Chord Frequency Ratio Calculator

Enter a root frequency and select a chord quality to instantly calculate the Hz value, just ratio, and cent distance for every note in the triad.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter Root Frequency (Hz)
Input the fundamental frequency of the chord's root note in Hertz (Hz). Middle C is commonly 261.63 Hz.
2
Select Chord Quality
Choose the desired chord quality from the dropdown: Major, Minor, Diminished, or Augmented. Each quality defines specific interval relationships.
3
View Chord Frequencies and Ratios
The calculator will display the precise frequencies for the root, third, and fifth of the chord, along with their just intonation ratios and cents from the root.

Example Calculation

A music producer wants to understand the exact frequencies and ratios for a C Major chord, starting with Middle C (261.63 Hz) as the root.

Root Frequency

261.63 Hz

Chord Quality

Major (semitones: 0, 4, 7)

Results

C Major (261.63Hz, 329.63Hz, 392.00Hz)

Tips

Understand Equal Temperament

This calculator uses 12-tone equal temperament, the standard tuning system for modern Western music. Each semitone is an equal logarithmic step, allowing instruments to play in any key without retuning.

Experiment with Different Roots

Try different root frequencies to see how the chord frequencies scale proportionally. For example, use 440 Hz (A4) as a root to explore chords based on that pitch.

Listen for Harmonic Series

The frequencies generated are derived from the harmonic series, which is the basis of musical consonance. Notice how the ratios simplify for consonant intervals like the perfect fifth (3:2) or major third (5:4) in just intonation.

Deconstructing Harmony with the Chord Frequency Ratio Calculator

The Chord Frequency Ratio Calculator offers a deep dive into the mathematical underpinnings of music, revealing the precise Hz frequency and interval ratio for every note in Major, Minor, Diminished, or Augmented triads. By inputting a root frequency, such as Middle C at 261.63 Hz, and selecting a chord quality, the tool provides the exact frequencies for the constituent notes. For a C Major chord, this translates to 261.63 Hz (root), 329.63 Hz (major third), and 392.00 Hz (perfect fifth), showcasing the acoustic purity of harmonic intervals.

The Mathematical Foundations of Musical Harmony

Musical harmony is deeply rooted in mathematical ratios and the physics of sound, particularly the overtone series. Ancient civilizations, notably the Pythagoreans, discovered that consonant musical intervals correspond to simple integer ratios of frequencies. For example, a perfect fifth has a frequency ratio of 3:2, and a major third has a ratio of 5:4 in what is known as 'just intonation'. However, modern Western music primarily uses '12-tone equal temperament', which slightly compromises these pure ratios to allow instruments to play in all keys without retuning. This system divides the octave into 12 logarithmically equal semitones, where each interval's frequency ratio is the 12th root of 2 (approximately 1.05946).

Calculating Frequencies and Ratios in a Musical Chord

This calculator determines the frequencies and ratios of notes within a chord using the principles of 12-tone equal temperament.

Interval Semitones: Each chord quality (Major, Minor, Diminished, Augmented) corresponds to a specific set of semitones above the root (e.g., Major = 0, 4, 7 semitones).
Frequency Calculation: For each note (n semitones above the root), its frequency (f_n) is calculated using the root frequency (f_root) and the 12th root of 2: f_n = f_root × (2^(1/12))^n
Just Ratio: The calculator also provides an approximate "just ratio" which reflects the simpler integer ratios found in the harmonic series, offering a comparison to the equal-tempered values.

💡 To explore other aspects of sound, our Harmonic Series Frequency Calculator can show you the natural overtones of any fundamental pitch.

Worked Example: Analyzing a C Major Chord

Let's analyze a C Major chord, using Middle C as the root frequency, which is 261.63 Hz.

Input Root Frequency: Enter "261.63" Hz.
Select Chord Quality: Choose "Major (semitones: 0, 4, 7)".
Calculate Root Frequency (0 semitones): 261.63 Hz. The just ratio is 1:1.
Calculate Third Frequency (4 semitones): 261.63 × (2^(1/12))^4 ≈ 329.63 Hz. The just ratio for a major third is 5:4.
Calculate Fifth Frequency (7 semitones): 261.63 × (2^(1/12))^7 ≈ 392.00 Hz. The just ratio for a perfect fifth is 3:2.

The calculator provides a Chord Summary: C Major (261.63Hz, 329.63Hz, 392.00Hz), along with precise frequencies and ratios for each note.

💡 For other statistical and mathematical analyses, our Harmonic Mean Calculator can compute a specialized average for rates and ratios.

Comparing Equal Temperament with Just Intonation

The Chord Frequency Ratio Calculator utilizes equal temperament, the prevailing tuning system in modern Western music, where each semitone interval is mathematically identical. This allows instruments like pianos to play in any key without sounding out of tune. However, this system slightly deviates from just intonation, which tunes intervals based on pure, simple integer ratios derived from the harmonic series (e.g., a major third at 5:4 or 1.25, a perfect fifth at 3:2 or 1.5). In equal temperament, a major third is slightly wider (a ratio of approximately 1.2599) and a perfect fifth is slightly narrower (a ratio of approximately 1.4983) than their just counterparts. The trade-off is versatility across all keys in equal temperament versus the perceived "purity" and consonance of just intonation, which sounds best in a single key but becomes dissonant when modulating.

Frequently Asked Questions

What is a chord frequency ratio?

A chord frequency ratio describes the relationship between the fundamental frequencies of the notes within a musical chord. These ratios are derived from the harmonic series and are crucial for understanding musical consonance and dissonance. For example, a perfect fifth has a ratio close to 3:2, meaning the higher note's frequency is approximately 1.5 times that of the lower note, forming a fundamental building block of harmony.

How are musical frequencies calculated in equal temperament?

Musical frequencies in 12-tone equal temperament are calculated using a geometric progression where each semitone is multiplied by the 12th root of 2 (approximately 1.0594635). Starting from a reference frequency (e.g., A4 = 440 Hz), the frequency of any other note 'n' semitones away is given by F_n = F_ref * (2^(1/12))^n. This ensures that all semitones are equally spaced logarithmically across the octave.

What is the difference between a Major and a Minor chord?

The fundamental difference between a Major and a Minor chord lies in the quality of the third interval above the root. A Major chord consists of a root, a major third (4 semitones above the root), and a perfect fifth (7 semitones). A Minor chord consists of a root, a minor third (3 semitones above the root), and a perfect fifth. This single semitone difference in the third creates distinct emotional qualities, with major often sounding 'happy' and minor 'sad'.

What is a 'cent' in music theory?

A 'cent' is a logarithmic unit of measure used for musical intervals, where one octave is divided into 1200 cents, and each semitone in equal temperament is exactly 100 cents. It allows for precise measurement and comparison of the pitch difference between two notes, even very small ones. For instance, the difference between an equal-tempered major third and a just-intonation major third is approximately 14 cents, a subtle but perceptible difference to trained ears.