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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 ?
While the differential system of intervallic relations creates a "link" from the past to the present, this link is constituted in and as the destruction of the subject's immediate, authentic, and invisible relation to "its own" past.
Its dynamic swells resonate with the vocal swell on "sinnend," and its drop of a major sixth (B-D) echoes the voice's intervallic drop on "hinaus.
Residue-Class Sets in the Music of Iannis Xenakis: An Analytical Algorithm and General Intervallic Expression.
By calculating the intervallic values through the geometrical proportional mean and the subdivision of the syntonic comma, he presents a table in which the string is hypothetically divided into 10,000,000 parts (pp.
Lehr does discuss in passing some similarities of thematic approach, and he includes a brief but unsatisfactory section dealing with the formal design of one scene, but the heart of his analysis consists of tabulating the intervallic content of the vocal lines (and character-associated themes), from which he derives a statistical summary of the type and direction of intervals for each character in a variety of contexts, including, for example, the intervals used when characters address each other by name.
20]) Although this technical term was adumbrated vaguely in treatises written during several centuries in diverse languages, such as Greek, Latin, Italian, French, Spanish, and German, as well as English, ultimately its application became unambiguous: today 'key' (italicized as a technical term) applies to a definitive system of intervallic relations among tones.
25)Of the examples given, 15:10, 30:20; 12:9, 40:30, only 12:9 is of musical interest, being part of the intervallic formula 12:9:8:6.
From the folky lyrics and chiming guitars of the Beatles and Byrds to Led Zeppelin drum-bashing and Rolling Stones raunch, from looping Motown-inspired bass lines to flat-out punk-fired raves, from heartthrob vocals a la Patsy Cline and Duane Eddy-style twanging to throaty Booker T-ish organ sounds and the sudden intervallic leaps of Little Feat, the Palominos graps a mind-boggling number of musical bits in their teeth, and taken them to places they might never have gone.
These melodies are utilized to experience and practice off-staff notation, intervallic reading on the grand staff, lead sheet notation, left-hand harmonization using accompaniment styles, and two-handed accompaniments for sing-and-play.
At the same time, the resultant effect of augmentation - intervallic expansion - is a very effective means of gradation.
Pedagogically, this is a nice collection of rhythmic, intervallic, and expressive challenges, great for high school or good middle school level players, and the piano part is equally accessible.
Rhythm refers to "explicit divisions of time or space into intervallic time systems, recurrent and often (but not always) characterized by periodicity" (Thaut, 2005, p.