An octave is the interval between a note and the next note that has the same letter name, one higher or one lower. Play an A, then the very next A above it, and you have moved up an octave. The two notes sound so alike that we give them the same letter, which is why the octave is the interval that pitch itself seems to fold around.
Plain theory, no instrument required. An octave means the same thing on a piano, a guitar, a synth or in a piano roll, in any key and any style. The frequency figures below are the standard tuning values and are exact for that reference.
An octave is the interval between one note and the next note that has the same letter name, one higher or one lower. Play an A and then the very next A above it, and the distance you have crossed is an octave. Do the same with any letter, C up to the C above it or G up to the G above it, and you have another octave.
An octave is one particular interval, not intervals in general. An interval is the distance in pitch between any two notes, and there are many of them: seconds, thirds, fifths and the rest. The octave is the single interval that lands back on the same letter name, which makes it the point where the note names start over rather than a step to a fresh letter.
Measured in the smallest steps of Western music, an octave spans twelve semitones, the twelve half steps you cross going from one note up to its namesake. On a piano that is twelve keys along, counting every black and white key in between, and you arrive at a note that sounds like where you began, only higher.
Going up an octave doubles a note's frequency, and going down an octave halves it. Frequency is how many times a sound wave repeats each second, measured in hertz, and the octave is the interval where that number exactly doubles or halves.
The usual reference note is the A above middle C, tuned to 440 Hz. The A one octave above it sits at 880 Hz, twice as fast, and the A one octave below it sits at 220 Hz, half as fast. Keep doubling or halving and you keep stepping by octaves, each one landing on another A. This is why frequency and octaves are so closely tied, though they are not the same thing: a frequency is a single number in hertz, while an octave is a relationship between two of them, a ratio of two to one.
Here is the same note, A, at several octaves, each row double the frequency of the one below.
| Note | Frequency | Relationship |
|---|---|---|
| A2 | 110 Hz | Two octaves below A4 |
| A3 | 220 Hz | One octave below A4 |
| A4 | 440 Hz | Reference, the A above middle C |
| A5 | 880 Hz | One octave above A4 |
| A6 | 1760 Hz | Two octaves above A4 |
If A is 440 Hz, the A an octave up is 880 Hz and the A an octave down is 220 Hz. Up an octave doubles the frequency; down an octave halves it. The rule is the same for every note, not just A, so it is the one number relationship in pitch worth holding on to.
Notes an octave apart sound like the same note because the higher one vibrates exactly twice as fast as the lower one. Every second cycle of the upper note lines up with a cycle of the lower note, so the two blend together and the ear reads them as one note in a higher or lower place rather than as two different notes.
Musicians call this octave equivalence, and it is the reason the octave feels less like a leap to a new note and more like the same note moved. Because of it, notes an octave apart share a single letter name, and the seven letters A to G repeat over and over up and down an instrument instead of the alphabet running on forever. A low C and a high C are both simply C.
This is also what separates the octave from every other interval. A fifth or a third joins two notes that clearly keep their own identities, while an octave joins two notes that sound like versions of one another. That closeness is why singers of different ranges can sing the same tune an octave apart and still sound like they are in unison rather than in harmony.
The most common use of the octave is doubling: playing the same line an octave higher or lower at the same time, which thickens and reinforces it without adding any new notes. Because the doubled note is heard as the same note, doubling changes the weight and colour of a part rather than its harmony.
Drop a bassline an octave and it gains depth and weight; lift a melody an octave and it gains brightness and cuts through more clearly; play both octaves together and the line sounds fuller and thicker. It is one of the simplest ways to change how big a part feels, and it turns up everywhere from orchestral writing to synth leads.
Octaves also give an instrument its map. On a keyboard or a synth, notes are labelled with a letter and an octave number, so C3 and C4 are the same note one octave apart, with C4 the higher of the two, and the number tells you which octave you are in. One thing to watch: makers do not fully agree on where the numbering starts, so the note some call middle C is C4 in one system and C3 in another, even though the gap of one between neighbouring octaves is always the same.
The word itself comes from counting. In a major scale you step up through eight notes to reach the same letter again, as in C, D, E, F, G, A, B and back to C, and that eighth note is the octave. Oct means eight, as in an octagon's eight sides, and the name simply records that the octave is the eighth note of the scale.
We built ARGISH to make this easy to hear. It is a self-playing chord synth: set a key and it plays chords and notes in that key, moving them up and down through the octaves, so you can hear the same note an octave higher or lower instead of working it out on a page.
It runs free in your browser to try, and installs as AU, VST3, AAX or a standalone app when you want it inside your own sessions.
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