Understanding Chords: Part 1, Intervals

Understanding Chords – Featured Image

This post is part one in a four-part series on chords.

  • Part one covers intervals, the building blocks of chords.
  • Part two will cover the construction of major and minor chords.
  • Part three: augmented and diminished chords.
  • And Part four will be on seventh chords.

To understand how major, minor, and other chords are constructed, it’s helpful to look at the fundamental building block of chords: intervals – in particular, half steps (minor seconds) and thirds (both major and minor thirds).

Let’s cover each of these, and then combine them to create some chords.

I’ll try to be somewhat comprehensive, so feel free to skip over any sections and just grab what you need. (You can also skip down to the quiz at the bottom of this post.)


Intervals

Definition: An interval is the distance between two notes.

An analogy is that an interval is like a unit of measure – like a centimeter or an inch. And when we talk about music, we can say, essentially, “The distance between this note and that note is three centimeters, or is 22 centimeters,” etc.

The unit of measure we use in music is called a half step.

And with most chords (in their basic form), the distance between each of the notes is either three half steps or four half steps. (We’ll cover this in Part two of this series.)

Half Steps

In standard Western music, the smallest interval is the half step. Half steps are also known as minor seconds or semitones – depending on the context. (In more experimental music, there can be smaller intervals – anything imaginable, really. Though we’ll stick with the standard stuff here.)

In standard Western music, the distance between two notes can always be defined by how many half steps encompass the distance (the frequency space) between those two notes.

So, half steps are a core building block to understand.

One way to think of a half step is that it’s the difference in pitch between any two piano keys that are right next to each other (or any two nearest notes in standard music) – for example, C to D flat, or E to F, etc.

We can see a few half steps on the piano keyboards below.

Usually, on the piano keyboard, a half step will be the distance between one white key and one black key next to each other:

Piano Keyboard Showing Half Steps – C to D Flat

Though there are two notable exceptions – as you can see on the piano keyboard below. There’s no black key between E and F, or between B and C. Those are the two instances where a half step occurs between two white keys:

Piano Keyboard Showing Half Steps – E to F

A note for guitarists: On one string, moving from one fret to the next fret is a half step. For example, on any string, moving from fret 1 to fret 2 would be one half step.

Recognizing Intervals

Each interval has its own, unique sound – and its own “look” on the musical staff. And each interval is defined by how many half steps occur between its two notes.

One octave (for example, the note C up to the next note C) encompasses 12 half steps. In music theory, each number of half steps within an octave is given is own designation/name.

For example, a distance of:

  • 1 half step is called a minor second
  • 2 half steps is called a major second
  • 3 half steps is called a minor third
  • 4 half steps is called a major third

… and so on, up to 12. These 12 intervals are known as simple intervals. And intervals larger than an octave (spanning more than 12 half steps) are called compound intervals.

Compound intervals also each have a name correlating to their number of half steps, but they’re less important for our current discussion. So we’ll stick with just the intervals within an octave for now.

And in fact, we can simplify things even more.

The main intervals we want to look at when studying major and minor chords (and augmented, diminished, and seventh chords) are minor thirds, major thirds, and perfect fifths. Here’s some info on each:

Notice below how each interval has its own, recognizable sound.

Minor third
A distance of three half steps between two notes is called a minor third. A minor third can be heard in the first two notes of the song, Hey Jude, by The Beatles. Here’s how it sounds:

Major third
Four half steps between two notes is called a major third. Swing Low, Sweet Chariot starts with a major third: (Can you hear how a major third is one half step wider than a minor third?)

Perfect fifth
Seven half steps is called a perfect fifth. The first two notes of the Star Wars theme music form a very recognizable perfect fifth:

There are 12 half steps (and therefore 12 intervals) within an octave. So far, we’ve looked at four of these intervals (minor seconds, minor thirds, major thirds, and perfect fifths). Further below is a chart that defines and gives info on all 12 of the simple intervals.

A brief aside: Western classical music essentially derives all of its notes by dividing the octave into 12 segments – half steps. Almost all of the music we know is based on this system. It’s good to remember, though, that this is just one possible system of many.

Contemporary music theorists often emphasize that frequency space can be divided in infinite ways. And we see examples of this:

20th-century composer, Harry Partch, for example, often divided the octave into 43 segments. (He had to build his own instruments so his music could be played.)

There’s a whole stream in contemporary classical music called microtonality – where smaller and smaller intervals are used.

And nowadays, with the help of computers, the octave can be divided into thousands and thousands of free-flowing segments. So anything is possible, really. Frequency space can be divided in infinitesimal ways.

So what we’re talking about in this article are simply the rules or systems that are used to create the most standard types of notes and chords. And since music is an art, it’s always good to reflect on how, ultimately, there are no set rules. And it’s really about creating music to express ourselves in a meaningful way, and creating sounds that we like.

That’s always a worthwhile caveat when talking about any “rules” in music.

Why are Intervals Named this Way?

If it seems weird/arbitrary why one interval is called a second, another is called a third, and so on, here’s a good way of thinking of it:

An interval of a second spans:

  1. two letters in the music alphabet (for example, A to B, or E to F, etc.);
  2. and two places on the musical staff – a line and a space, like below:

And this system holds true for each interval. For example, an interval of a third spans:

  1. three letters in the music alphabet (like A to C, or E to G, etc.);
  2. and three places on the staff – like below:

Interval Song List (for the 12 Simple Intervals)

For learning each interval’s sound, we’re often shown a list of recognizable songs, along with what interval is occurring between the first two notes of each song’s melody. (This helps us get to know and recognize the sound of each interval, and even be able to accurately sing them.)

Here are some example songs for each of the 12 simple intervals.

Note: For standard chords, we only really need to look at three intervals:

  • minor thirds
  • major thirds
  • perfect fifths.

So, you may want to focus on those intervals below. But I’ll include all of the intervals here – just to give a complete picture.

One weird aside: There are two forms of each interval. Seconds, thirds, sixths, and sevenths can be minor or major. Fourths can be perfect or augmented. And fifths can be diminished or perfect. And an augmented fourth and a diminished fifth are two different names for an interval of six half steps.

As you keep going with theory, you see more of the “why” behind these kinds of details. But for now, you can just know that there are mathematical, and sometimes historical, reasons for most of these things and naming conventions.

Interval Chart

Interval Number of Half Steps Example Song(s)
minor second 1 Jaws (Theme)
Pink Panther (Theme)
Für Elise
major second 2 Happy Birthday
Mary Had a Little Lamb
minor third 3 Brahms’ Lullaby
Georgia on My Mind
O Canada
Hey Jude
major third 4 Oh When the Saints
Ob-La-Di Ob-La-Da (The Beatles)
Beethoven’s Fifth
Swing Low, Sweet Chariot
perfect fourth 5 Here Comes the Bride
Auld Lang Syne
Harry Potter (Hedwig’s Theme)
Love Me Tender
Eine kleine Nachtmusik (Mozart)
augmented fourth
or diminished fifth
6 The Simpsons (Theme)
Maria (West Side Story)
perfect fifth 7 Twinkle, Twinkle
Star Wars (Theme)
Blackbird (The Beatles)
Scarborough Fair
Can’t Help Falling in Love
(Elvis, et al)
minor sixth 8 We are Young (Fun)
major sixth 9 My Bonnie Lies over the Ocean
Hush, Little Baby
Nobody Knows the Trouble I’ve Seen
minor seventh 10 Nothing Compares 2 U (Sinead O’Connor/Prince)
Lady Jane (Chorus) (The Rolling Stones)
major seventh 11 Take on Me (A-Ha)
Don’t Know Why (Norah Jones)
perfect eighth
or octave
12 Somewhere Over the Rainbow (Chorus)
Take Me Out to the Ballgame

Melodic and Harmonic Intervals

Just a quick note on this. Intervals in music occur in two ways:

  1. with the two notes occurring one at a time. This is how intervals occur in melodies (and in the song examples above). We call these melodic intervals:
  2. Or intervals can occur (as they do in chords – a.k.a. harmony) with both notes occurring at the same time. We call these harmonic intervals:

We’ll be dealing with harmonic intervals as we look at chords.

How Intervals Look on the Staff

Along with being recognizable by its sound, each interval is also recognizable on the musical staff. Here’s how seconds, thirds, fourths, and fifths appear:

Seconds occur on a line and space next to each other on the staff. (Minor seconds can also occur with both notes on the same line or space – if one of the notes is sharped or flatted. But the above is the usual look of a second.)

Thirds can be thought of as “Line to Line” or “Space to Space” – notes on two lines or two spaces next to each other on the staff. They’re easily recognizable. You’ll want to remember how thirds look. These are the building blocks of chords.

Fourths will always be one note on a line and one on a space – and a bit wider than a second or third.

Fifths look similar to thirds (in that both notes occur on lines or spaces). I like to say, “Line and Line with Line In Between” or “Space and Space with Space In Between.” Note: The outer two notes of major, minor, augmented, and diminished chords span an interval of a fifth. So fifths are the next most important interval to familiarize ourselves with here.

Sixths, sevenths and eighths are less important to recognize on the staff right now – and they’re a bit less recognizable, too. As we continue our series on chords, we’ll focus mainly on thirds and fifths.

Chords

Definition: A chord is three or more notes occurring at the same time.

Major, minor, augmented, and diminished chords each contain three notes. And seventh chords contain four notes.

A three-note chord (by the power of math :) ) contains two intervals. (The distance between the bottom note and the middle note is one interval; and the distance between the middle note and the upper note is another interval.) And a four-note chord contains three intervals.

And whether the distance between each of the notes in a chord is three half steps (a minor third) or four half steps (a major third) determines whether the chord is major, minor, augmented, diminished; or any of the six types of seventh chords.

These chords are all built just by stacking up major and minor thirds (in all possible configurations).

We’ll talk more about this in Part 2…

Quiz Time

Jump here to take a quick, 12-question quiz on this article. One of the best ways to learn new ideas in music theory is to read info (like on this page), and then to answer questions on the material in some musical examples.

There’s a link to an answer key at the bottom of the quiz. I’d recommend taking the quiz first, and then checking your answers after.

Questions?

Music theory concepts can be tricky at first (though they usually get really simple once you’ve worked with them a bit). If you have a question, feel free to contact me here. I’m happy to answer a few questions about chords.

If you live in Seattle, I’m also available for private lessons in piano, music theory, and composition. Let me know also if you’d happen to live elsewhere and have an interest in Skype lessons. It’s something I’m just trying out. Feel free to contact me to talk more.

You can also sign up to the Email List to be notified the next time a post like this is published (like the next post in the chords series); or to stay in the loop with me, if you’d like.