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Intervals

An interval is simply the distance between two notes. Understanding intervals and training your ear to recognize them is one of the most important skills as a musician, because a firm grasp on intervals establishes a link between your mind, your instrument, and your emotions.

Intervals are measured by the number of half steps (also called semitones) between two notes. Half steps are the smallest interval (aside from unisons, which are explained after the diagram) in Western music.

Interval Numbers & Qualities

Every interval is described by an interval number and an interval quality.

The interval number is the number of letters that the interval spans:

• C to D (ascending) has an interval number of 2, because it spans the letters C & D
• F# to Db (descending) has an interval number of 3, because it spans the letters F, E, & D
• G to Db (ascending) has an interval number of 5, because it spans the letters G, A, B, C, & D

and so on...

The interval quality describes the sound of the interval and helps specify the exact number of half steps in the interval. The possible interval qualities are:

• Perfect (P)
• Major (M)
• Minor (m)
• Diminished (d)
• Augmented (A)

We will learn exactly what these interval qualities mean and how to use them soon, but we must learn some prerequisite knowledge first.

To notate an interval, we write the interval quality followed by the interval number, for example:

• M2 — Major 2nd
• P4 — Perfect 4th
• d5 — Diminished 5th

Simple Intervals

There are 13 simple intervals, which are intervals spanning 12 half steps or less. Take some time to memorize them:

More on Interval Qualities

To figure out what interval quality to use when naming an interval, you first need to know three things about the interval:

• the interval's number (which the number of letters the interval spans, as stated earlier)
• the number of half steps in the interval
• the common name for intervals with that number of half steps

If the common name for that number of half steps matches with what you determined to be the interval number, you can simply use the common name.

For the interval from C to E, for example:

• The interval number is 3.
• There are 4 half steps between the two notes.
• The common name for intervals with 4 half step is "Major 3rd".

Because the common name is a 3rd, and the interval number between C and E is 3, we can simply name the interval a "Major 3rd" (M3).

The interval from C to D#, for example, is not as straightforward to name:

• The interval number is 2.
• There are 3 half steps between the two notes.
• The common name for intervals with 3 half steps is "Minor 3rd".

In this case, we can't use the common name for intervals with 3 half steps ("Minor 3rd") because it doesn't match our decided interval number of 2. Instead, we will keep the interval number of 2 and change the quality of the interval to make it span 3 half steps.

We have memorized the simple intervals above, so we know that the largest interval with an interval number of 2 is a Major 2nd (M2), which spans 2 half steps. We need to change the quality to increase the number of spanned half steps to 3. To do this, we follow this chart which describes how interval qualities change as half steps are added (+) or removed (-):

From the chart we see that, to change the Major 2nd interval's quality to make it span an additional half step, we need to change the quality to "Augmented". So, the name for the interval from C to D# is "Augmented 2nd" (A2).

NOTE: Some intervals (such as from C to D♯♯) require interval qualities that exceed the ones in the chart above. In these cases, you can simply use "doubly augmented" (AA), "triply augmented" (AAA), and so on, or "doubly diminished" (dd), "triply diminished" (ddd), and so on.

Compound Intervals

Beyond the simple intervals there are compound intervals, which span more than 12 half steps (P8). Some examples of compound intervals are:

• Minor 9th (m9) - 13 half steps, or 1 octave and 1 half step
• Perfect 15th (P15) - 24 half steps, or 2 octaves
• Major 17th (M17) - 28 half steps, or 2 octaves and 4 half steps
• and so on...

When analyzing the sound and function of compound intervals, however, we generally reduce compound intervals to simple intervals by subtracting octaves until you are left with a simple interval. So:

• m9 would reduce to m2
• P15 would reduce to P8
• M17 would reduce to M3

and so on...

Ear Training

Finally we have come to one of the most important skills a musician should have: recognizing intervals by ear. This skill allows you to translate the music you hear in your mind (or in your ear) to your instrument, and helps you identify and understand fragments of music and why they make you feel a certain way.

One way to train your ear is by associating every simple interval with a memorable part of a song. The table below associates each ascending and descending simple interval with a song, and also describes how consonant or dissonant each interval is.

Consonant intervals sound pleasing to the ear, and dissonant intervals sound harsh or tense to the ear. The categories of consonance/dissonance we will use, from most consonant to most dissonant, are:

• Perfect Consonance
• Imperfect Consonance
• Mild Dissonance
• Sharp Dissonance

When training your ear to recognize intervals using the table below, pay close attention to how consonant or dissonant each interval is, and how each interval makes you feel.

Interactive Exercises

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