Music Performance
Convert frequency ratios to cents and interval names.
Ideal for just intonation and tuning experiments.
A frequency ratio and interval calculator is a music theory and acoustics tool that converts between musical intervals (the distance between two pitches) and their corresponding frequency ratios. In music, every interval has a mathematical relationship—octaves are 2:1, perfect fifths are 3:2, perfect fourths are 4:3, and so on. This calculator bridges the gap between perceptual music theory (how intervals sound) and the underlying physics (frequency ratios). Musicians, sound engineers, synthesizer programmers, and music theorists use this tool to understand harmonic relationships, design soundscapes, and verify intonation. It's essential for understanding why certain interval combinations sound consonant or dissonant, how temperament systems work, and how to calculate microtonal intervals.
The calculator uses the fundamental relationship: Frequency Ratio = f₂ ÷ f₁, where f₂ is the higher frequency and f₁ is the lower frequency. You input either two frequencies (and it calculates the ratio and interval name) or an interval name (and it calculates the frequency ratio). For equal temperament (the standard modern tuning system), each semitone is 2^(1/12) ≈ 1.0595 times the previous note. To find the ratio for any interval in semitones: Ratio = 2^(semitones/12). The tool also displays just intonation ratios, which are the pure mathematical ratios that produce the most consonant sounds (like 3:2 for perfect fifths).
Frequency Ratio = f₂ ÷ f₁. For equal temperament: Ratio = 2^(n/12), where n = number of semitones. Interval in cents = 1200 × log₂(frequency ratio). Just intonation ratios: Unison (1:1), Minor Second (16:15), Major Second (9:8), Minor Third (6:5), Major Third (5:4), Perfect Fourth (4:3), Tritone (45:32), Perfect Fifth (3:2), Minor Sixth (8:5), Major Sixth (5:3), Minor Seventh (9:5), Major Seventh (15:8), Octave (2:1).
Equal temperament divides the octave into 12 equally-spaced semitones mathematically (each is 2^(1/12) ≈ 1.0595 times the previous). Just intonation uses simple whole-number ratios like 3:2 for perfect fifths, which sound mathematically pure but are hard to play live. Equal temperament is slightly out-of-tune for most intervals except octaves, but enables key modulation and modern music.
For equal temperament: A major third is 4 semitones up, so ratio = 2^(4/12) ≈ 1.260. For just intonation: A major third is exactly 5:4 = 1.25. The difference is tiny (1.260 vs 1.25) but noticeable to trained ears. The calculator instantly gives you both values.
Cents divide the semitone into 100 equal parts, so one octave has 1200 cents. This logarithmic scale lets you compare tiny intonation differences precisely. Humans can perceive differences of about 10 cents. Cents let synthesizer programmers and tuning specialists discuss microtonal adjustments.
Yes! Measure or calculate the frequencies of both notes, input them into the calculator, and it shows the resulting ratio and how many cents apart they are. If they should be in unison, they should show a 1:1 ratio (0 cents difference). Any deviation shows you how out of tune they are.
