Scale Degree Frequency Calculator
Every note in a major or minor scale sits a fixed number of equal-tempered semitones above the tonic, so its frequency follows directly from the tonic pitch. Enter the tonic frequency in hertz, choose the scale type, and pick the scale degree from 1 (the tonic) to 8 (the octave). This calculator returns the frequency of that degree in hertz, how many semitones it lies above the tonic, and the size of the interval in cents.
Scale degree frequency formula
major steps = [0, 2, 4, 5, 7, 9, 11]
minor steps = [0, 2, 3, 5, 7, 8, 10]
semitones = steps[(degree - 1) mod 7] + 12 * floor((degree - 1) / 7)
frequency = tonic * 2^(semitones / 12)
cents = 100 * semitones
Degree 8 wraps to the octave (12 semitones). The cents value is exactly 100 times the semitone count because each equal-tempered semitone is 100 cents.
Major scale degrees from A4 = 440 Hz
- Degree 1 (tonic): 440.00 Hz.
- Degree 3 (major third, 4 semitones): about 554.37 Hz.
- Degree 5 (perfect fifth, 7 semitones): about 659.26 Hz.
- Degree 8 (octave, 12 semitones): 880.00 Hz.
- Each semitone multiplies the frequency by about 1.059463.
Scale degree frequency: frequently asked questions
How is a scale degree frequency calculated?
Each scale degree sits a fixed number of equal-tempered semitones above the tonic. The frequency is the tonic frequency times 2 raised to the power of (semitones divided by 12). For a major scale, the degrees 1 to 7 are 0, 2, 4, 5, 7, 9, and 11 semitones above the tonic.
What are the semitone steps of a major and minor scale?
The major scale degrees are 0, 2, 4, 5, 7, 9, 11 semitones above the tonic. The natural minor scale degrees are 0, 2, 3, 5, 7, 8, 10 semitones. Degree 8 returns the octave at 12 semitones, twice the tonic frequency.
What tonic frequency should I use?
Use the frequency of the key note. If the key is A and you tune to A4 = 440 Hz, enter 440. For C major you might use middle C at about 261.63 Hz. The tonic is a user-editable input so it always matches your tuning reference.
Does this use just intonation or equal temperament?
Equal temperament, the standard tuning of modern keyboards, where each semitone is exactly the twelfth root of 2. For pure whole-number ratios, use our just intonation ratio calculator instead.
Sources and definitions
- Equal-tempered pitch (f = tonic * 2^(semitones/12)) and the diatonic scale step patterns are standard music-theory definitions.
- National Institute of Standards and Technology: SI units reference (frequency in hertz).
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.