Music Scale Calculator

Build any musical scale from a root note and see the note names, frequencies, and interval pattern, using standard 12-tone equal temperament tuned to A4 = 440 Hz.

Quick Facts

Tuning system
12-tone equal temperament (12-TET)
Every semitone is a frequency ratio of the twelfth root of 2 (about 1.05946), so 12 semitones exactly double the frequency.
Reference pitch
A4 = 440 Hz (ISO 16 concert pitch)
Note frequency f = A4ref x 2^((n-69)/12), where n is the MIDI note number.

Your Results

Calculated
Root note frequency
-
Frequency of the starting note
Scale notes
-
Ascending note names in the scale
Scale frequencies (Hz)
-
Each note's frequency, 12-TET
Interval pattern
-
Semitone steps between notes

Ready

Choose a root note, octave, scale type, and reference pitch, then press Calculate.

Understanding the Music Scale Calculator

This tool builds a musical scale from any root note and reports the note names, exact frequencies, and the interval pattern that defines the scale. It uses 12-tone equal temperament (12-TET), the tuning system used by pianos, guitars, and virtually all modern Western instruments, in which an octave is divided into 12 equal semitones.

The frequency formula

Every note's frequency is calculated from its position relative to A4 (the A above middle C) using the standard 12-TET formula:

f = A4ref × 2(n − 69) / 12

Here n is the note's MIDI number (A4 itself is MIDI note 69, C4 or "middle C" is MIDI note 60) and A4ref is the reference pitch, almost always 440 Hz. Because the exponent divides by 12, each semitone step multiplies the frequency by the twelfth root of 2 (≈ 1.059463), and 12 semitones (one full octave) exactly doubles the frequency.

How scale types are built

A scale is simply a specific pattern of whole steps (W, 2 semitones) and half steps (H, 1 semitone) measured upward from the root note. This calculator supports the most common patterns:

  • Major (Ionian): W-W-H-W-W-W-H — semitone offsets 0, 2, 4, 5, 7, 9, 11
  • Natural Minor (Aeolian): W-H-W-W-H-W-W — offsets 0, 2, 3, 5, 7, 8, 10
  • Harmonic Minor: offsets 0, 2, 3, 5, 7, 8, 11 (raised 7th degree)
  • Melodic Minor (ascending): offsets 0, 2, 3, 5, 7, 9, 11 (raised 6th and 7th)
  • Dorian, Phrygian, Lydian, Mixolydian, Locrian: the remaining five modes of the major scale, each starting the same seven-note pattern from a different degree
  • Major and Minor Pentatonic: five-note subsets that omit the half-step intervals, common in folk, blues, and rock melodies
  • Blues scale: the minor pentatonic plus a "blue note" (flattened 5th)
  • Chromatic: all 12 semitones with no gaps

Worked example

For a C major scale starting at octave 4 with A4 = 440 Hz: the root C4 is MIDI note 60, giving f = 440 × 2(60−69)/12 ≈ 261.63 Hz. Applying the major-scale offsets (0, 2, 4, 5, 7, 9, 11) in semitones produces C4, D4, E4, F4, G4, A4, B4 at approximately 261.63, 293.66, 329.63, 349.23, 392.00, 440.00, and 493.88 Hz — ending one whole step below C5 (523.25 Hz), which completes the octave.

Why the reference pitch matters

440 Hz for A4 became the international standard (ISO 16) in 1955, but it is a convention, not a law of physics. Some orchestras tune to 442 or 443 Hz for a slightly brighter sound, and older or historical tunings can differ more. Because every note in the calculator is derived from the A4 reference, changing that one value shifts every frequency in the scale proportionally while the note names and interval pattern stay the same.

Frequently Asked Questions

What formula does this calculator use?
It uses 12-tone equal temperament (12-TET): f = A4ref × 2^((n−69)/12), where n is the note's MIDI number and A4ref is the reference pitch for A4 (usually 440 Hz). Each semitone is the same ratio, the twelfth root of 2 (≈ 1.05946), so 12 semitones exactly double the frequency and complete one octave.
What is the difference between a whole step and a half step?
A half step (semitone) is the smallest interval in 12-TET — the distance from any key to the very next one, black or white, on a piano. A whole step (whole tone) equals two half steps. Every scale type is just a fixed pattern of whole and half steps counted up from the root; the major scale, for example, is whole-whole-half-whole-whole-whole-half.
Why is A4 usually 440 Hz?
440 Hz was adopted as the international tuning standard (ISO 16) in 1955 and remains the most common reference pitch today. Some ensembles tune slightly higher, such as 442 or 443 Hz, for a brighter sound. This calculator lets you change the A4 reference pitch to match any tuning convention.
Why do some scales share the same notes?
Modes such as Dorian, Phrygian, and Mixolydian reuse the same seven note names as a major scale but start counting from a different scale degree, which shifts the whole/half-step pattern and gives each mode its own character. D Dorian, for instance, uses the same notes as C major but starts and ends on D.

Related calculators