Pitch and frequency
Why a note sounds lower or higher, what a hertz is, and how the octave, the semitone and the reference pitch relate.
Essential
Content under musical review. It may contain inaccuracies.
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Why a note sounds lower or higher, what a hertz is, and how the octave, the semitone and the reference pitch relate.
Essential
Pitch is the quality that makes you hear a note as low or high. It depends mainly on frequency: how many times per second the vibration repeats. It's measured in hertz (Hz). A string vibrating 110 times per second produces a 110 Hz note.
The same note, A, in several octaves. Each has twice the frequency of the one before:
| A1 | 55.00 Hz | |
|---|---|---|
| A2 | 110.00 Hz | |
| A3 | 220.00 Hz | |
| A4 | 440.00 Hz | |
| A5 | 880.00 Hz | |
| A6 | 1760.00 Hz |
On a guitar in standard tuning, the open strings have these approximate frequencies, with the A reference at 440 Hz:
| String | Note | Frequency |
|---|---|---|
| 6th | E | 82.41 Hz |
| 5th | A | 110.00 Hz |
| 4th | D | 146.83 Hz |
| 3rd | G | 196.00 Hz |
| 2nd | B | 246.94 Hz |
| 1st | E | 329.63 Hz |
Fretting at the 12th fret halves the string and doubles the frequency: it sounds an octave higher.
String 6, Fret 5: A2 · 8 · Scale tone
Open the tuner and play each open string. Watch the frequency it detects and how far off it is in cents:
Tuner in standard tuningOn a string, frequency depends on three factors: the vibrating length (shorter is higher), the tension (tighter is higher) and the mass per unit length (thicker is lower). Tuning changes tension; fretting changes length.
Because every semitone multiplies the frequency by the same factor, every fret shortens the string by the same proportion, not the same distance. That's why frets get closer together towards the body. The 12th fret sits exactly at half the vibrating length, and the 24th at three quarters.
Consonant intervals approximate simple whole-number ratios: the perfect fifth 3 to 2, the fourth 4 to 3, the major third 5 to 4. Equal temperament spreads a small error across all intervals so you can play in every key: the tempered fifth is about two cents flat of pure, and the major third about fourteen cents sharp. The frequency-ratios animation shows it.