Day Three: The Musical Intervals

Intervals are units of music that happen on the smallest level.

This post is part of 14 Days of Harmony, a free course for musicians who want to deepen their understanding of harmony, and learn how to develop their connection with sound as a result. You can view the entire course here.

The musical intervals are commonly thought of as the distance between two notes. An interval implies a lived connection between two notes. Melodies are built with them. Harmonies are delivered to us in time through the intervals. The intervals seem to connect sound with its concrete and mathematical origins to our inner world of feeling—and thank goodness. 

The intervals are a basic element of music, and their importance shouldn't be overlooked. Working with the fundamental intervals refines and nurtures our direct connection to our musicality. As this article aims to show, the intervals are the first opportunity that we have to experience a musical unity.

Basic foundations: What are the intervals? 

Let's set the foundation by discussing the intervals as the "distances" between two tones. The distances can be measured between two notes on a staff or on an instrument. Counting the number of notes between the two notes that you are measuring (including the first note) is the first way to find and learn the musical intervals.

The easiest way of learning them is to look at an ascending major scale.

Figure 1. The diatonic C major scale, built from major and minor seconds. 

The distance between the tonic (note 1) and the second note in the scale is a second, and the distance between the tonic and the fourth note of the scale is a fourth, and so on. The chromatic scale contains all 12 notes, and provides all of the possible intervals within an octave.

Figure 2. The 12 possible intervals have labels that indicate their size (the distance expressed as number) and their quality (M for major, m for minor, and P for perfect). M3 is read as "major third," m6 is read as "minor sixth," and P4 is read as "perfect fourth." T.T. is the tritone.

1. Figure 2 shows the musical intervals within one octave. The 12 intervals are outlined as increasing in size between each successive note of the ascending chromatic scale and the tonic, C. If you can, go ahead and sing or imagine each of the intervals and hear what they sound like. 

2. Each of the intervals have a quality. Fifths, fourths, and octaves can be described as perfect. The seconds, thirds, sixths, and sevenths can be described as either major or minor. Typically major intervals are larger than minor intervals by 1 half step.

3. The intervals can be inverted by raising the lower note up by one octave.

4. Intervals also have directions. You can play them going up, or down.

Figure 3. Inverting each of the intervals in Figure 1 is done by raising the lower note one octave, and shows a new pattern of intervals, revealing a symmetry.

Octave inversions of intervals always add up to 9. For example, the inversion of a 3rd is a 6th. Inversion of a 2nd is a 7th, and inversion of a 4th is a 5th. Major intervals become minor when inverted, and when inverted minor intervals become major. Perfect intervals remain perfect when they are inverted.

Figure 4. Series 2 from Paul Hindemith's Craft of Musical Composition

Figure 4 shows the 12 intervals arranged in a much more useful way. The intervals in this series are arranged based on the same order that they appear in the harmonic series: first the octave, then the fifth, followed by the fourth, the major third, the minor third, the major second, and so on. 

It reveals a remarkable pattern: 5 pairs of intervals and their inversions—fifths and fourths, major thirds and minor sixths, minor thirds and major sixths, major seconds and minor sevenths, minor seconds and major sevenths—flanked by the octave and the tritone. 

Even if you don't understand this fully yet, keep reading on. I hope to introduce an approach that will let you access the significance of the intervals. Knowledge of this full theory will come with time. Since intervals are what builds scales, melodies, chords, and is the basic unit of musical construction, how can we develop our relationship with them? 

Hear all that goes on when you sing an interval.

Figure 5. A minor third up.

What is it like to sing an interval? What does singing one reveal?

Try this out. Sing a minor third. 

The first thing that I hear is the stability of the first tone. While singing the first note, I have to imagine the next tone in my head. I almost have to hear the second note inside the sound of the first note. Now, I move to the second note. 

When I sing the second tone, I am moved by a whole bunch of sensations. For me, I think of Batman (thanks, Hans Zimmer) and I'm also moved emotionally. Why? How does this happen? The reason that these associations arise is that while I am singing the second tone I am still connected to the first tone. 

Consider the following. I sing one note. Then take a break. Then I come back. And sing the second note. I've already forgotten how the first note felt. There is no meaning. No connection, no association. 

But when I actually connect the two notes and live the relationship between them, the interval arises. 

Try it! Pay attention to the inner hearing of the second note of the interval that is being sung before you actually move to the second note. 

If you manage to do that, then you have successfully lived an interval. It feels good, doesn't it! 

By listening to the interval and letting it arouse our inner sensations, the body allows us to appreciate what nature has built into sound.