What is "interval"

Interval \In"ter*val\, Intervale \In"ter*vale\, n. A tract of low ground between hills, or along the banks of a stream, usually alluvial land, enriched by the overflowings of the river, or by fertilizing deposits of earth from the adjacent hills. Cf. Bottom, n., 7. [Local, U. S.]

The woody intervale just beyond the marshy land.
--The Century.

Interval \In"ter*val\, n. [L. intervallum; inter between + vallum a wall: cf. F. intervalle. See Wall.]

1. A space between things; a void space intervening between any two objects; as, an interval between two houses or hills.

   'Twixt host and host but narrow space was left, A dreadful interval.
   --Milton.

2. Space of time between any two points or events; as, the interval between the death of Charles I. of England, and the accession of Charles II.

3. A brief space of time between the recurrence of similar conditions or states; as, the interval between paroxysms of pain; intervals of sanity or delirium.

4. (Mus.) Difference in pitch between any two tones.

   At intervals, coming or happening with intervals between; now and then. ``And Miriam watch'd and dozed at intervals.''
   --Tennyson.

   Augmented interval (Mus.), an interval increased by half a step or half a tone.

early 14c., from Old French intervalle (14c.), earlier entreval (13c.), from Late Latin intervallum "space, interval, distance," originally "space between palisades or ramparts," from inter "between" (see inter-) + vallum "rampart" (see wall (n.)). Metaphoric sense of "gap in time" was present in Latin.

n. 1 A distance in space. 2 A period of time. 3 (context music English) The difference (a ratio or logarithmic measure) in pitch between two notes, often referring to those two pitches themselves (otherwise known as a dyad). 4 (context mathematics English) A connected section of the real line which may be empty or have a length of zero. 5 (context chiefly British English) An intermission. 6 (context sports English) half time, a scheduled intermission between the periods of play

1. n. a definite length of time marked off by two instants [syn: time interval]

2. a set containing all points (or all real numbers) between two given endpoints

3. the distance between things; "fragile items require separation and cushioning" [syn: separation]

4. the difference in pitch between two notes [syn: musical interval]

Interval may refer to:

In music theory, an interval is the difference between two pitches. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C and D. Intervals can be arbitrarily small, and even imperceptible to the human ear.

In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio.

In Western music theory, the most common naming scheme for intervals describes two properties of the interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.). Examples include the minor third or perfect fifth. These names describe not only the difference in semitones between the upper and lower notes, but also how the interval is spelled. The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G and G–A.

Interval is a 1973 romantic drama film starring Merle Oberon in her final performance. Oberon also produced the movie, and fell in love with her co-star in it, Robert Wolders, divorcing her husband to marry Wolders in 1975.

Interval is a 1939 play by Sumner Locke Elliott. It was popular and was performed throughout Australia at a time when this was not common for local plays.

The play is set behind the scenes of a long-running stage show in London.

It was published in 1942.

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers satisfying is an interval which contains and , as well as all numbers between them. Other examples of intervals are the set of all real numbers $\R$, the set of all negative real numbers, and the empty set.

Real intervals play an important role in the theory of integration, because they are the simplest sets whose "size" or "measure" or "length" is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.

Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.

Intervals are likewise defined on an arbitrary totally ordered set, such as integers or rational numbers. The notation of integer intervals is considered in the special section below.

In graph theory, an interval I(h) in a directed graph is a maximal, single entry subgraph in which h is the only entry to I(h) and all closed paths in I(h) contain h. Intervals were described in 1976 by F. E. Allen and J. Cooke. Interval graphs are integral to some algorithms used in compilers, specifically data flow analyses.

The following algorithm finds all the intervals in a graph consisting of vertices N and the entry vertex n, and with the functions pred(n) and succ(n) which return the list of predecessors and successors of a given node n, respectively.

H = { n0 } // Initialize work list
while H is not empty
remove next h from H
create the interval I(h)
I(h) += { h }
while ∃n ∈ { succ(I(h)) — I(h) } such that pred(n) ⊆ I(h)
I(h) += { n }
while ∃n ∈ N such that n ∉ I(h) and // find next headers
∃m ∈ pred(n) such that m ∈ I(h)
H += n

The algorithm effectively partitions the graph into its intervals.

Each interval can in turn be replaced with a single node, while all edges between nodes in different intervals in the original graph become edges between their corresponding nodes in the new graph. This new graph is called an interval derived graph. The process of creating derived graphs can be repeated until the resulting graph can't be reduced further. If the final graph consists of a single node, then the original graph is said to be reducible.