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# Interval Interval (from lat. Intervallum – interval, distance) in music – the distance between two sounds of a certain height.
The distance between sounds in music is measured in semitones.

Halftone is the smallest unit of measurement for the musical interval, the closest distance between two sounds, that is, two adjacent sounds. If you are guided by the piano, then this is the distance between two adjacent keys.

A tone is equal to two semitones.

Intervals less than half a tone are called microintervals.

Two main characteristics of the interval
On the one hand, an interval can be represented as an abstract mathematical quantity expressed by the ratio of two numbers (in Russian musicology it is often incorrectly called “proportion”), on the other hand, as an element of specific musical logic, a category of harmony expressed in letter or graphic notation. The mathematical value of the interval, as a rule, cannot be directly derived from the musical, and vice versa.

Therefore, the interval has a step (musical) and tone (mathematical) characteristic.

Interval step value – the number of steps (different notes) placed between two sounds of the interval, regardless of how it actually sounds). For example: mi-lyab is a smaller quart, although it sounds like a big third (mi-sol #), but if you count the number of steps (mi-fa-sol-lyb), you get a quart.

The determination of the tonal (mathematical) value of the interval is necessary because the step (musical) value determines it only approximately. Even the homogeneous intervals between the main steps of the scale are not all the same in the number of tones enclosed in them. For example, seconds do-re, re-mi, fa-salt, salt-la, la-si contain 1 whole tone; seconds, mi-fa and si-do-semitone. Thus, the step size of the interval cannot determine it quite accurately.

The tonal value and the quality of the interval depending on it are determined by adjectives: pure, large, small, increased, decreased, double increased and twice reduced. These adjectives are written and pronounced before the numeral denoting the step value (for example, pure prima, but not prima pure).

Classification of intervals in music
Intervals are classified:

1. By capture (game)

– simultaneous (harmonic, or vertical, interval)
– sequential (melodic, or horizontal, interval). It is played by enumerating the steps included in the interval.

2. By the volume (number) of steps enclosed in them. A number indicating the number of steps in an interval is also a short designation of this interval in musical literacy.

Number of steps Interval name
1 prima
2 seconds
3 Tercia
4 Quarts
5 Quintas
6 Sextus
7 Septima
8 Octave
Intervals from prima to octave are called simple, from octave to quintdecima – compound. Intervals wider than quintdecime are traditionally not considered independent.

Number of steps Interval name
9 Nona (second through an octave)
10 Decima (third through octave)
11 Undecima (quart through an octave)
12 Duodecima (fifth through octave)
13 Terzdecim (sixth through an octave)
14 Quartdecim (Septima through an octave)
15 Quintdecim (Double Octave)
3. By “quality” (the number of tones and midtones in the interval with a known number of steps). The “quality” of the interval is defined by the words “large” (abbreviated b.), “Small” (m.), “Clean” (h.), “Increased” (uv.), “Reduced” (d.), “Twice increased “(Dv. Uv.) And” twice reduced “(dv. Mind.). The qualitative characteristic of the interval in the elementary theory of music complements its quantitative characteristic.

– Prima (p1) = 0 tones
– Small second (m2) = half tone
– Big second (b2) = 1 tone
– Small third (m3) = 1.5 tones
– Big third (b3) = 2 tones
– Quart (h4) = 2.5 tones
– Triton (SW4 or UM5) = 3 tones
– Quinta (h5) = 3.5 tones
– Small sexta (m6) = 4 tones
– Big sixth (b6) = 4.5 tones
– Small septima (m7) = 5 tones
– Big septima (b7) = 5.5
– Octave (ch8) = 6 tones

Intervals are:

– large (b), small (m), clean (h), increased (uv), reduced (mind)
– harmonic (2 sounds simultaneously)
– melodic (2 sounds sound in turn)
– simple (up to an octave): prima (1), second (2), third (3), quart (4), fifth (5), sixth (6), septima (7), octave (8)
– complex, compound (more than an octave): nona (9) = second through an octave, decima (10) = a third through an octave, undecime (11) = a quarter through an octave, duodecium (12) = a fifth through an octave, terzdecium (13) = sixth through an octave, quartdecime (14) = septima through an octave, quintdecim (15) = two octaves
– consonances (harmonious)
– perfect consonances (pure: prima (1), quart (4), fifth (5), octave (8))
– imperfect consonances (large and small: third (3) and sixth (6))
– dissonances (dissonant) – (second (2), septima (7), newt, all increased and decreased intervals)

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