Intervaalit

Intervaalit is a term that can refer to several distinct concepts depending on the context, primarily in music theory and mathematics. In music theory, an interval is the difference in pitch between two notes. These intervals are classified and named based on their size, such as a major third or a perfect fifth. The quality of an interval (major, minor, perfect, augmented, diminished) and its size together determine the specific sound and harmonic function of the interval. Intervals are fundamental building blocks of melody and harmony.

In mathematics, an interval represents a set of real numbers that lie between two given numbers. These numbers, called endpoints, can either be included in the interval or excluded. Intervals are denoted using parentheses for open intervals (endpoints excluded) and square brackets for closed intervals (endpoints included). For example, the open interval (a, b) includes all numbers x such that a < x < b, while the closed interval [a, b] includes all numbers x such that a ≤ x ≤ b. There are also half-open intervals like [a, b) and (a, b]. Intervals are a crucial concept in calculus and real analysis for defining continuity, limits, and measure. The specific meaning of "intervaalit" is therefore derived from the field in which it is being used.