Naming INTERVALS

Intervals are named by their number and quality.

Interval number

An interval number is the number of the staff positions that are located between two notes. When counting the staff positions, both the staff lines and the staff spaces must be counted. Also, the staff positions of both the notes must be included in the counting. The next figure shows an example where we can count five staff positions. 

Figure: Determining an interval number by counting the staff positions (the staff position counts are marked in red)

The interval numbers (up to an octave) are:  the prime (or unison), second, third, fourth, fifth, sixth, seventh and octave. The prime corresponds to two notes sharing the same staff position. The second corresponds to notes that span two adjacent staff positions. The third corresponds to notes that span three adjacent staff positions. The fourth corresponds to notes that span four adjacent staff positions and so on. This is illustrated in the next figure. 

Figure: The interval numbers, from the prime to the octave

Interval quality

An interval quality can be: major, minor, perfect, diminished or augmented. It depends on the number of pitches between the notes. The following rules apply: 

• A prime, fourth, fifth and octave can have only the following qualities: a diminished, perfect or augmented. 

• Other intervals (a second, third, sixth and seventh) can have only the following qualities: a diminished, minor, major or augmented.

If we know the number of pitches for perfect prime, fourth or fifth, we can easily calculate the number of pitches for the other two possible interval qualities. This is explained in the next table.

If we know the number of pitches for major second, third, sixth or seventh, we can easily calculate the number of pitches for the other three possible interval qualities. This is explained in the next table.

The next table lists down all the possible combinations of the interval qualities and numbers (and thus all the possible intervals), from the prime to the octave, also giving the number of staff positions and the number of pitches between the notes of each interval. When counting the pitches, the pitches of the notes themselves are also counted. 

Intervals with the same number of pitches are called enharmonically equivalent intervals. For instance, the augmented fourth and the diminished fifth are enharmonically equivalent.

On first looking, the given table looks complex but it can be easily understood if we imagine the C major scale on the piano keyboard. Although we shall define scales later, it is not difficult to imagine the C major scale on a piano keyboard because it consists of the white keys only (C, D, E, F, G, A and B). After this, all the intervals can be found between the piano key C and the other piano keys that are positioned on the right of it.  Also, we can easily count the number of pitches as the number of the piano keys (both the white keys and the black keys must be counted). The next figure illustrates how the major and perfect intervals (the blue rows in the previous table) can be found between the piano key C and the other white piano keys. 

Figure: The C major scale and the perfect and major intervals

The other intervals can then be understood in relation to the major and perfect intervals. The next figure shows a piano keyboard where the diminished, minor and augmented third are compared with the major third. As before, the intervals are between the piano key C and the other piano keys on the right of it. Since the lower note name of the interval is C, the upper note name must be E with or without an accidental so that the interval spans 3 staff positions. The accidental determines the number of pitches (which is the same as the number of piano keys) and the interval quality. 

Figure: The diminished, minor and augmented third compared with the major third

The next figure shows a piano keyboard where the diminished and augmented fourth are compared with the perfect fourth. As before, the intervals are between the piano key C and the other piano keys on the right of it. Since the lower note name of the interval is C, the upper note name must be F with or without an accidental so that the interval spans 4 staff positions. The accidental determines the number of pitches (which is the same as the number of piano keys) and the interval quality.

Figure: The diminished and augmented fourth compared with the perfect fourth

Tritone

A tritone is any interval that spans 3 whole steps (or 6 half steps, which is the same). The half step and whole step were explained in chapter Half step and whole step. 

For instance, the interval between the notes F4 and B4 is a tritone because it spans 3 whole steps: the first whole step is between the notes F4 and G4, the second one is between G4 and A4 and the third one is between A4 and B4. This is shown in the next figure.

Figure: A tritone and its whole steps

The interval in the previous figure spans 4 staff positions and 7 pitches. In the table from the previous chapter, we find that the interval that spans 4 staff positions and 7 pitches is an augmented fourth. We can conclude that any augmented fourth is the tritone. Remember that when we count pitches in an interval, we also count the starting pitch and that is the reason why an interval that spans 6 half steps does not span 6 but 7 pitches. Therefore, the tritone must span 7 pitches.

In the table from the previous chapter, we see that the diminished fifth also spans 7 pitches. Thus, any diminished fifth is also the tritone. The next figure shows an example of the tritone realized with the augmented fourth together with an example of the tritone realized with the diminished fifth. In fact, both intervals in the figure are between the same pitches.

Figure: The tritone realized with the augmented fourth and diminished fifth

During the Renaissance, sacred vocal compositions were the most important type of compositions and the tritone was considered sounding too harsh and hard to sing to be used in them. The legend says that the tritone was labeled as “devil’s interval” and forbidden.