Musical intervals
An interval is the distance between two notes. It is measured in semitones and written with the degree number of the major scale: 3 for a major third, b7 for a minor seventh. This table lists the intervals used in jazz harmony with an example on C.
Interval table
| Semitones | Interval | Symbol | On C |
|---|---|---|---|
| 1 | Minor second | b2 | D♭ |
| 2 | Major second | 2 | D |
| 3 | Minor third | b3 | E♭ |
| 4 | Major third | 3 | E |
| 5 | Perfect fourth | 4 | F |
| 6 | Tritone | b5 / #4 | G♭ / F♯ |
| 7 | Perfect fifth | 5 | G |
| 8 | Minor sixth | b6 | A♭ |
| 9 | Major sixth | 6 | A |
| 10 | Minor seventh | b7 | B♭ |
| 11 | Major seventh | 7 | B |
| 12 | Octave | 8 | C |
Tensions (compound intervals)
| Tension | Semitones | Name | On C |
|---|---|---|---|
| b9 | 13 | Minor ninth | D♭ |
| 9 | 14 | Major ninth | D |
| #9 | 15 | Augmented ninth | E♭ / D♯ |
| 11 | 17 | Eleventh | F |
| #11 | 18 | Augmented eleventh | F♯ |
| b13 | 20 | Minor thirteenth | A♭ |
| 13 | 21 | Major thirteenth | A |
The tritone, engine of resolution
The tritone (6 semitones) is the interval that gives a dominant its urge to resolve. In G7 it is formed by the third (B) and the minor seventh (F): B rises to C and F falls to E. Without the key’s tritone (F and B in C), as with Gm7 or B♭7, the chord loses its dominant pull.
The rule for tensions
A tension is available if it sits a whole step above the chord tone below it. If it sits a half step above, it is an avoid note: over CMaj7, the 9 (D) is a whole step above C and sounds good, while the 11 (F) is a half step above the third (E) and clashes. The dominant is the exception: it accepts almost every tension except the 11.
Compound intervals
Tensions are scale intervals moved up an octave: the 9 is a 2nd, the 11 is a 4th and the 13 is a 6th. That is why D over a C chord is the 9 and A is the 13.
Frequently asked questions
How many semitones are in a perfect fifth?
Seven semitones. From C to G there are seven.
What is the tritone?
It is the interval of six semitones (an augmented fourth or a diminished fifth). It is the heart of the dominant chord.
Why is the 11 an avoid note over a major chord?
Because it lies a half step above the chord third and clashes with it; over CMaj7, F clashes with E.
Based on the jazz harmony principles of Joe Mulholland and Tom Hojnacki (Berklee Press).
Circle of fifths · American chord notation · Scales and modes in every key