interval, in music, the difference in pitch between two tones. Intervals may be measured acoustically in terms of their vibration numbers. They are more generally named according to the number of steps they contain in the diatonic scale of the piano; e.g., from C to D is a second, C and D being the first two notes of the scale of C. The fourth, fifth, and octave are termed perfect intervals as they have a characteristic sonority quite unlike any other interval. An interval between two natural notes, neither note being a sharp or a flat, is a major interval; if it is reduced by a semitone, it becomes minor. If a perfect or a minor interval is made half a step smaller it is called diminished, and when half a step larger, augmented. An interval may also be expressed by means of the ratio of the frequencies of its two tones. For example, the octave may be expressed by the ratio 2:1 because its upper tone has a frequency twice that of its lower tone.
In music, the inclusive distance between one tone and another, whether sounded successively (melodic interval) or simultaneously (harmonic interval). In Western music, intervals are generally named according to the number of scale-steps within a given key that they embrace; thus, the ascent from C to G (C–D–E–F–G) is called a fifth because the interval embraces five scale degrees. There are four perfect intervals: prime, or unison; octave; fourth; and fifth. The other intervals (seconds, thirds, sixths, sevenths) have major and minor forms that differ in size by a half step (semitone). Both perfect and major intervals may be augmented, or enlarged by a half tone. Perfect and minor intervals may be diminished, or narrowed by a half tone.
interval
interval [′in·tər·vəl]
interval
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Examples of simple musical intervals.
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interval
1. Music the difference of pitch between two notes, either sounded simultaneously (harmonic interval) or in succession as in a musical part (melodic interval). An interval is calculated by counting the (inclusive) number of notes of the diatonic scale between the two notes
2. the ratio of the frequencies of two sounds
3. Maths the set containing all real numbers or points between two given numbers or points, called the endpoints. A closed interval includes the endpoints, but an open interval does not
interval [′in·tər·vəl]
(acoustics)
The spacing in pitch or frequency between two sounds; the frequency interval is the ratio of the frequencies or the logarithm of this ratio.
(mathematics)
A set of numbers which consists of those numbers that are greater than one fixed number and less than another, and that may also include one or both of the end numbers.
(physics)
The time separating two events, or the distance between two objects.
(relativity)
In special relativity, the Lorentz invariant quantityc2(Δt)2-(Δx)2-(Δy)2-(Δz)2, wherecis the speed of light, Δtis the difference in the time coordinates of two specified events, and Δx, Δy, and Δzare differences in theirx,y, andzcoordinates, respectively.
In general relativity, a generalization of this concept, namely the sum over the indices μ and ν ofgμνdxμdxν, wheredxμanddxνare the differences in thexμandxνcoordinates of two specified neighboring events, andgμνis an element of the metric tensor.
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