Octave

The same pitch class, a different register

The octave is the most perfect consonance after the unison and the most fundamental of all intervals. Tones an octave apart carry the same letter name: C3, C4 and C5 are all called C. Because the seven names repeat in every octave, you need a way of writing the register. This site uses scientific pitch notation: the octaves are numbered, middle C is C4, the C above it C5, the C below C3, and A4 is the standard pitch at 440 Hz. German-speaking countries also use the older Helmholtz names: great octave (capital letters), small octave (lowercase), one-line octave (c′, where middle C lies) and two-line octave (c″). So C4 and c′ are the same note.

A string that vibrates at twice the frequency produces the same tone an octave higher. This kinship is used in practically every musical culture to divide the tonal space. More on the page Intervals.

On the guitar

The octave lies exactly at the 12th fret, which is marked with a double dot because it is the midpoint of the string. The high E string (329.63 Hz) sounds there at 659.26 Hz, the frequency has doubled exactly. If you touch the string lightly above the 12th fret, the same tone sounds as a harmonic: the second partial. Most notes you play already contain the octave as the first overtone in their timbre.

Octave and tuning

Octaves can be tuned without beating and therefore unambiguously, which is why the tuning problem lies not in the octave but in the stack of fifths. If you stack twelve pure fifths on top of each other, you miss seven octaves by the Pythagorean comma of 23.46 cents. This error cannot be removed, as the article Equal, meantone, just: why your piano is slightly out of tune shows.

Common mistakes

• Eight notes but twelve semitones: The octave spans eight degrees when you count the starting note, and twelve semitones.
• Forgetting the register: Without a number it stays open which C is meant.
• Equating octave and unison: They sound very closely related, but they are different pitches.