Interval

Definition of interval

An interval in music is the sound of exactly two tones sounding together, or one after the other.

All intervals can be measured by the number of diatonic steps and by their semitone distances.

More technically, an interval can also be described as a frequency ratio relationship between two stable vibrations.

All intervals can occur on (above or below) all tones.

Contents 1 Definition of interval 2 One sound 3 Basic intervals 4 Wide intervals 5 Perception of the interval 6 Basic intervals from c 7 Full names of the intervals 8 Intervals in order of chromatic size 9 Inversions of the intervals 10 Augmented and diminished intervals and their harmonic resolutions 11 Notes 12 See also 13 External link

One sound

The sounding together of two tones creates a blending of the two into a new, specific sound, is called the interval. Within the sound of each interval, partial tones can be perceived, emerging from the interaction of frequencies as sum- and difference tones. Each interval thus consists of far more than just the two tones played or performed, it is a complex sound which is at first perceived as a whole.

Basic intervals

Due to notation, intervals are named by the distance between the two basic tones they consist of.

When the lowest tone is counted as 1, the name of the interval follows from counting in diatonic steps upwards (although reversing this direction gives the same result):

See Basic interval for a further description; each also has a separate page for still more details.

Wide intervals

Wider than the octave, music theory describes larger intervals. Though similar, some of these sound quite different than their related narrower intervals.

See Wide interval for a further description; each also has a separate page for still more details.

Perception of the interval

The unique sound of each interval can be immediately recognized by hearing, making it in fact a truly fundamental element of all music.

When listening to two simultaneous tones, their pitches and frequencies mix and react, creating even more tones sounding together: interference tones. This complex of tones becomes one comprehensive sound, and the individual pitches become acoustically more or less absorbed into the human perception of the single interval: the interval itself is in fact perceived as louder than the individual tones it consists of. It is human perception which "summarizes" the tones into the single interval, but it has good acoustic reasons to do so. Thus the interval is equally the basic prerequisite for all melody as it is for harmony.

Basic intervals from c

The basic intervals using only basic tones from c are shown below (click to play the examples).

The second series consists in fact of inversions of the first, in reverse order.

Full names of the intervals

A full name of an interval consists of the name plus the nature, such as minor second (m2), perfect fifth (P5), or augmented sixth (A6) etc.
Each interval thus has a "first" and a "last name".

For shorter and easier writing the names of the intervals are abbreviated in the following way: the intervals are represented by numbers, their nature by a preceding letter.

Summary of the abbreviations:

• M = Major, m = minor, P = Perfect, A = Augmented, d = diminished
• 1 = unison, 2 = second, 3 = third, 4 = fourth, 5 = fifth, 6 = sixth, 7 = seventh, 8 = octave

The table below lists all possible basic intervals, these are also presented in notation, with c as reference tone (remember, all intervals can occur on -above or below- all tones!).

	d	m	P	M	A
unisons	d1		P1		A1
seconds	d2	m2		M2	A2
thirds	d3	m3		M3	A3
fourths	d4		P4		A4
fifths	d5		P5		A5
sixths	d6	m6		M6	A6
sevenths	d7	m7		M7	A7
octaves	d8		P8		A8

Intervals in order of chromatic size

The table below lists all possible basic intervals in order of number of semitones, these are also presented in notation with their enharmonic equivalents, with c as reference tone (remember, all intervals can occur on -above or below- all tones!).

semitones	-1	0	1	2	3	4	5	6	7	8	9	10	11	12	13
interval	d1	P1, d2	A1, m2	M2, d3	A2, m3	M3, d4	A3, P4	A4, d5	P5, d6	A5, m6	M6, d7	A6, m7	M7, d8	A7, P8	A8

The possibility of writing one and the same sound with two different diatonic spellings is called enharmonic equivalence; such two intervals are enharmonically the same. When listened to separately, the number of semitones will determine the sound, and in ear-training usually the simpler spelling is heard, interpreted and given. Within a certain musical context however, more complex phenomena may occur, requiring specific writing, spelling and nomenclature, giving prevalence to one of the two possibilities for contextual reasons.

Inversions of the intervals

The inversions describe close relationships between intervals in pairs: an interval and its inversion use the same notes, but in different order or position. The two inversions together span a perfect octave, 12 semitones, thus the inversion of a Major third is the minor sixth, calculated as M3 (4 semitones) and m6 (8 semitones), together 4 + 8 = 12 semitones (P8).

The close relationship between inversions can be clearly heard, as well as the fundamental difference in sound. No interval should be mixed up with its inversion, they are not identical, nor is one derived from the other^[1].

The inversions are below presented in notation, with c as reference tone (remember, all intervals can occur on -above or below- all tones!).

The inversion of a perfect interval is always a perfect interval, the inversion of a major interval always a minor interval, the inversion of a diminished interval always an augmented interval, and all vice versa as well. The inversion of a second is a seventh, of a third a sixth, of a fourth a fifth, and vice versa. The tritone is the only interval which is enharmonically the same as its inversion, such as can be heard by clicking and playing the above example.

A table to help quickly find the names of the inversions is given here:

nature	type
P ↔ P	2 ↔ 7
M ↔ m	3 ↔ 6
A ↔ d	4 ↔ 5

Augmented and diminished intervals and their harmonic resolutions

The tension of dissonance in augmented and diminished intervals can be led into resolution with relative consonance by treating the constituent tones as voices and resolving each by a minor second (not just any chromatic semitone, but a precise minor second) in opposite directions.

The respective resolutions are found as follows:

• The tension in an augmented interval is caused by the widening, so resolution is found widening further outwards.
• The tension in a diminished interval is caused by the narrowing, so resolution is found narrowing further inwards.

The following tables summarizes the results:

Augmented or diminished interval

d1

A1

d2[2]

A2

d3

A3

d4[3]

A4

d5

A5[4]

d6

A6

d7

A7[5]

d8

A8

Harmonic resolution

m3

m3

M2 (d3)

P4

P1

P5

M2

m6

M3

m7

P4

P8

P5

M9 (m10)

M6

m10

In notation below are summarized all augmented and diminished intervals with resolutions ranging from unison up to and including the octave; all augmented and diminished intervals of "tension" are here on c for better auditive appreciation:

The same intervals once again, now in order of the number of semitones in their resolutions; all resolutions are here intervals on c or an enharmonic equivalent, for better auditive appreciation:

In these augmented and diminished intervals and their resolution, we are able to as it were hear the microscopic forces of functional harmony; they can be and are in fact used both as harmonic and melodic intervals. Careful study of these is highly recommended for the professional musician, as they allow for 'listening on the inside of harmony'.

Notes

1. ↑ Rameau, Treatise on Harmony (1722)
2. ↑ Since the diminished second is enharmonically identical to the perfect unison, the first is consonant and the second in fact dissonant. Although the theoretical solution is the major second, to perception, to musical hearing this sounds therefore as the reversed order of the resolution of d3, the diminished third.
3. ↑ Although the diminished fourth is enharmonically identical to the major third, and hence the first is consonant and its resolution, a major second, is dissonant, this resolution is indeed still acceptable to perception, to musical hearing.
4. ↑ Although the augmented fifth is enharmonically identical to the minor sixth, and hence the first is consonant and the its resolution, a minor seventh, is dissonant, this resolution is indeed still acceptable to perception, to musical hearing.
5. ↑ Since the augmented seventh is enharmonically identical to the perfect octave, the first is consonant and the second in fact dissonant. Although the theoretical solution is the major ninth, to perception, to musical hearing this sounds therefore as the reversed order of the resolution of d10, the diminished tenth.

See also

• Outline of basic music theory
• Basic interval
• Wide interval
• Triad
• Seventh chord
• Special:Browse/Interval - browse this page to find whiteboards treating intervals.

External link

• List of musical intervals on Wikipedia (with sound examples)