Musical Interval Calculator (Semitones to Name)
Converts a semitone count into the interval name, from unison and minor 2nd through the tritone to the major 7th, wrapping within one octave.
Intervalo
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Musical intervals as frequency ratios: rule and example
At its core, a musical interval is just a ratio between two frequencies. The octave sits at 2:1, the perfect fifth at 3:2 (the Pythagorean ratio), the perfect fourth at 4:3. The major third lands on 5:4 if you tune in just intonation, or on 2^(4/12) ≈ 1.260 under equal temperament. To get the frequency of a note n semitones above some base, you compute f₀ · 2^(n/12). Run that with A4 = 440 Hz and you get A5 = 880 Hz, while C8, the highest piano key, comes out around 4186 Hz.
Context and applications
Equal temperament cuts the octave into 12 identical semitones, each one a constant ratio of 2^(1/12) ≈ 1.0595. That's the bargain that lets a piano modulate freely into any key, paid for with thirds and fifths that come out a touch impure. The reference pitch A4 = 440 Hz was nailed down by ISO 16 in 1955. The same math shows up everywhere musicians work with pitch: tuning instruments, writing music, designing synth oscillators like Moog or Serum, exploring microtonal theory, and building audio plugins that shift pitch by semitones.
FAQ
Why does the just-intonation fifth (3:2) sound "better" than the tempered one? The 3:2 ratio gives you simple, slow beat patterns. The tempered fifth sits about 2 cents flat, and trained ears can hear it.
What is a "cent"? It's a hundredth of a tempered semitone, or 2^(1/1200), and it's the unit people reach for when they want to describe how far off a note is.
How do I calculate any note's frequency? Start from A4 = 440 Hz and multiply by 2^(n/12). Here n counts the semitones between your note and A4: positive if you're going up, negative if you're going down.
Why is A4 sometimes 432 Hz? A handful of musicians favor 432 Hz on esoteric grounds. In practice, modern orchestras stick to the ISO standard of 440 Hz, or bump it to 442 in parts of Europe.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.