In
music, an interval is the relative difference in
pitch between two successive
notes. Therefore we speak of
ascending and
descending intervals.
In traditional Western music, the notes are basically identical to what you find on the piano: it uses octaves equally divided in twelve. A selection of these notes - the white keys on the piano - roughly suffices to play most melodies (try Row, row, row your boat for an explanation), and the naming of intervals was based on this selection.
To be precise, the names indicate how many white keys are spanned in total.
The typical distance between successive white keys is called a whole note;
the distance between white and black, and between some white keys, is half of that, a half-note. As a result, we end up with:
- the second ("secundus" in Latin)
- the interval separated by one whole note, i.e., 1/6th of the octave; e.g., C-D on the piano
- a third (tertius)
- 2 notes, i.e., 1/3rd of the octave, e.g., C-E
- a fourth (quartus)
- 2.5 whole notes, or C-F
- a fifth (quintus)
- 3.5 notes, or C-G
- a sixth (sextus)
- 4.5 notes, or C-A
- a seventh (septimus]
- 5.5 notes, or C-B
- an eighth (octavus)
- 6 notes, 12 half-notes; C-C'
This leaves some gaps; these gaps are filled by speaking of
diminished intervals, e.g. the interval of 4.0 tones is called a
diminished sixth.
The only excuse for the weirdness of this naming scheme is its gradual development over many hundreds of years.
Combinations of more than two notes are known as chords. Musically, most chords contain a dominant interval (obtained by omitting all other notes); this explains why chords are named after intervals.