The name of the interval between two notes (for example, D#-B
b) is assigned keeping in mind that our musical system uses twelve notes (C, C#, D, D#, E, F, F#, G, G#, A, A#, B), but their names are only seven (C, D, E, F, G, A, B).
Depending on how many names of notes (including the ends) are included, the interval is said second, third, fourth, and so on. Note that D#-A
b, is a fifth interval (D, E, F, G, A are five), exactly as D-A or D
b-A#, although the three intervals are different in terms of number of included semitones. Here are the various possibilities:
| NAME |
No. NAMES OF NOTES |
EXAMPLE |
NAMES OF INCLUDED NOTES |
| Unison |
1 |
C-C |
C |
| Second |
2 |
C-Db |
C-D |
| Third |
3 |
C#-Eb |
C-D-E |
| Fourth |
4 |
C-F# |
C-D-E-F |
| Fifth |
5 |
C#-Gb |
C-D-E-F-G |
| Sixth |
6 |
C#-A |
C-D-E-F-G-A |
| Seventh |
7 |
C-B |
C-D-E-F-G-A-B |
| Octave |
8 |
C#-Cb |
C-D-E-F-G-A-B-C |
| Ninth |
9 |
C-Db |
C-D-E-F-G-A-B-C-D |
| Tenth |
10 |
C#-Eb |
C-D-E-F-G-A-B-C-D-E |
Of course, after the tenth interval there are eleventh, twelfth, and so on.
Another element that can make different two intervals is the number of semitones that compose it: in other words, how many times you have to ascend by a semitone to move from the first to the second note (just count how many black and white keys there are, including the extremes, and subtract one): for example, between D# and B
b there are seven semitones (D#, E, F, F#, G, G#, A, B
b are eight).
The following table shows the main intervals:
| NAME |
EXAMPLE |
No. NAMES OF NOTES |
No. SEMITONES |
| Diminished unison |
C-Cb |
1 |
-1 |
| Perfect unison |
C-C |
1 |
0 |
| Augmented unison |
C-C# |
1 |
1 |
| Diminished second |
C#-Db |
2 |
0 |
| Minor second |
C-Db |
2 |
1 |
| Major second |
C-D |
2 |
2 |
| Augmented second |
C-D# |
2 |
3 |
| Diminished third |
C#-Eb |
3 |
2 |
| Minor third |
C-Eb |
3 |
3 |
| Major third |
C-E |
3 |
4 |
| Augmented third |
C-E# |
3 |
5 |
| Diminished fourth |
C#-Fb |
4 |
4 |
| Perfect fourth |
C-Fb |
4 |
5 |
| Augmented fourth |
C-F# |
4 |
6 |
| Diminished fourth |
C#-Gb |
5 |
6 |
| Perfect fifth |
C-Gb |
5 |
7 |
| Augmented fifth |
C-G# |
5 |
8 |
| Diminished sixth |
C#-Ab |
6 |
7 |
| Minor sixth |
C-Ab |
6 |
8 |
| Major sixth |
C-A |
6 |
9 |
| Augmented sixth |
C-A# |
6 |
10 |
| Diminished seventh |
C#-Bb |
7 |
9 |
| Minor seventh |
C-Bb |
7 |
10 |
| Major seventh |
C-B |
7 |
11 |
| Augmented seventh |
C-B# |
7 |
12 |
As you can be observe, the terms diminished, minor, perfect, major, augmented are assigned to the intervals according to the number of semitones; besides second, third, sixth and seventh can be minor and major but not perfect, on the contrary of unison, fourth and fifth. The octave can be perfect as unison, the ninth minor or major as second, and so on.
An interval is double augmented if it contains a semitone more than an augmented one, double diminished if it has one less than diminished (a parità di nomi di note compresi). For example, since F-B is an augmented fourth, F-B# is a double augmented fourth.
Ultimately, while second, third, sixth and seventh may be, in order, double diminished, diminished, minor, major, augmented and double augmented, unison, fourth and fifth are double diminished, diminished, perfect, augmented and double augmented.