Inflection

In grammar, inflection or inflexion is the modification of a word to express different grammatical categories such as tense, case, voice, aspect, person, number, gender and (on rare occasions) mood. The inflection of verbs is also called conjugation, and one can refer to the inflection of nouns, adjectives and pronouns as declension.

An inflection expresses one or more grammatical categories with a prefix, suffix or infix, or another internal modification such as a vowel change. For example, the Latin verb ducam, meaning "I will lead", includes the suffix -am, expressing person (first), number (singular), and tense (future). The use of this suffix is an inflection. In contrast, in the English clause "I will lead", the word lead is not inflected for any of person, number, or tense; it is simply the bare form of a verb.

The inflected form of a word often contains both one or more free morphemes (a unit of meaning which can stand by itself as a word), and one or more bound morphemes (a unit of meaning which cannot stand alone as a word). For example, the English word cars is a noun that is inflected for number, specifically to express the plural; the content morpheme car is unbound because it could stand alone as a word, while the suffix -s is bound because it cannot stand alone as a word. These two morphemes together form the inflected word cars.

Inflection point

In differential calculus, an inflection point, point of inflection, flex, or inflection (inflexion) is a point on a curve at which the curve changes from being concave (concave downward) to convex (concave upward), or vice versa.

A point where the curvature vanishes but does not change sign is sometimes called a point of undulation or undulation point.

In algebraic geometry an inflection point is defined slightly more generally, as a point where the tangent meets the curve to order at least 3, and an undulation point or hyperflex is defined as a point where the tangent meets the curve to order at least 4.

Definition

A differentiable function has an inflection point at (x, f(x)) if and only if its first derivative, f′, has an isolated extremum at x. (This is not the same as saying that f has an extremum). That is, in some neighborhood, x is the one and only point at which f′ has a (local) minimum or maximum. If all extrema of f′ are isolated, then an inflection point is a point on the graph of f at which the tangent crosses the curve.

Diatonic and chromatic

Diatonic (Greek: διατονική) and chromatic (Greek: χρωματική) are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.

These terms may mean different things in different contexts. Very often, diatonic refers to musical elements derived from the modes and transpositions of the "white note scale" C–D–E–F–G–A–B. In some usages it includes all forms of heptatonic scale that are in common use in Western music (the major, and all forms of the minor).Chromatic most often refers to structures derived from the chromatic scale, which consists of all semitones. Historically, however, it had other senses, referring in Ancient Greek music theory to a particular tuning of the tetrachord, and to a rhythmic notational convention in mensural music of the 14th through 16th centuries.