The interval is the distance between two consecutive tones (source and target tones).
Interval | pure | major | minor | diminished | augmented | complementary | level |
---|---|---|---|---|---|---|---|
half tone steps | |||||||
First | 0 | – | – | -1 | 1 | Eighth | 1 |
Second | – | 2 | 1 | 0 | – | Seventh | 2 |
Third | – | 4 | 3 | 2 | 5 | Sixth | 3 |
Fourth | 5 | – | – | 4 | 6 | Fifth | 4 |
Fifth | 7 | – | – | 6 | 8 | Fourth | 5 |
Sixth | – | 9 | 8 | 7 | 10 | Third | 6 |
Seventh | – | 11 | 10 | 9 | 12 | Second | 7 |
Octave | 12 | – | – | 11 | 13 | First | 8 |
Only the pure as well as the big and small intervals are diatonic (build with tones in the scale only); the diminished and augmented intervals are chromatic. Chromatic intervals regularly lead to enharmonic change.
Although the second is probably "the most common interval" of all, it is often considered to have a transitional rather than a harmonic function: It is perceived as dissonant and therefore should be quickly dissolved into another, consonant interval.
Thirds play the main part in the harmonization of melodies. They define the most important chords plus the major and minor tonalites in Western harmonic theory. To accompany the melody in descending thirds is part of the musical standard repertoire.
Technically the fourth belongs to the consonant (and thus „agreeable“) chords. Its effect on the listeners, however, makes a fourth either consonant if no other note of the chord comes between source and target notes („close position“), or dissonant if they are more distant („open position“).
In Middle Ages the fifth was considered a perfect interval, i.e., a melody could end on the fifth of its root note. This changed later decisively: The fifth frequently appears as semi cadence at the end of a period (= „opening fifth“), while the octave comes at the end of the melody (= perfect cadence). It is common to use fifths in a sequence with descending fifths.
The main function of the sixth is that it can be understood as the inversion of a third; third and sixth skips therefore alternate quite frequently. The minor sixth was considered markedly dissonant and sad-sorrowful until the 19th century.
The complementary interval is the interval between the target tone of an interval and the next octave above the source tone. (The sum of the level of interval and inversion interval always gives 9: second = 2 + seventh = 7 = 9 etc.) Pure intervals have pure complement intervals, major ones have minor ones and vice versa, diminished ones have augmented ones and vice versa.
Intervals and complementary intervals in C major |
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Above: interval; below: complementary interval |
* = major; ** = minor |
- = diminished; + = augmented. Enharmonic change: E# = F, B# = C |
Any interval exceeding one octave is considered a compound interval. Its complementary interval corresponds to the complementary interval of the interval added to the octave.
Interval | Interval added | Complementary interval |
---|---|---|
Ninth | Second | Seventh |
Tenth | Third | Sixth |