms a specific interval with a reference note:

Identify the frequency of the reference note (f₁) in Hz.
Determine the number of semitones (n) between the reference note and the target note.
Use the formula: f₂ = f₁ × 2^(n/12) to calculate the frequency of the target note.

f₂ = f₁ × 2^(n/12)

For example, if you have a reference note at 440 Hz (A4) and you want to find the frequency of the note that forms a perfect fifth (7 semitones) above it:

f₂ = 440 × 2^(7/12) ≈ 659.25 Hz

This calculation shows that the note a perfect fifth above A4 (440 Hz) is approximately 659.25 Hz.

Common Musical Intervals

Here are some common musical intervals and their frequency ratios:

Interval	Semitones	Frequency Ratio	Example
Minor 2nd	1	2^(1/12) ≈ 1.0595	C to C#
Major 2nd	2	2^(2/12) ≈ 1.1225	C to D
Minor 3rd	3	2^(3/12) ≈ 1.1892	C to E♭
Major 3rd	4	2^(4/12) ≈ 1.2599	C to E
Perfect 4th	5	2^(5/12) ≈ 1.3348	C to F
Perfect 5th	7	2^(7/12) ≈ 1.4983	C to G
Octave	12	2^(12/12) = 2	C to C

These intervals form the foundation of Western music theory and are essential for understanding harmony and melody.

Practical Applications

Understanding musical intervals in Hz has several practical applications:

Music Composition: Composers use interval calculations to create harmonious melodies and chords.
Audio Engineering: Engineers use frequency calculations to tune instruments and mix audio tracks.
Music Education: Students learn about intervals to understand music theory and improve their playing skills.
Instrument Tuning: Musicians use interval calculations to tune their instruments accurately.

By mastering interval calculations, musicians and audio professionals can create more precise and harmonious music.

FAQ

What is the difference between a major and minor interval?

A major interval is larger than a minor interval by one semitone. For example, a major third is 4 semitones, while a minor third is 3 semitones.

How do I calculate the frequency of a note that is a perfect fifth above A4 (440 Hz)?

Use the formula f₂ = f₁ × 2^(7/12). For A4 (440 Hz), the calculation is 440 × 2^(7/12) ≈ 659.25 Hz.

What is the frequency ratio of an octave?

An octave has a frequency ratio of 2:1, meaning the higher note is twice the frequency of the lower note.

How do I use this calculator to find the frequency of a specific interval?

Enter the frequency of the reference note, select the interval you want to calculate, and click "Calculate". The calculator will display the frequency of the target note.