Chapter 10: Intervals and Chords

Introduction to Intervals

Now it’s time for a little more music theory. But don’t worry, I’ll try to make it as painless as possible! Besides, you’re going to need this stuff to build intervals and chords, two very important components of all those cool songs that you’ll soon be playing.

An interval in music is the distance between two notes. We already got to know some intervals in the earlier chapters, such as the half step and whole step. Now we’re going to derive some larger intervals, based on the distance between the notes on the staff. Let’s look at the following interval:

The first thing we need to determine is the interval number . To do this, we count up from the bottom note (starting at 1), and include all the letter names in between, including the top note. So, if the bottom note (C) is “1,” then D (2), E (3), F (4), G (5), and finally, A (6), thus we have a sixth. Now be aware that there are different types (qualities) of sixths, the most common being major and minor, but we’ll learn more about interval quality later.

Use the same technique to find the interval number for any two notes. The simplest is the second , which are always adjacent letter names. Skipping one letter name is a third , etc. When going from one letter to the same letter up or down, it is 8 or the octave . Some intervals that go beyond the octave such as 9ths, 10ths, and 11ths are named as such. When we get to an interval such as a twelfth, we can label this as a fifth plus an octave, etc.

Creating Intervals from the Major Scale

You remember the C major scale that we built in Chapter 7? Now we’ll look at all of the intervals created between the starting note (C) and the other notes in this scale:

Play each of these intervals on the piano to get the different sounds “in your ear.” Since the notes are placed one above the other, or vertically, they get played at the same time try this (intervals whose pitches are played at the same time are called harmonic intervals. More about this soon!) For the second line, you’ll want to play one note in each hand.

Notice that the interval numbers are shown with an interval description, which is either major or perfect. The 4th, 5th and octave (and 11th, 12th and two octaves) are the perfect intervals, and the remaining intervals are major. Again, don’t worry too much about these interval descriptions just yet. For now, just remember that from the first note of the major (In Other Words) scale to all other notes will produce either major or perfect intervals.

Using Intervals in Songs

Next, we’ll see how some of these intervals are used in famous songs. We’ll also see how major intervals reduced by a half step, become minor intervals. We’ll start out with the 2nd:

In the first measure we have the major 2nd (C up to D). When this is reduced by a half step, we get a minor 2nd interval (C up to D♭ ) as is shown in the second measure.

Notice that the major 2nd is equivalent to a whole step, and the minor 2nd is equivalent to a half step.

Because whole steps (major 2nds) and half steps (minor 2nds) are the building blocks of scales, you might expect these intervals to show up very frequently in melodies. Well, you’d be right! Here’s our first melody excerpt, containing major and minor 2nds. The intervals are shown above the staff for the first measure (M2=major 2nd, m2=minor 2nd).

Jazz Standards

“Fly Me to the Moon” is a great example of a jazz standard. Jazz standards are vocal tunes, generally written between the 1920s–1950s, which have very strong and enduring melodies. Successive generations of jazz musicians to this day, always “cut their teeth” on the standards. Most jazzers will either play the standards from memory, or from a “fake book,” showing the melody and chords (more about using fake books in Chapters 14 & 15). Here are ten more jazz standards that all piano players should be acquainted with. Although pretty much everything else will most likely change over the next 100 years, it’s a safe bet that these tunes will still be played by 22nd-century piano players!

• All the Things You Are (Jerome Kern)
• Autumn Leaves (Johnny Mercer)
• Body and Soul (Johnny Green)
• A Foggy Day (George Gershwin)
• On Green Dolphin Street (Kaper/Washington)
• Misty (Erroll Garner)
• My Romance (Richard Rodgers)
• Night and Day (Cole Porter)
• Our Love Is Here to Stay (George Gershwin)
• Stella by Starlight (Victor Young)

Next, we’ll spotlight some 3rd intervals (major and minor):

In the first measure we have the major 3rd (C up to E). When this is reduced by a half step, we get a minor 3rd interval (C up to E♭ ).

Here’s our next melody excerpt, one from the classic Four Tops’ song “I Can’t Help Myself.” (I had the pleasure of meeting the co-writer Brian Holland when he visited my home studio in Los Angeles a couple of years ago. He was very down-to-earth, and had a nice dry wit!) This excerpt contains both major and minor 3rds (“M3”=major 3rd, “m3”=minor 3rd):

Next, we’ll look at an excerpt of a song which uses perfect 4th intervals. This is “We Are the Champions,” one of the most popular and enduring hits from the rock band Queen (written by Freddie Mercury).

The previous example contains 2nds and 3rds, as well as 4ths. As you play this excerpt on the piano, try to identify the 2nds and 3rds!

“We Are the Champions” was released in October 1977, and spent ten weeks on the charts, reaching number two and achieving gold status. The song’s great melody and triumphant spirit made it a favorite anthem of soccer fans in Great Britain. Queen’s classic songs and tremendous showmanship made them one of rock’s most important bands of the 1970s and 80s. One of my favorite Freddie Mercury quotes is: “People are apprehensive when they meet me. They think I’m going to eat them. But underneath it all, I’m quite shy.”

Our next song excerpt uses perfect 5th intervals. “Everybody Wants to Rule the World” is one of the best known anthems from the ’80s synth-pop band Tears For Fears.

About Tears For Fears

The British pop duo Tears For Fears was one of the most innovative bands to emerge from the 1980s synth-pop era. The band was actually a duo, formed by Roland Orzabal and Curt Smith in the early ’80s, after they had both played in a ska revival band called Graduate. The name Tears For Fears was taken from the writings of Arthur Janov, whose “primal scream therapy” influenced much of the band’s work, notably their debut album The Hurting . This became a major hit in Great Britain, generating three Top-Five singles.

By the mid-1980s, it had become a high priority for the band to have a major success on the U.S. charts. This goal was achieved with the hit single “Everybody Wants to Rule the World,” which had a harder-edged, more “American” pop sound.

With its wonderful chorus and innovative guitar work, this song is a classic of the period.

Both this song and the band’s other number one U.S. hit “Shout,” came from their hugely successful Songs from the Big Chair album, which set a new standard for melodic synth-pop.

Next, we’ll spotlight some 6th intervals (major and minor):

In the first measure we have the major 6th (C up to A). When this is reduced by a half step, we get a minor 6th as in the second measure (C up to A♭ ).

Our next melody excerpt is from the song “Where Do I Begin,” which was the main theme from the movie Love Story. This excerpt contains major and minor 6ths:

Creating Three-Note Chords (Triads)

OK, let's take a deep breath and plunge into the fun world of chords. A chord is created when three or more notes are played at the same time. A three-note chord is known as a triad. Most popular styles are harmonically organized around chords. We'll now use some of the intervals developed in this chapter to "spell" some triads (i.e., figure out what notes we need to build them), starting with the major triad.

You'll see that I've measured the intervals (major 3rd and perfect 5th) up from the root of the triad in each case. The root is the note from which the triad is based. We refer to the middle note as the third of the chord, and the top note is called the fifth. You'll remember (at least I hope you will!) that these major and perfect intervals are found within the major scale. This triad consists of the first, third and fifth degrees of a C major scale.

Also note the letter C shown above the triad. This is our first example of a chord symbol, which tells you the name of the chord; it is placed above the staff.

A chord symbol that consists of a note name with no additional suffix or description indicates a major triad built from the note indicated, so the chord symbol C means a C major triad.

The major triad is the most basic and fundamental chord, and is used throughout pop and classical styles. So it would be a great idea to learn all of the major triads (i.e., not just C major), don't you think? Well, here they are!

Play through all of these major triads on your piano to learn the sounds and "shapes" of the major triad built upon each of these notes. Use fingers 1, 3, and 5, and try playing the triads with each hand.

Next up, we have the minor triad, which we're also going to spell by using intervals as follows:

Again, the intervals (this time minor 3rd and perfect 5th) are measured up from the root of the triad. When comparing this triad to the major triad, we see that the third interval (between the root and the middle note, or "third" of the chord) is now a minor 3rd instead of a major 3rd. So another way this C minor triad can be derived is by taking the previous C major triad and lowering the third by a half step (in this case the note E becomes E♭). This is true of all major triads: take any major triad, lower the third a half step, and you have a minor triad.

The chord symbol above the staff is now Cm. There are two components to this chord symbol: the root (C) and the "suffix" or description (m). A chord symbol which consists of a note name followed by the suffix "m," indicates a minor triad built from the note indicated, so the chord symbol of Cm means a C minor triad.

The minor triad is used just about as widely as the major triad, so it's another good candidate for learning in all keys. Note the chord symbols (with the "m" suffix) above each chord:

Although the major and minor triads are the most common, there are two more triads that we will sometimes use, the augmented and diminished triads:

These two new triads are shown above, and we can compare them to the C major triad on the left.

• If we raise the 5th of the C major triad by a half step, we get a C augmented triad. Note there are two chord symbols above this chord—both the "+" and "aug" suffixes are commonly used alternatives.
• If we lower the 3rd and 5th of the C major triad by half steps, we get a C diminished triad. Note there are two chord symbols above this chord—both the small circle and "dim" suffixes are commonly used alternatives.

Play the C major triad on your piano, and then alter it to create the C minor, C augmented, and C diminished triads. Then try the same exercise, starting with different major triads (i.e., not just C major!).

Diatonic Triads and Progressions

Let’s define a couple of terms that will help you understand this section. “Diatonic” means “belonging to the major scale.” “Diatonic triads” are therefore triads that are contained within the major scale. Here are all of the triads contained within the C major scale:

What we’re doing here is building a triad from each note in the C major scale, making sure that all notes used are contained with the scale (which in this case means they are all white keys… pretty easy huh?). This gives us the various triad “qualities” shown here, from left to right (major, minor, minor, major, major, minor, diminished, major).

The Roman numeral under the staff indicates chord function. Each chord within a key has different tendencies in terms of what kinds of chords they lead to, what kinds of chords they follow, and other tendencies within the context of a piece of music. These Roman numerals actually serve as symbols for chords that have particular functions, or different roles within a key. For more on the specifics of chord function, please see my book Contemporary Music Theory, Level 2, published by Hal Leonard Corporation. For now, all you need to know is that within the key of C, a C major triad is a “I” chord; a D minor triad is a “II” chord, and so on, based on scale degrees.

Now we’ll start looking at triad progressions. These are simply sequences of chords used in songs. Our first example is the chord progression used in “Mr. Jones,” a hit for the rock band Counting Crows in the 1990s. This will also be our introduction to repeat signs in the music.

A repeat sign is made up of a thin bar line and a thick bar line, like that of the end of a song. The addition of two dots around the middle line completes this sign, which means to repeat back either to the beginning, or to a previous repeat sign with the dots to the right of the pair of barlines.

Each measure in this song contains a whole-note triad, with a chord symbol above the staff. The key signature of “no flats and no sharps” tells us we are in the key of C major, and all of the chord symbols are diatonic triads from the C major scale (check the previous diatonic triad example as needed). The first line is the verse of the song, and the repeat signs around measures 1–8 tell us to play this line twice (i.e., 16 measures total). Then the next line is the chorus of the song, which is also repeated.

It’s a good exercise to figure out the function (i.e., Roman numeral) of each chord in this song by comparing it to the diatonic triads in the key of C. For example, the first triad is Am (which is a VI in C), the next triad is F (which is a IV in C) and so on. The chords for many simpler songs can be analyzed this way, which helps when you’re communicating with other players, as in, “Hey Nigel, the chorus is a I-IV-V in C!”

Play through the triads of this “Mr. Jones” to get a feel for the progression, and have a listen to the original song if you can. Although it’s a great tune, the chord progression is very simple and basic!

Of course, we can have diatonic triads in any key, not just in C major! So now we’ll derive the triads within a couple more keys, and look at some songs using these triads. Next up are the diatonic triads within F major:

Again, note the chord qualities above the staff, and the Roman numerals underneath. The famous Beatles’ song “Hey Jude” was written in the key of F, and here’s an excerpt from the chord progression from this song:

Again, try to analyze the function (I, V, etc.) of each chord in the key of F. Also play through the triads of this song. Many songs use this simple I-IV-V progression, although there are few examples better than “Hey Jude”!

A lot of simpler pop, rock, and country songs use diatonic triads exclusively for their chords. So you get a lot of “bang for the buck” from these. Learn them in as many keys as you can!