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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 and acoustics, the correlation of two tones according to pitch, that is, the frequency of sound vibration. The lower tone of an interval is known as its foundation, the upper its top. Tones employed in succession form a melodic interval; when used simultaneously, a harmonic interval. Each interval is determined by the volume, or quantitative, magnitude—that is, the number of steps it comprises—and the tonal, or qualitative, magnitude—that is, the number of whole tones or semitones it contains. Intervals formed within the limits of an octave are called simple intervals, and larger ones are called compound intervals. The names of intervals indicate the number of steps each embraces: the tonal size of the intervals determines whether they are minor, major, perfect, augmented, or diminished.

The simple intervals are perfect unison, minor second (a half tone), major second (one tone), minor third (1½ tones), major third (two tones), perfect fourth (2½ tones), augmented fourth (three tones), diminished fifth (three tones), perfect fifth (3½ tones), minor sixth (four tones), major sixth (4½tones), minor seventh (five tones), major seventh (5½tones), and perfect octave (six tones).

Compound intervals are created by adding a simple interval to the octave. They retain the characteristics of the analogous simple intervals; thus, there are ninths, tenths, elevenths, twelfths, thirteenths, fourteenths, and fifteenths (two octaves). Wider intervals are called a second above (or below) two octaves, a third above two octaves, and so on.

The enumerated intervals are known also as fundamental, or diatonic, intervals. Diatonic intervals can be increased or diminished by raising or lowering the foundation or top of the interval one chromatic semitone. If, simultaneously, both steps of an interval are subjected to alteration by a chromatic semitone in different directions, a double-augmented interval results; if one step is altered by one chromatic tone a double-diminished interval is produced. All intervals changed through alteration are called chromatic intervals. Intervals that differ in the quantity of steps they contain but are alike in tonal makeup (sound) are considered enharmonically equal—for example, F to G sharp (an augmented second) and F to A flat (a minor third).

All harmonic intervals are divided into consonant and dissonant intervals. The consonant intervals are the perfect unison and the octave (perfect consonance), the perfect fourth and the perfect fifth (very good consonance), and minor and major thirds and sixths (imperfect consonance). The dissonant intervals are minor and major seconds, the augmented fourth, the diminished fifth, and minor and major sevenths. The transference of the tones of an interval, during which the foundation becomes the upper tone of the interval and the top its lower tone, is called inversion; a new interval results. In inversion all perfect intervals remain perfect, minor intervals become major, major become minor, augmented become diminished, diminished become augmented, double augmented become double diminished, and double diminished become double augmented.



The spacing in pitch or frequency between two sounds; the frequency interval is the ratio of the frequencies or the logarithm of this ratio.
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.
The time separating two events, or the distance between two objects.
In special relativity, the Lorentz invariant quantity c 2t)2-(Δ x)2-(Δ y)2-(Δ z)2, where c is the speed of light, Δ t is the difference in the time coordinates of two specified events, and Δ x, Δ y, and Δ z are differences in their x, y, and z coordinates, respectively.
In general relativity, a generalization of this concept, namely the sum over the indices μ and ν of gμν dx μ dx ν, where dx μand dx νare the differences in the x μand x νcoordinates of two specified neighboring events, and gμνis an element of the metric tensor.


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
References in periodicals archive ?
Benamou proves to be an elegant, efficient, and very sympathetic cataloger as he identifies the musical and extramusical components of a Javanese performance that experienced musicians take into account in judging the appropriateness of garap (interpretation and expression): duration, pitch height and intervallic relations of particular tunings, dynamics, ornamentation, timbre, genres of vocal texts, melodic contour, compositional structure.
The intervallic structure of the first full measure of Op.
Focusing particularly on the Danny Elfman scores for the films of Tim Burton, Halfyard demonstrates how modern horror comedies have effectively used the tritone, the hitherto intervallic representation of evil, the long-standing diabolus in musica.
16) In this first song of the cycle; Mompou uses the piano with intervallic variation between the stanzas, always with slightly altered melodic and harmonic implications.
In his article "Schoenberg's First Chamber Symphony, Formalism, and Adorno's Critique of Twelve-Tone Composition," Murray Dineen develops a notion of tonality, or "tonal perspective," based on intervallic relationships rather than on fundamental pitches or chords.
The first chapter advocates building students' listening skills by having them learn by ear from the beginning of piano study, developing skills in rhythmic and intervallic reading independently.
He points out that while it is possible to duplicate the exact intervallic structure of a motive if it also begins on one of the scale's "tonics," it is impossible to do so if the motive first appears on a "tonic" and is later duplicated on a "dominant.
Likewise, the left-hand B in measure 1 may appear to be an arbitrary leap if not for the awareness of the line to which B belongs (C-sharp-B-A-sharp) or of its intervallic relation to the right hand.
Schoenberg's text describes the intervallic structure of a motive and traces it through repetitions and permutations, following it in the orchestra and the voice.
This collection also fits the bill for teachers seeking a supplementary series that provides extra reinforcement of intervallic learning and picturesque solo repertoire for recitals.
Susan Rankin's examination of musico-spatial systems associated with the doctrine of Music of the Spheres emphasizes the role of medieval theorists-especially ninth-century theorist John Scot Eriugena--in reformulating classical models setting out intervallic relationships between celestial bodies.
For example, the sight-singing student who depends upon intervallic content alone in rendering pitches will view the passage C-D-E-F as two whole steps followed by a half step.