Compound Intervals

Intervals get their number by counting letter names from the bottom note to the top note. A third spans three letter names, an octave spans eight. Once you go past the octave, you get compound intervals: a tenth, an eleventh, a thirteenth. These feel bigger on the page, but your ear still groups them with their simple cousins, because an octave transfer doesn't change which note class is sounding against the bass, just which register it's in. A singer who jumps from a third above middle C to a tenth above it is still singing the same letter name, just an octave higher.

To find what a compound interval really is, subtract seven from its numeric size. A tenth minus seven gives three, so a tenth is a compound third. A ninth minus seven gives two, so a ninth is a compound second. A thirteenth minus seven gives six, so a thirteenth is a compound sixth. The quality word, major, minor, perfect, augmented, or diminished, carries over unchanged: a major third stays major when it becomes a major tenth. The half-step count follows a parallel rule: moving a simple interval up an octave adds twelve half steps, since an octave itself is twelve half steps.

This matters because chord and interval labeling further along, especially in four-part writing and figured bass, often produces spacing wider than an octave between voices. Recognizing that a thirteenth is just a sixth in disguise keeps your analysis of harmony and voice-leading consistent, no matter how far apart the soprano and bass have drifted.