Tenth

What it means

The tenth is the interval of ten scale degrees, counted including the starting and the target note — that is, a third plus an octave. Like the third, it exists in a major and a minor form; the major tenth spans sixteen semitones, the minor fifteen. The spelling “Decim” stands here for the same interval that is usually called Dezime (tenth).

Musical use

Intervals larger than the octave are called compound; in effect they correspond to the basic interval but sound more open and transparent, because the notes lie farther apart. A third in close position sounds dense and can become murky in a low register — the same third set as a tenth sounds clear. This observation is of practical significance for writing: wide spacing is recommended especially in low registers.

In figured bass and in the study of composition, compound intervals are often reduced to their simple form; the figure 10 is accordingly treated like a 3. The same holds for the rules of voice-leading: parallel tenths are parallel thirds and allowed, parallel twelfths by contrast parallel fifths and forbidden.

As a stretch of the hand, the tenth is a well-known difficulty on keyboard instruments, because it is larger than the octave; corresponding passages are, depending on the size of the hand, played broken or distributed differently.

In harmony the tenth often takes the place of the third when bass and upper voice lie far apart; in two-voice writing, parallel tenths are allowed and sound full and clear. On the piano the tenth counts as the limit of what one hand can span, which is why in the literature it is often notated broken or executed as an arpeggio. In counterpoint the double counterpoint at the tenth plays a role, in which a voice is displaced by a tenth.

Performance practice

Do not grasp large intervals by counting lines but by way of the octave: recognize the root and the third above it, and the distance is immediately clear. With stretches beyond the octave, check whether breaking the chord is an appropriate solution — in many editions it is expressly provided for. And use wide spacing when arranging if a low texture sounds murky.