What is an interval? 

The distance in pitch between two notes is called an interval. 

An interval can be thought of as the basic unit from which scales, harmonies, and melodies are built.  Indeed, intervals are the building blocks of all three. 

Before we continue, let's define the terms above. 

A melody is a series or sequence of (typically) single notes played in succession that together produce a sound that is memorable and/or pleasant to hear, whereas harmony in music refers to a combination of notes that are sounded out simultaneously (chords).  Rhythm refers to the pattern of the sound (and silence) produced over time.  Together with dynamics (how soft or loud the sound is), melody, harmony, and rhythm represent the core elements of music.  In general terms, pitch describes how low or high the sound is.  The slower the vibrations of the sound wave that produce the sound (low frequency), the lower the pitch, and thus the higher the vibrations (high frequency), the higher the pitch.

We can also think of intervals in terms of steps.  Imagine a person climbing a ladder.  Before climbing the ladder, imagine that the person's feet are next to each other.  Starting at this stationary position, when both feet are at the same level, taking a foot up one rung (or climbing one rung up the ladder) represents taking a "half-step" or semitone and two rungs represent a "whole-step" or whole tone (or simply tone as whole tone and tone can be used interchangeably).  

We can also think of a rung as being a certain note, such as A for instance, and thus the step from one rung to an adjacent one (A to A#) would be a half-step (semitone). Two half-steps equal a whole-step, and therefore two semitones represent a whole-tone (or tone).

On the fretboard, a half-step is the shortest distance from one fret to the next, up or down. Starting on a note on any given string, going a half-step is going up (or down) one fret, such as from A to A♯ (up) or A to A♭ (down). A whole-step is going up (or down) two frets, such as from A to B (up) or A to G (down).

Thus, the step from A to A♯ is a half-step (semitone):

.and from A to B is a whole-step (whole tone or tone)

The step from B to C is a half-step (semitone), as B and C are adjacent to each other, and from B to C# is a whole-step (whole tone or tone):

How does an interval get its name?

An interval gets its name based on the the distance between the two adjacent notes and is named using the two descriptors of Quality and Size.

Two adjacent notes that are separated by one semitone (half-step) represent a minor 2nd (also known as ♭2 or m2) Two adjacent notes separated by two semitones (whole-step or tone) are called a Major 2nd (or M2).

(from this point forward, we'll use tone in place of whole tone)

As we can see, there are two parts to the name of an interval: Quality and Size.

The quality of an interval can be described as being either: minor, Major, Perfect, Diminished, or Augmented.

The size of an interval refers to how far apart the two notes of the interval are.

In minor 2nd interval, minor represents the quality and 2nd represents the size.

In Major 2nd interval, Major represents the quality and 2nd represents the size.

In the diagram below, the interval (distance between two notes) that's formed by A and A♯ is a minor 2nd:

The interval between A and B is a Major 2nd:

Applying the same interval guidelines, it follows then that the interval between B and C is a minor 2nd and between B and C♯ is a Major 2nd:

The interval between A♯ and C is a Major 2nd:

You get the idea...

Harmonic Interval vs. Melodic Interval

Previously, we established that an interval is the distance in pitch between two notes. How these two notes are sounded determines the type of interval they collectively form.

When we play two notes on the guitar at the same time, the interval is in harmonic form. When we play two notes one after the other (as in a melody), the interval is in melodic form.

A melodic interval can be either ascending or descending.

When we play the A note then B, the interval is a melodic, ascending interval.

When we play the B note then A, the interval is a melodic, descending interval.

Simple Interval vs. Compound Interval

Before discussing simple vs. compound intervals, let's first cover sound, frequency, and octave.

A simple or basic interval refers to an interval that spans an octave or less. An octave is an interval of one note to the next bearing the same name, as in from C to a higher C or lower C. An octave therefore has the same letter name, but different frequency.

But what is frequency?

Frequency describes the vibrations of sound waves. Simply put, when we pluck a guitar string and hear a sound, it's as a result of the string vibrating back and forth creating waves of energy or sound waves that travel through the air, water, or even solid objects.

Our eardrums are extremely delicate and sensitive, and when they come in contact with the sound waves, they will also vibrate. In comes the brain, which then translates these vibrations into what we know to be sounds, sounds that are produced by different things. And in our case by the vibrations of the guitar string after we pluck it with our finger.

The type of sound we hear is determined by the shape as well as size of the sound waves.

A high-pitched sound is produced by sound waves that are high in frequency. That is, these sound waves vibrate fast, "more frequently," and therefore in short intervals. A low-pitched sound is produced by sound waves that are low in frequency or slow and thus in long intervals.

Ask yourself this. When you wave your hands in the air, are you able to hear the sound that makes? Chances are, not.

This is because the vibrations caused by your hands waving in the air are too slow, and thus not producing the sounds waves that our human ear can hear.

What is the lowest sound a human ear can hear? It's a sound that's produced with vibrations that occur 20 times a second. I'm not exactly sure what kind of sound this is, but it's a very LOW sound.

What is the highest sound a human ear can hear? A sound with vibrations of 20,000 times per second. This is a very high-pitched sound!

I never like the word "homework," and seldom use it as it has a certain negative stigma; however, perhaps this is our homework: to come up with the sounds that are produced by low-frequency sound waves and high-frequency sound waves!

It's all About Vibrations

We've discussed the science of sound and frequency, but how is frequency measured? It's measured in Hertz, or Hz.

You might have heard that the tuning standard used for the note A above middle C has the audio frequency of 440 Hz. What does this mean?

It means when you pluck the A note above middle C on the guitar, that A note vibrates 440 times per second. It vibrates 440 times a second to produce the sound waves that eventually reach your eardrums that our brain interprets it to be an A note.

Where do we find that A note on the fretboard, or middle C for that matter?

The diagram below shows where both notes are located on the fretboard:

A above Middle C

Middle C on the guitar

Middle C on the guitar is located on the 3rd string, 5th fret. A above Middle C: 1st string, 5th fret.

Back to octave..

We discussed how, in musical terms, "an octave is an interval of one note to the next bearing the same name, as in from C to a higher or lower C."

But how would we define an octave as it relates to frequency? An octave is an interval (distance) between one note and another note that's either doubled or halved in frequency.

The diagram below from Interactive Mathematics provides a great illustration:

Source: https://www.intmath.com/trigonometric-graphs/music.php

As you can see, the A above middle C vibrates at 440 Hz per second and it's higher octave vibrates at 880 Hz, exactly double the vibrations. Similarly, it's lower octave A vibrates half the frequency, at 220 Hz.

What is the frequency of middle C? 261.6 Hz (no splitting hairs needed)

Back to Simple Interval and Compound Interval..

A simple interval is an interval that spans an octave or less. A compound interval is an interval that spans more than an octave.

In the diagram below, A (5th fret) to B (7th fret) is a simple interval. As we have learned, this interval is a Major 2nd. It is a simple interval because the distance between A and B is less than an octave.

Whereas A (5th fret) to B (9th fret) is a compound interval because the distance is between these two notes is greater than an octave. This interval is a compound Major 2nd, or Major 9th as it's commonly known.

Simple Interval :

A (5th fret, 6th string) to B (7th fret, 6th string)

Compound Interval :

A (5th fret, 6th string) to B (9th fret, 4th string)

There are a total of 12 notes in Western music. This means that all the melodies and harmonies that you hear in Western music collectively were created using only 12 notes. That's pretty incredible, isn't it? It's incredible that essentially only these 12 notes, known as the chromatic scale, were used to create all the pieces in Western music.

It makes me think about the fact that it's no wonder many songs sound really similar to each other. It also makes me wonder about how is it that we can write anything that hasn't been written before. Yet, time and again, we come across a song, harmonies, or melody lines that may sound familiar, however, they are noticeably unique in their own way. How many times have you heard a piece of music or guitar solo that gives you pause and might perhaps even blows you away due to its originality? I have, and that makes me think that there's still more room to write "original" stuff.