Intervals
An interval is the distance between two notes.
Counting
Count letter names, including both notes. C to E is C-D-E, so a third. C to G is a fifth. Same letter an octave up is an octave.
Quality
The number is not enough. Semitones give the quality:
| Semitones | Interval |
|---|---|
| 1 | minor second |
| 2 | major second |
| 3 | minor third |
| 4 | major third |
| 5 | perfect fourth |
| 6 | tritone |
| 7 | perfect fifth |
| 8 | minor sixth |
| 9 | major sixth |
| 10 | minor seventh |
| 11 | major seventh |
| 12 | octave |
Fourths, fifths and octaves are perfect; the others are major or minor.
Spelling matters
C♯ to G is a diminished fifth (6 semitones), not an augmented fourth, because the letters C to G span five steps.
Inversion
Flip an interval and the numbers add up to 9; major becomes minor and perfect stays perfect. A major third inverts to a minor sixth, a perfect fifth to a perfect fourth.