An octave is the interval between a note and the same note twelve semitones higher, with exactly double the frequency. Middle C, C4, vibrates at 261.63 Hz, and the C an octave above it, C5, vibrates at 523.25 Hz, and the two notes sound like the same note in a higher place.
What is an octave?
An octave is the interval between a note and the same note twelve semitones higher, or twelve semitones lower, and it is the most consonant interval in music after the unison. Middle C, C4, vibrates at 261.63 Hz, and the C an octave above it, C5, vibrates at 523.25 Hz, exactly double the frequency. That 2:1 ratio is why the two notes sound like the same note: the higher note's sound wave fits exactly twice into the lower note's wave, so the ear hears them as one pitch in two places. The octave is the frame of all music theory. Scales repeat every octave, which is why the C major scale is C, D, E, F, G, A, B and then C again, and why the same chord shapes repeat up the guitar neck every twelve frets. The piano is laid out in octaves, with the pattern of white and black keys repeating every twelve semitones, and the guitar's fretboard repeats every twelve frets for the same reason. Once you understand the octave, you understand why music is organised in repeating cycles rather than in a straight line.
How the octave works
The octave is defined by frequency doubling: each octave up doubles the frequency, and each octave down halves it. A4, the A above middle C, is the standard tuning note at 440 Hz. The A an octave above, A5, is 880 Hz, and the A an octave below, A3, is 220 Hz. The same doubling applies to every note: C4 is 261.63 Hz, C5 is 523.25 Hz, C6 is 1046.50 Hz, and C3 is 130.81 Hz. That simple arithmetic is why the octave sounds so pure, and why it is the first interval a beginner learns to hear. Octaves are named by the octave numbering system, where middle C is C4 and the notes run from C4 to B4 in the fourth octave, C5 to B5 in the fifth, and so on. The guitar's open strings are E2, A2, D3, G3, B3 and E4, which is why the low E string and the high E string are two octaves apart. The piano spans just over seven octaves, from A0 at 27.50 Hz to C8 at 4186 Hz, which is the widest range of any common instrument. The piano note finder shows the octave of any note, and the note frequency calculator works out the frequency of any pitch.
Worked example — octaves on the guitar. The low E string is E2 at 82.41 Hz. The E at the 12th fret of the same string is E3 at 164.81 Hz, exactly double, one octave higher. The E at the 24th fret, if your guitar has one, is E4 at 329.63 Hz, another octave higher. The high E string, open, is also E4, which is why the 12th fret of the low E string and the open high E string are the same pitch, two octaves apart. The fretboard note finder shows the octave of every note on the neck, and the E major guitar chord uses notes from three different octaves, which is why the same chord can sound both deep and bright at once.
How to practise octaves
Octave practice is about hearing the sameness: the two notes should sound like one pitch in two places, not like two different notes.
- Play middle C on the piano, then the C an octave above it, and listen for the two notes sounding like the same pitch, higher up.
- On guitar, play the 12th fret harmonic on any string, then the open string, and listen for the octave relationship between them.
- Play the C major scale ascending and descending, and notice that the scale ends on the same note an octave higher than where it started.
- Sing an octave above a note played on the piano, then check yourself, aiming to feel the doubling rather than guessing the pitch.
- Use the note frequency calculator to work out the frequencies of the octaves above and below A4 at 440 Hz.
Common mistakes
- Counting the octave as thirteen notes — An octave spans twelve semitones and eight letter names, C to C, not thirteen. Counting the steps between the notes instead of the notes themselves gives the wrong answer.
- Confusing octaves with unisons — A unison is two notes of the same pitch, zero semitones apart, while an octave is two notes of the same name, twelve semitones apart. They sound similar in their purity, but they are different intervals.
- Thinking all octaves sound the same — An octave in the low register sounds darker and less pure than an octave in the middle register, because the low overtones are stronger. The interval is the same, but the sound changes with the register.
Quick reference
This table lists the C notes across six octaves with their frequencies, so you can see the doubling rule working down the rows: each octave up doubles the frequency, and each octave down halves it. Middle C is C4, and the table runs from the low C2, below the bass staff, to the high C7, near the top of the piano.
| Note | Octave | Frequency (Hz) |
|---|---|---|
| C2 | 2nd octave | 65.41 |
| C3 | 3rd octave | 130.81 |
| C4 (middle C) | 4th octave | 261.63 |
| C5 | 5th octave | 523.25 |
| C6 | 6th octave | 1046.50 |
| C7 | 7th octave | 2093.00 |
Play the table on piano, starting from middle C and walking up an octave at a time, and listen for each note sounding like the same pitch in a higher place. When you reach the top, walk back down, and notice that the doubling rule works in reverse too: each octave down halves the frequency, and the note sounds like the same pitch in a lower place.
Frequently asked questions
What is an octave in music?
An octave is the interval between a note and the same note twelve semitones higher or lower, with exactly double or half the frequency. Middle C is C4 at 261.63 Hz, and the C an octave above it is C5 at 523.25 Hz.
Why does an octave sound like the same note?
Because the higher note vibrates at exactly twice the frequency of the lower note, a 2:1 ratio, so its sound wave fits exactly twice into the lower note's wave. The ear hears that perfect fit as sameness, and treats the two notes as one pitch in two places.
How many semitones are in an octave?
Twelve. An octave spans twelve semitones and eight letter names, from C to the next C, and it is the distance after which the pattern of notes repeats itself.
What is the range of a piano in octaves?
Just over seven octaves, from A0 at 27.50 Hz to C8 at 4186 Hz. The guitar spans about four octaves, from E2 to around E6, and the human voice spans about two octaves for most singers.
Why do scales repeat every octave?
Because the octave is the point at which the pattern of notes starts again: the C major scale is C, D, E, F, G, A, B, C, and the second C is the same note an octave higher, so the scale can continue from there in exactly the same pattern.