Interval
The distance between two tones.

Interval, in music, is the distance between two tones. An interval can be sounded successively (as in a melody) or simultaneously (as in a chord). An example of an interval, sounded in these two ways, is:

[Example 1: minor sixth, pitches e-c, played (1) successively low-high, (2) simultaneously]

Names of Intervals

Musicians give names to intervals. First and foremost, those names use ordinal numbers, principally "second" through "seventh." These give a rough "measure" of the distance between the two tones.

In two cases, the ordinal numbers are replaced by special names: "unison" and "octave."

All musical intervals are counted inclusively. That is, the first and last tones are both counted. Imagine a ladder being placed between our two tones. For this demonstration, we need to make a slightly counterintuitive distinction between the rungs of the ladder, which are the physical bars on which you place your feet, and the steps, which for our purposes are the distances between the rungs. You will need to keep this distinction in mind as we proceed.

Fig 1: two tones, with ladder against them.

[Example 2: definition of intervals, examples 2a-2c]

A unison (uni = "one"; son = "sound") [Example 2a] is thus an interval whose imaginary ladder has only one rung -- that is, no step! An octave (oct = "eight") [Example 2b] is an interval whose ladder has eight rungs, hence seven steps. A sixth [Example 2c] has six rungs, hence five steps (as you can see in the diagram), and so on.

Added to these ordinal numbers are adjectives, which refine the rough measurement into an exact one. The most important of these adjectives are:

[Example 2 (cont.): pure and perfect intervals, examples 2d-2h]

To understand how these apply, you need to know one further thing. Of the eight intervals listed above, four have special acoustical properties that make them sound "pure." These are the unison [Example 2d], fourth [Example 2e], fifth [Example 2f], and octave [Example 2g]. These intervals all have just one normal state, called "perfect" [Example 2h].

The remaining four -- second, third, sixth, and seventh -- have two normal states: each can be either "minor" or "major." We can thus set out the normal states of all eight intervals as in the following table:

The adjective always precedes the ordinal number. Thus the interval that we heard at the beginning of this entry, for example, was a minor sixth. Other intervals are major third, perfect fourth, and so on.

In addition, every one of these intervals can be "squeezed" or "stretched" by a small extra amount. For these -- less normal -- states, we need two more adjectives:

So a perfect fourth can the "squeezed" to a diminished fourth or "stretched" to an augmented fourth; a minor third can be "squeezed" to a diminished third, a major seventh "stretched" to an augmented seventh, and so on. Diminished and augmented intervals occur less frequently than the other three, and happen usually when the music to which they belong is in a style that we call chromatic.

If you work it out, you will see that for the intervals from the unison through the octave there are 28 possible states in all. Twelve of these are normal (that is, perfect, minor, or major), and sixteen are less normal (that is, diminished or augmented)

[Example 3: third in all its states, examples 3a-3f]

To clarify all of this, let us take one interval and hear all its states. The third is an interval of particular importance for tonal music. Here are its two normal states: first minor [Example 3a], and now major [Example 3b]. Let's hear them one after the other for comparison [Example 3c]. The augmented third is slightly larger than the major third, so let us hear major followed by augmented [Example 3d]. The diminished third is slightly narrower than the minor third, so let us hear minor followed by diminished [Example 3e]. Finally, we will hear them all from small to large: diminished--minor--major--augmented [Example 3f].

The Contents of an Interval

In practice, things are a bit more complicated, and this entry cannot spell out all the complications here. You can get much more information by going to the separate entries on individual intervals (the ordinal numbers, and the adjectives).

But one thing should be explained at this point. While the distance between two tones in our modern musical system is absolute -- when measured, that is, in a scientific way -- its name is not absolute. This is because when a third (to take the example we have just used) is "squeezed" and becomes diminished, it actually crosses a borderline and enters the normal space of the second. And when it is "stretched" and becomes augmented, it crosses its other borderline and enters the normal space of the fourth.

The result is that, in the absence of any other indicators:

Let us now take the interval we heard at the beginning of this entry:

[Example 4: minor sixth, pitches e-c, played (1) successively low-high, (2) simultaneously]

These two tones are a fixed distance apart, scientifically speaking, and yet they can be called by either of two different names. This is because in reality the ladder that we showed in our diagram can have not just one size of step but two. It can be a mixture of what we call whole steps and half-steps. Moreover, these different sizes of steps can be placed in differing orders on the ladder. Here are two examples, both of which correspond to the interval we just heard:

Fig 2: two pairs of tones, each with ladder against it: (1) minor 6th, (2) augmented 5th.

If we now place a musical tone on each of the rungs of the ladder in the left-hand half of the diagram, we get:

[Example 5: scale e-f-g-a-bb-c : play twice slowly, first and last tones sustained]

The number of rungs is six, therefore the number of tones is six; and because the interval contains two half-steps, it is the minor sixth. (In fact, this is only one of several internal arrangements of whole and half-steps that can make up the minor sixth.)

And if we do the same for the ladder in the right-hand diagram we get:

[Example 6: scale e-f#-g#-a#-b# : play twice slowly, first and last tones sustained]

Now we have only five rungs, hence only five tones. Notice that all the steps are whole steps. That means that the fifth is stretched to its ultimate length; in other words, it is an augmented fifth.

Let us now play them one after the other so that you can listen to the difference:

[Example 7: scale e-f-g-a-bb-c, then scale e-f#-g#-a#-b# : each once]

What you are hearing is the difference between the contents of two intervals whose outer two tones are the same distance apart. The difference of content is enough to give the interval two different names: minor sixth, and augmented fifth.

Larger Intervals

Larger intervals than those so far discussed do exist, and play a useful role in music. Any interval larger than an octave is called a compound interval.

The Role of Interval in Music

Interval is one of the most powerful driving forces in music of all types. Take this tune, for example:

[Example 8: Irish jig]

This tune, called The Irish Washerwoman, is full of incessant, bustling energy. Where does it get its energy from? -- In large part from its intervals. Most melodies make frequent use of tones adjacent to one another: that is, they rely heavily on seconds, which sound continuous. When a melody moves mostly in seconds, we call its motion stepwise. We shall hear an example in a moment.

This one, on the contrary, almost entirely avoids seconds. It moves in skips. Literally, its intervals jump over their intervening notes. How appropriate, in this case, when the dance that it accompanies involves constant jumping!

Our Irish jig uses only medium-sized intervals: thirds and fourths. If melodies employ even wider intervals, they can become frantic; or if the melody itself moves reasonably slowly, it can become majestic. Here is an example almost everybody knows:

[Example 9: Strauss: Also sprach Zarathustra: CD 204]

Fig 3: Strauss opening.

--The opening of Richard Strauss's tone-poem Also sprach Zarathustra is also the theme music for the movie 2001. Its melody immediately leaps up a fifth, followed by a fourth (which makes an octave), and then a further third: 5--4--3. Finally, it turns the major third into a minor third -- a very powerful effect.

Take a moment now to sing The Star-spangled Banner silently to yourself. Just the first fourteen notes will do. Here are the intervals, with arrows to show whether up or down:

Fig 4: "Star-spangled Banner": 14 notes.

The wide-striding intervals, especially the sixths, give the melody a brimming confidence and bravery.

Melodies that proceed stepwise generally (not always!) exude a feeling of calm, or restfulness. Here is one that moves almost entirely in major and minor seconds, with only an occasional third:

[Example 10: Barber: Adagio for Strings, CD 2822]

Fig 5: Barber opening.

--Samuel Barber's Adagio for Strings, one of the most serene pieces of music ever written.

Finally, a melody can change its intervallic character during its course. Here, now, is the opening of Debussy's orchestral piece The Afternoon of a Faun (1894). The flute begins entirely with seconds, a lot of them minor seconds, making the line chromatic. It falls, then rises, in a slithering line. It repeats this, then opens up into wider intervals: fourth--third--sixth--third. It suggests something very languid, which slowly stirs itself into motion.

[Example 11: Debussy: Prélude à l'après-midi d'un faune: opening]

The opening up of the intervals at the midpoint suggests that the faun, sleeping in the sun, stretches and finds energy.

Summary:

• Interval is the distance between two tones.
• Intervals are named by ordinal number: second, third, etc.
• That ordinal number is qualified by an adjective: perfect, minor, and major are the normal states, diminished and augmented the less normal states.
• The size of an interval is determined not just by distance, but also by its contents.
• Some intervals have not one name but two, depending on their contents.
• Interval is one of the most powerful driving forces in music.

Note: If you want to learn more about intervals, we recommend that you next go to Octave, and then to Fifth and Third. After that, there are the other numbered intervals, and also the definitions of Perfect, Major, Minor, Diminished, and Augmented. There are also Consonant and Dissonant.

Copyright © Columbia University, Visual & Sound Materials from the Gabe M. Wiener Music & Arts Library of Columbia University
Interval written by: Ian Bent Recording & Mixing: Terry Pender & Douglas Geers	Narration: Ian Bent Technology & Design: Maurice Matiz