Twelfth

Twelve steps

If you count twelve scale steps upwards from C you arrive at G5: C4 D4 E4 F4 G4 A4 B4 C5 D5 E5 F5 G5. That is an octave and a fifth. The twelfth is thus a compound interval, one made up of an octave and a simple interval.

In the glossary: Octave · Ninth · Natural scale

The interval at a glance

Like the other intervals above the octave it can be traced back to its simple interval. The ninth goes back to the second, the tenth to the third, the twelfth to the fifth.

The semitone count of the twelfth is 19. With ninth, tenth and thirteenth it depends on whether the simple interval is major or minor.

Why it matters for sound

The ratio 3:1 makes the twelfth the third partial of the overtone series. On the guitar it corresponds to the harmonic above the 7th fret, which sounds a twelfth higher than the open string. For wind instruments it has a special role: the clarinet, when overblown, jumps not to the octave but to the twelfth. That is due to its construction as a cylindrical tube closed at one end, which emphasises only the odd-numbered partials.

The interval is also found on the organ: the quint register (2⅔′) lets the row of pipes sound a twelfth above the foundation stop and so strengthens the overtone series.

Part-writing

In part-writing and figured bass compound intervals are traced back to their simple form. For the voice-leading rules the tenth counts as a third, the twelfth as a fifth. From this it follows: parallel tenths are allowed, parallel twelfths are forbidden, just like parallel fifths.