Intervals are the names given to the distances between two pitches. They be expressed in terms of relative scale degrees (minor 3rd, tritone, unison, octave) or exact ratios (3:2, 16:9, 5:4).
The system of defining intervals with a ratio is typically only used in alternate tuning systems. For all tonal music (and much atonal music written in 12-TET), the system of scale degrees is appropriate. These names are listed in the following chart according to the number of semitones between the two pitches. When more than one name is listed, the correct name will be a quality of the distance between the note letter names. For example, when evaluating the enharmonic intervals
C-D# (both distances of 3 semitones),
C-Eb is identified as a minor 3rd due to the fact that 3 letter names exist between C and E inclusive, whereas
C-D# is an augmented 2nd, due to the fact that 2 letter names exist between C and D inclusive.
Intervals larger than an octave are possible and would follow the same pattern. These in particular are useful in a jazz context when talking about chord members extending to the 9th, 11th, or 13th.
| Number of | Diatonic | Augmented or | | Semitones | intervals | diminished | |:---------:|:-----------:|:-----------------:| | 0 | Unison | Diminished 2nd | | 1 | Minor 2nd | Augmented unison | | 2 | Major 2nd | Diminished 3rd | | 3 | Minor 3rd | Augmented 2nd | | 4 | Major 3rd | Diminished 4th | | 5 | Perfect 4th | Augmented 3rd | | 6(tritone)| Augmented 4th/Diminished 5th | | 7 | Perfect 5th | Diminished 6th | | 8 | Minor 6th | Augmented 5th | | 9 | Major 6th | Diminished 7th | | 10 | Minor 7th | Augmented 6th | | 11 | Major 7th | Diminished octave | | 12 | Octave | Augmented 7th |