Intervallen

Intervallen is a term used in two main domains: music theory and mathematics. In mathematics, an interval is a connected portion of the real number line between two endpoints, inclusive or exclusive, such as [a, b], (a, b), [a, b), or (a, b]. Intervals can be finite or infinite and form a foundational concept in analysis and interval arithmetic. They provide a way to describe ranges, domains, and uncertainty.

In music theory, an interval is the pitch distance between two notes. It is measured in semitones on the chromatic scale or in diatonic steps within a scale. Intervals are named by their size (second through seventh, and the octave) and by quality (perfect, major, minor, augmented, diminished). Examples include the major third (four semitones), the perfect fifth (seven semitones), and the octave (twelve semitones). Simple intervals occur within one octave; those larger than an octave are called compound intervals. Inversion exchanges the interval with another so that their sizes sum to an octave; for example, major becomes minor and vice versa, while perfect intervals remain perfect.

Practical use: Intervallen underpin harmony, melody, tuning, and musical analysis. Tuning systems assign fixed sizes to intervals; equal temperament fixes all semitone steps, while just intonation and other systems adjust sizes for consonance. Intervals are also evaluated in terms of consonance and dissonance, with perfect and certain major/minor intervals considered stable. Beyond music, the term interval is also used in statistics and science to denote a range of values, such as confidence intervals; however, the core sense here is the distance or separation between two elements.