Intervals

An interval, in music, is the difference in pitch between two notes.

Here’s Wikipedia’s definition:

In music theory, an interval is the difference between two pitches. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

These two usages are very different from each other. “Interval” is used to describe pitch differences in both melodic space, the world of pitch, and harmonic space, the world of harmony. I think that’s a bit unfortunate in the case of harmony, because what drives the quality of a harmonic interval is not the difference in pitch (up, down) so much as the ratio between the two frequencies. The same interval may look very different in one space than in the other. Many intervals that are very close in pitch are far apart harmonically, and many harmonically close intervals are far apart in pitch.

Take the perfect fifth, for example. Here are two ways to describe the interval of a fifth:

1. A pitch distance of 7 half steps, and
2. Multiplication by 3.

The first way is simpler for thinking about melody, and the second is simpler for thinking about harmony.

Multiplying by three is the smallest harmonic move you can make, except for unisons and octaves. In harmonic terms, it’s the Note Next Door. But in melodic space, seven half steps is a long jump. Bass singers are kind of heroic in that way.

The following video shows a perfect fifth, in both harmonic space (the lattice) and melodic space (the keyboard).

Another example is the major second. This interval is a compound of two fifths, so the original note is multiplied by 3 twice. The major second means multiplication by 9. Harmonically, this interval is bigger than the fifth.

But in the melodic realm, the notes come out only two half steps apart.

Here’s the split screen version of the major second:

The major second is close in the melody and distant in the harmony. Notice how the major second sounds more dissonant than the fifth?

The word “interval” is also used to describe two notes sounding at once. An interval is the simplest harmony. Three or more notes is a chord, or a collection.

One note, all by itself, doesn’t have much of a personality, besides the timbre or sound of the instrument it’s played on. Without harmonic context, one pitch sounds pretty much like another. Some are higher, some lower, but that’s about the only distinction.

When two notes are played together, they create something new. Intervals have personalities, and each one is different from the others.

I think of intervals as the atoms of harmony. Intervals can be combined into larger collections, or molecules with more complex properties. Intervals and chords look entirely different on the lattice than they do on the keyboard, and I find that the patterns they form deepen my understanding of harmony. The lattice gives a window into harmonic space.

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