Suomeksi | In English

Intervals

An interval is formed by two simultaneous (a harmonic interval) or two successive (a melodic interval) tones. The basis of intervals lies in the octave identity and a diatonic scale.

Octave identity means that all music cultures of the world perceive tones an octave apart as similar. The physical basis of this phenomenon is the double frequency of the tone an octave up. In the western tonal system, the frequency of a1, for example, is 440 Hz, and that of a2 is 880.

The diatonic scale is considered the basis of the tonal system. Note names, intervals, and notations are based on this system. A simple description of the diatonic scale is a sequence of notes …C, D, E, F, and so on. The scale does not have a "first" note and can actually be considered to represent a generic scale (see Scales and Generic Scales).

Interval names derive partly from Latin ordinal numbers. Ancient Romans were not familiar with the concept of nought, so the bottom note must always be taken into account. If the number of steps or degrees between two notes is nought, the interval is named unison (and marked with number 1). If the number of steps or degrees is one, the interval is called second (2), and so on.

Below is a list of intervals and their numeric symbols, which refer to distance on a staff based on the diatonic scale:


unison

1

octave

8

15th

15

second

2

ninth

9

 

third

3

tenth

10

fourth

4

11th

11

fifth

5

12th

12

sixth

6

13th

13

seventh

7

14th

14

The chart shows intervals an octave apart in parallel boxes.  Numeric symbols have been used ever since the Baroque era; in that period, chords could be identified with interval numbers of over 20.

Diatonic intervals can be perfect (abbreviated with a P or indicated only with a number, for example 5 for a perfect fifth), major (M), minor (m), diminished (d), or augmented (A).

The diatonic scale consists of both tones and semitones, in other words, intervals of different qualities.

The intervals are counted upwards from the bottom note of a major scale; the unison (1), fourth (4), fifth (5), and octave (8), are perfect.

When the intervals are counted upwards from the bottom note of a major scale, the second (2), third (3), sixth (6), and seventh (7) are major. Counted downwards from the root note, they are minor.
In practice, a major second is the same as a tone or whole step in a scale, and a minor second is the same as a semitone or half step.

The tritone, somewhat erroneously equated with an augmented fourth and a diminished fifth, was originally a sequence of three tones or whole steps. In a major scale, a tritone occurs only between the fourth and the seventh notes, for example, in C major, notes F and B. The official name of this interval is either the augmented fourth or diminished fifth, depending on the distance between the notes on the staff. Other augmented and diminished intervals are not part of the diatonic scale. A major third is sometimes called a ditone (two tones or whole steps).

The example below shows all diatonic intervals up to the octave. The clef is not shown on the two upper staves, so it is not possible to determine the quality of these intervals. It should be noted that the name of an interval is mainly determined by the distance of the notes on the staff. For example, an augmented fourth and a diminished fifth sound alike in an equal temperament, but on the staff, the distances between the respective notes are different.

Diatonic intervals

Intervals on the staff

The two first lines of the example below show diatonic intervals, that is, intervals found, for example, in a major scale. The first bar shows the location of semitones or half steps. As stated earlier, the quality of an interval is determined by the location of its semitones.

In bar eight, the fourth is augmented as it contains no semitones. The diminished fifth, which sounds the same but looks different on the staff, includes both semitones.

A harmonic minor scale is not diatonic; it contains an augmented second (bar 15) and other diminished and augmented intervals.

Harmonic minor scale

The quality of an interval can be changed with the help of accidentals. Raising the upper note or lowering the bottom note increases the interval. Likewise, an interval can be reduced by lowering the upper note or raising the bottom note:

Chromatic changes

Interval perception

Students of music traditionally learn to discuss intervals in terms of the staff. In this chapter, we will discuss them as such, without connection to notation.

The figure below shows intervals and their qualities. Each interval can be inverted. Inverted intervals include, for example, 8-1 and 5-4, here connected by a line. When inverted, the quality of an interval changes, except if they are perfect intervals. Major intervals become minor (for example, M3 and m6), and diminished intervals become augmented (A4 and d5). The tritone, the midpoint of an octave, does not change its quality when inverted. Inverted intervals are either consonant or dissonant; for example, sixths and thirds are consonant. The figure below can be thought of as a folding object where inverted intervals face each other.

Inverted intervals

For someone beginning music theory studies, it may be difficult to recognize the quality of an interval on the staff. There are several ways to make it easier. Here is one:
To start with, we must know the location of semitones in the diatonic scale.

"The Sixths and Sevenths Rule":
If there are two semitones between the notes, the interval is minor; if there is just one semitone, the interval is major.

"The Thirds and Seconds Rule":
If there is one semitone between the notes, the interval is minor; otherwise it is major.

The location of semitones is shown in the figure below, where note names are arranged in the form of a circle. The larger gaps between the names are tones or whole steps, and the smaller ones are semitones or half steps. Any major scale can be presented using the following syllables:

C = Doh
D = Ray
E = Me
F = Fah
G = Soh
A = Lah
H = Te

In the Romance Languages, these syllables are actual note names, also used in chord names (for example, So7 = G7)

According to the rule above, the doh-me third is major as there is no semitone between the notes. The te-soh sixth is minor as, read clockwise, there are two semitones between the notes. The note ray is highest for reasons of symmetry. The figure below also illustrates the concept of inverted intervals as it can be read both clockwise and counter-clockwise: the doh-lah sixth (clockwise) is major; the third doh-lah (counter-clockwise) is minor.

Inverted intervals as circles