Intervals

An interval is the distance between two notes. Almost all music is created by using notes at different distances and thus different sizes of intervals. The notes in an interval may be played simultaneously, which is the case in chords, or played successively, which is the case in melodies.

1. Characteristics

Intervals can be categorized according to different criteria:

Harmonic and melodic intervals

Intervals can be harmonic or melodic. When the notes are played simultaneously, it is a harmonic interval. When the notes are played in sequence, it is a melodic interval. Melodic intervals can be ascending or descending:

Even and uneven intervals

Intervals can be even or uneven. If one note falls on a line and the other in a space, it is an even interval. If both notes fall on a line or in a space, it is an uneven interval:

Consonant and dissonant intervals

Intervals can be consonant or dissonant. If the notes sound pleasant and relaxed, the interval is a consonant interval. If the notes sound unpleasant and tense, the interval is a dissonant interval:

Dissonant intervals are not necessarily undesirable. Dissonant intervals are used in many contexts to build tension and momentum in the music.

The perception of consonance and dissonance is subjective. The Western world considers the following intervals to be consonant: unison, minor third, major third, perfect fourth, perfect fifth, minor sixth, major sixth, and octave. The following intervals are considered dissonant: minor second, major second, tritone, minor seventh, and major seventh.

2. Interval names

The intervals are named after the number of degrees between the notes. It is the number of degrees alone, and not the specific notes that determine the names. The table below lists the interval names and degrees.

Name	Degrees	Example (click to play)
Unison	1
Second	2
Third	3
Fourth	4
Fifth	5
Sixth	6
Seventh	7
Octave	8

The list continues with the ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, and fifteenth intervals, but they are rarely used.

To find the name of an interval, count the number of degrees between the notes, including both notes. Each natural note (C, D, E, F, G, A, and B) with or without accidental represents a degree. Each line and space on the staff also represent a degree.

For example, there are five degrees between the notes D and A, therefore, it is a fifth. There are three degrees between the notes E♭ and C, therefore it is a third:

3. Interval qualities

The exact distance between the notes in an interval with the same name may vary. An example is the two different versions of a third found below. They have the same name, but the first third is a half step smaller than the second third:

To specify the exact distance between the notes in an interval, a quality is added to the interval name. There are five different interval qualities:

• perfect intervals
• minor intervals
• major intervals
• diminished intervals
• augmented intervals

As a general rule, the intervals unison, fourth, fifth, and octave are only found in one quality. They are always perfect. As a general rule, the second, third, sixth, and seventh are found in two qualities. They are either minor or major. In rare cases, all intervals can be diminished and augmented (see section 6 for details).

The table below lists the interval names, qualities, and distances measured in half steps. To find the quality of an interval, count the number of half steps between the notes excluding the first note. For example, the interval between the notes D and F♯ is a third, and there are four half steps between the notes:

The quality of an interval can also be found by listening to it. Each interval has a unique sound that you’ll recognize through practice. It may help to distinguish between consonant and dissonant intervals (see section 1) and associate each interval with a song (see the Interval song chart page).

Unison, second and third

As a general rule, the unison is perfect, and the second and third are minor or major. A minor second is also called a half step. A major second is also called a whole step. Typically, the term perfect unison is not used as it implies that it is perfect.

Name	Degrees	Half steps	Example (click to play)
Unison	1	0
Minor second	2	1
Major second	2	2
Minor third	3	3
Major third	3	4

Fourth and fifth

As a general rule, a fourth and fifth are perfect. Between the two intervals is an interval spanning six half steps, which can be an augmented fourth or a diminished fifth. The interval is also called a tritone, because it spans three whole steps.

Name	Degrees	Half steps	Example (click to play)
Perfect fourth	4	5
Augmented fourth	4	6
Diminished fifth	5	6
Perfect fifth	5	7

Sixth, seventh and octave

As a general rule, the sixth and the seventh are minor or major, and an octave is perfect. Usually, the term perfect octave is not used because it implies that it is perfect.

Name	Degrees	Half steps	Example (click to play)
Minor sixth	6	8
Major sixth	6	9
Minor seventh	7	10
Major seventh	7	11
Octave	8	12

4. Interval inversions

An inverted interval is an interval turned upside down by moving the lower note up an octave, or the upper note down an octave. The inversion of the original interval results in a new interval:

In the example above, the note C has moved up an octave. The original interval is a sixth (6 degrees) and its inversion is a third (3 degrees). The number of degrees in an interval plus its inversion always equals 9 degrees:

Below is a list of interval inversions:

• unison ↔ octave
• second ↔ seventh
• third ↔ sixth
• fourth ↔ fifth

The quality of an inverted interval is the opposite quality of the original interval, but perfect intervals remain perfect. For example, the inversion of a major second is a minor seventh, and the inversion of a perfect fourth is a perfect fifth.

Below is a list of interval qualities under inversion:

• minor ↔ major
• perfect ↔ perfect
• diminished ↔ augmented

In particular, interval inversions are useful for finding sevenths and sixths more easily. Instead of finding the original interval, you can move the lowest note up an octave and simply find its smaller inversion:

5. Compound intervals

A compound interval is an interval which is larger than an octave. Like other intervals, the compound intervals are named by counting the number of degrees between the notes, including both notes. Their names are ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, and fifteenth:

Compound intervals consist of one octave and another interval which is typically smaller than one octave. For example, a ninth consists of an octave and a second, and a tenth consists of an octave and a third.

There are two alternative ways to name compound intervals. They can be named according to the interval they comprise without the octave, for example, compound second and compound third. Or they can be named by describing both intervals, for example octave plus a third.

Compound intervals exist in the same qualities as the corresponding intervals smaller than an octave. For example, a tenth (a compound third) can be minor or major, just like a third can be. Below is a list of compound intervals:

Name	Degrees	Half steps	Composition
Minor ninth	9	13	Octave + minor second
Major ninth	9	14	Octave + major second
Minor tenth	10	15	Octave + minor third
Major tenth	10	16	Octave + major third
Perfect eleventh	11	17	Octave + perfect fourth
Augmented eleventh	11	18	Octave + augmented fourth
Diminished twelfth	12	18	Octave + diminished fifth
Perfect twelfth	12	19	Octave + perfect fifth
Minor thirteenth	13	20	Octave + minor sixth
Major thirteenth	13	21	Octave + major sixth
Minor fourteenth	14	22	Octave + minor seventh
Major fourteenth	14	23	Octave + major seventh
Fifteenth	15	24	Octave + octave

A compound interval is found by moving the lower note up an octave and identifying the remaining interval. For example, if the remaining interval is a major third, the compound interval is a major tenth.

6. Augmented and diminished intervals

All intervals can be augmented and diminished. An augmented interval is a half step larger than a perfect or major interval, and a diminished interval is a half step smaller than a perfect or minor interval.

In the example below, there are four sixths of different qualities. In all cases, there are six degrees between the notes, but the diminished sixth is a half step smaller than the minor sixth, and the augmented sixth is a half step larger than the major sixth:

The intervals augmented fourth and diminished fifth are some of the only augmented and diminished intervals used regularly. This is because they have a quality of six half steps that do not correspond to a perfect, minor, or major interval.

All other augmented and diminished intervals have the same number of half steps as a perfect, minor, or major interval, and it is often more appropriate to notate them as such. Below is an example of an interval of three half steps notated as a major second and a diminished third, respectively:

Intervals with the same distance measured in half steps but with different names and notations are called enharmonic intervals. For example, an augmented fourth is enharmonic with a diminished fifth, and a minor third is enharmonic with an augmented second. The two intervals in the example above are enharmonic.