An interval is the apparent distance in pitch between two musical sounds. The ability to recognize and produce musical intervals is a vital skill for any singer.
When one sound has a frequency precisely twice that of another sound – that is, when the two frequencies are in the ratio of 2:1 – they “sound” like the same pitch to most listeners. We call the pitch difference or intervale between two such notes an octave. That is why, for example, a man, a woman, and a small child can all sing the same melody together – they are singing at intervals of an octave.
Listen to an example of an octave. You can sing an octave with ascending pitch or descending pitch, starting on any note.
Early musicians discovered that they could easily create an octave by doubling or halving the length of a plucked string, so it is not surprising that they experimented with other simple ratios in the form of music. It turns out that these ratio produced intervals that "sound good" to the human ear.
For example, adding 50% to a particular pitch (increasing the pitch by half, or a ratio of 3:2) creates an interval that we are familiar with as the sound of trumpet call. This interval eventually came to be called a perfect fifth.
Increasing a pitch by one third (a ratio of 4:3) creates another familar interval, one that we often associate with the words, "Here comes the bride." This interval came to be called a perfect fourth.
A perfect fourth followed by a perfect fifth, in either order, add up to an octave.
Increasing a pitch by one quarter (a ratio of 5:4) create another useful interval which we call a major third.
Increasing a pitch by one fifth (a ratio of 6:5) creates an interval which we call a minor third.
The major and minor thirds form a musical pair, one larger (Latin maior) and a smaller one (minor).
Increasing a pitch by one eighth (a ratio of 9:8) creates an interval which we call a major second.
This interval is also called a whole step, because (along with the half step, described below) it is one of the two basic elements in musical scale.
Increasing a pitch by one fifteenth (a ratio of 16:15) creates an interval which we call a minor second or half step.
Other pitch ratios create larger intervals ("sixths" and "sevenths", major and minor), as well as intervals larger than an octave, and a peculiarly dissonant interval caled a tritone (listen), larger than a perfect fourth and smaller than a perfect fifth. But the intervals described above are the ones normally using in plain chant.
The tonic or "home" pitch
When intervals are assembled to create a melody, they usually function in relation to a particular "home pitch" or base frequency which is called the tonic; this may be the starting note for the melody, and is very often the ending note as well. But even when the melody begins or ends on a different note, the tonic is the pitch around which the melody moves. (When the tonic changes in the course of a longer piece of music, this is called a modulation.)
The ascending minor second and perfect fourth have the peculiar tendency to emphasize the higher note, marking it as a (potential) tonic pitch. This chacteristic is sometimes used to emphasize a solid ending to a musical composition. For example, listen to the conclusion of the first movement of Ludwig van Beethoven's 's Symphony #1, which uses a string of perfect fourths (combined with minor seconds) to emphasize the tonic pitch.