interval


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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.

Interval

 

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.

V. A. VAKHROMEEV

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 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.

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
References in periodicals archive ?
When each comparison is processed into [[[a.bar].sub.ij]/[p.sub.ij*], [p.sub.ij*], [[bar.a].sub.ij]], the interval weight vector, W([p.sub.ij*]), is obtained by (16) replacing [p.sub.*] into [p.sub.ij*], [for all]i, j.
is called a proper interval. The set of all proper intervals on R is denoted by IR.
The CDC Environmental Health Laboratory already has experience developing reference ranges for chronic disease biomarkers in adults, and with additional funding it could use its expertise to generate accurate pediatric reference intervals as well.
Interval training proved the more effective method with almost a third more weight loss.
class="MsoNormalThe interval sessions likewise differed from one study to the next, but most involved intervals lasting for a few minutes at a time, at a pace just below all-out effort, which is typical of HIIT.
With an interval measurement, however, there are two degrees of freedom: the measurements of one and the other border of the interval.
The QT interval was measured from the beginning of the QRS complex to the end of the T wave and corrected for the heart rate using the Bazett formula:
QT interval, QTc, and Tp-Te/QT and Tp-Te/JT ratios at baseline were similar between the boys and girls.
The QTc interval of migraineurs was 416.33 [+ or -] 16.44 ms and that of controls was 402.13 [+ or -] 21.03 ms.
For comparison, the most commonly used QT correction formula was also calculated, namely, the one proposed by Bazett (QTcBZT) which is QT/(RR interval)'72 [13].
In Mombasa, Tana River, Kilifi, Lamu and Kwale, sunny intervals are expected with temperatures ranging from 21 degrees Celsius to 30 degrees Celsius.