Intervalli

Intervalli, singular intervallo, is the Italian term for "intervals" and is used across disciplines. In mathematics, an interval is a connected subset of real numbers defined by a pair of endpoints. Depending on whether the endpoints are included, intervals are open (a,b), closed [a,b], or half-open [a,b) or (a,b]. Infinite intervals include (-∞, b], [a, ∞), and the entire real line (-∞, ∞). Some definitions also allow the degenerate interval [a,a]. Intervals are ordered and have well-defined length (measure).

In music theory, an interval is the distance in pitch between two notes. It is commonly measured in semitones in the equal-tempered system or by frequency ratios in just tuning. Intervals are named by their numeric position (second, third, fourth, fifth, sixth, seventh) and by quality (major, minor, perfect, diminished, augmented). Examples include the major third (4 semitones), perfect fifth (7 semitones), and octave (12 semitones). Musical intervals can be formed melodically (successive notes) or harmonically (simultaneous notes). Inversion of intervals changes their quality: major becomes minor, minor becomes major, and perfect intervals remain perfect when inverted as their complements (for example, a perfect fourth inverts to a perfect fifth).

Outside mathematics and music, intervalli describe spans of time or space, such as the time interval between events or the spatial interval between objects. In statistics or measurement, intervals denote ranges or estimates, like confidence intervals.