Intervals [Music Theory Fundamentals: Part 1]

Music Theory Fundamentals Intervals

Music Theory Fundamentals. Part I: Intervals. Click here for Part 2.

Welcome to my Music Theory Fundamentals series. This is a series of posts covering the basics of tonal music – from intervals and scales, to triads, meter, chord progressions, and so much more. This series will be a good place to start for beginners, as well as a good refresher for those who have some knowledge of music theory already. You are currently reading Part 1, which is on the topic of intervals.

Over this series of blog posts, we will be covering much of the same content you would in a conventional music theory class, however there will be several key differences:

1. We will be using everyday examples from popular music. By doing this, we will stay true to the philosophy behind this blog, which is learning music theory with popular music.

Grandma

2. I will try to explain everything in a very simple and easy-to-understand way (and if you have any questions, ask in the comments – I am very responsive)

I do believe in the old saying “You do not really understand something unless you can explain it to your grandmother.” No offence to grandmothers, since my mom just became one! :)

3. I will notate everything on a piano roll. This is for the benefit of the 21st century producers and songwriters, many of whom, though they are extremely capable musicians, cannot “read music” in the old-fashioned sense. Rather, they spend hours in front of computerized piano rolls in Logic, Reason, Pro Tools, Fruity Loops, etc.. A piano roll is a very simple form of notation to read:

Piano Roll Notation

Piano Roll notation. This will be used throughout the Music Theory Fundamentals series. (Gold star to anyone who can name this tune – let me know in the comments)

This Music Theory Fundamentals Series may be good for you if…

  • You are a songwriter trying to learn how to write a better song
  • You’re someone who studied music theory before and found it boring or complicated
  • You are a music theory student looking for easy-to-understand supplemental lessons
  • You are a producer trying to write a hit song
  • You want to understand how a song works
  • You want to know why a song like Blackbird is so good (and why the song you wrote isn’t)
  • You feel like you are a beginner at all this
  • You are confused by traditional music theory constructs like modes which date back to the Middle Ages and you are wondering how it applies to this Beck album you are obsessed with
  • You want to learn music theory using examples from songs you actually listen to
  • You’ve always thought you should learn music theory but you just haven’t

Does this sound like you? Well then, let’s dive right in!

Interval Pop Music Theory

A cute little box guy playing an interval at the piano

Intervals: Music Theory Fundamentals Part 1

In this first installment of our Fundamentals Series, we will be covering intervals. But… since you can’t have intervals without notes, let’s start with the most basic unit of music, the note.

12 Notes

There are 12 and only 12 notes in all of tonal music. Virtually every single song you hear on Spotify or YouTube, or on that CD or Vinyl sitting on your shelf, uses only these 12 notes. Yes, there are other amazing types of music from around the world that use different notes and scales, but we will not be discussing those. We will be focusing on Western tonal music – whether that be Otis Redding or Weezer, Daft Punk or Lady Gaga, Pink Floyd or Beyoncé.

Here are our 12 notes:

12 Notes of Tonal Music

The slash indicates two different names for the same note. For example, C♯ can also be called D♭, they are two different names for the same note. To use a fancy term, you could say C♯ and D♭ are enharmonic equivalents.

Harmony

In last week’s post, I defined harmony as “what results from the interaction of two or more notes.” As soon as we are dealing with more than one note in the same song, harmony enters into the picture.

Below is a song that only uses one note. The song doesn’t use any harmony whatsoever – but it does, of course, use other elements of music like rhythm, dynamics, etc…

So, that song only uses one note. But most songs use more than one note.

As soon as you add that second note to a piece of music, there are really only two options:

Option #1 – The two notes are being played at the same time
Option #2 – The two notes are being played nearby one another

Think about it, if you have two notes that are in the same song, either they need to be played at exactly the same time, or they need to be played somewhat nearby each other.

If they weren’t played near enough to each other, then you wouldn’t realize they were part of the same piece of music or song and by definition, no harmony would result.

Two Types of Intervals

Going along with our two options above, there are two types of intervals:

Harmonic Interval Melodic IntervalThe two types of intervals. Harmonic intervals are two notes played together, whereas melodic intervals are two notes played nearby one another.

A harmonic interval is when two notes are played at exactly the same time, like when a guitarist strums her guitar.

A melodic interval is when two notes are played individually and consecutively/nearby each other.

Regardless of the interval type, if you have two different notes, the first and most obvious thing to do is to discuss the differences in pitch or distance between those two notes, which we call, in music theory, an interval.

It is the actual pitch distance between each note which is the interval. In the image above, for example, we have two notes, a C and an E. The pitch distance between the two notes (C and E) is the interval.

All tonal music – like the new Bowie album that so many are falling in love with – is simply made up of intervals between multiple notes. At the end of the day, everything comes back to the interval.

The interval is the unit of harmony.

Interval Unit of Harmony

Harmony from Simultaneously Played Notes vs. Notes Played over Time

A very important concept is coming up at this point.

The mind has an incredible ability to remember notes over the short-term. (It also has an amazing long-term memory as well, but that topic is for another post.)

Because of this amazing short-term memory for notes, harmony can be created over time.

What do I mean?

First, let’s look at an example of what I am NOT talking about. This is an example of harmony being created by simultaneously played notes. Have a listen to this song you may have heard before:

This is a very short excerpt of the piano part from “Hey Jude” by The Beatles.

Intervals F Major C Major

In between each simultaneously played note in the chord is a certain distance, which is the interval.

Listen to each chord played on the piano. The first chord is F major, the next chord is C major, and so on. Listen to these first two chords carefully. With each of these chords, the notes that comprise these chords are generally being played at the same time. This makes it very obvious that they are part of the same chord, and a wonderful harmony results.

Going back to our two types of intervals above – which kind of intervals are we seeing here?

Answer: Harmonic intervals!

By the way, we have been throwing around this word chord – what does it mean? Well a chord is just two or more notes played at the same time. So simple.

But, playing a chord isn’t the only way to create intervals and thus create harmony.

Tiny Fiddle

Quick side note: a man playing a tiny violin

Remember how we talked about the mind’s amazing short-term memory for notes? Because of this amazing memory, harmony can also be created by notes played over time.

Very intriguing, right? Well, let’s listen to an example of that.

This is a short excerpt from the beautiful fiddle tune “Ashokan Farewell.”

Notice the type of intervals that are created by the fiddle as it plays each consecutive note. What kind of intervals are we hearing here?

Answer: Melodic intervals!

Melodic intervals take advantage of the mind’s ability to remember notes over time and create harmony out of them.

Melodic Intervals

Harmony is created in the mind of the listener with each consecutively played note. The wavy yellow lines represent the mind’s ability to remember these notes over time, even as they are no longer being played.

For example, during the first seven notes in the notation above, the fiddle is creating a harmony of a D major chord, as the melody is emphasizing the notes D, F♯, and A – which are the 3 notes in a D major triad (by the way, we are getting way ahead of ourselves – triads will be coming in a few lessons from now).

The melody then goes on to create a G major harmony, in the same way.

Even if the entire piece was a solo melody, with no harmony instruments, like a guitar, the listener would nevertheless get a good sense of the harmony of the song, just using the melodic intervals created by the fiddle.

The 12 Intervals

Just like we have 12 notes, there are 12 possible intervals that make up the songs we love so much!*

Imagine that. Everything from the Happy Birthday song to Flight of the Bumblebee boils down to 12 simple intervals.

So, on with it. Let’s learn them!

*We are not counting “perfect unison” or “perfect prime” as one of our possible 12 intervals, as defined here, since it is just two of the same note. Also, there are intervals that go beyond the octave as well, but we will consider those to be an octave + one of our 12 fundamental intervals (sometimes called “Compound intervals”)

The IntervalsAll interval audio examples below were created by me in Pro Tools, a Digital Audio Workstation (a.k.a. DAW)


Minor 2nd (aka Half Step)

Here we have the minor 2nd, A.K.A. the half step or semitone. In this example, the notes are C and C♯/D♭. The notes are exactly a half step apart (one note away on the piano). This is a very dissonant interval.


Major 2nd (aka Whole Step)

Here is a major 2nd, which is also called a whole tone or a whole step. This interval is two half steps apart. Our example notes are C and D.


Minor 3rd

The minor 3rd – a very minor sounding interval. This is comprised of three half steps (C to C♯/D♭, C♯/D♭ to D, and D to E♭). The example notes here are C and E♭.


Major 3rd

The major 3rd – a very major sounding interval. Sometimes a major 3rd is said to be “happy” sounding. Comprised of four half steps. The notes here are C to E.


Perfect 4th

Perfect fourth is made up of five half steps. This interval is the same distance down from the 1st scale degree* as the Perfect 5th is up from it. It is comprised of five half steps. The notes here are C and F.

*What is a scale-degree? We will cover this in next week’s post about scales.


Tritone

The tritone is sometimes called the devil’s note, or “diabolus in musica.” It is exactly half way between the 1st scale degree (for example, a C) and the octave (a higher or lower C) – Six semitones (half steps) up and six down. It is said to be an evil sounding interval. Notes here are C and F♯/G♭.


Perfect 5th

The perfect 5th spans seven semitones and is the most stable* interval other than the octave/perfect unison.  As we get further in the series, you will see that this interval is very important in harmony. Notes here are C to G.

*We will explore what this means in a future post


Minor 6th

The 6th intervals, both minor and major, are my favorite intervals! And yes, it is possible to have favorite intervals. (OK, OK…. I am admittedly a music theory geek, in fact you can follow me on twitter at @musictheorygeek!) This interval is eight half steps. Notes here are C and G♯/A♭


Major 6th

My other favorite interval. This interval is nine half steps. Notes are C and A.


Minor 7th

We’re almost done! The Minor seventh is 10 half steps. This interval is important for seventh chords in rock music, folk music and other genres as well. Notes are C and A♯/B♭.


Major 7th

The major 7th is 11 half steps, or one half step down from the octave. Our notes here are C and B.


Perfect Octave

We’ve circled back around and reached the end. The perfect octave is comprised of 12 half steps. Both notes are exactly the same note, just an octave apart. This interval is important for building compound intervals (like 9ths), which are common in jazz music, for example.


Untitled design (7)
Identifying an Interval

We will finish up our lesson today by discussing how to identify an interval. Let’s say you have a C and an E. You count up from C to D to E – 3 steps, so we know we that it’s some kind of third.

Along those same lines, a C to F will always be some kind of 4th, a C to G some kind of 5th, a C to A some kind of 6th, and so on.

Going back to our C and E, we know it is some kind of third. Whether it is a minor 3rd (4 half-steps) or a major 3rd (5 half-steps) depends on the precise nature of that E, whether it is an E-natural (no sharps or flats), or an E♭, etc. The iron clad way to accomplish this last step and identify the interval is to count the number of half steps and compare it to the chart listed above.

Conclusion

And that concludes our first installment in the Music Theory Fundamentals series, which was all about intervals.

Click here to read part 2 in this series, on the topic of music notation.

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16 Comments

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  • Good introductory article on intervals.

    Have you noticed though that intervals are always taught from the lower note to higher?

    I think this is a major failing in most ear training. I find it hard to hear interval drops, e.g. root to flat 6 – this is because I have not done enough ear training to hear interval drops.

    • David,

      Glad you enjoyed the article.

      That is an excellent point you bring up. I love that idea. If you think about your typical melody, I would think there must be as many “dropping” intervals as there are intervals going up, right? So it would only make sense to train those as well.

      Thanks for contributing this original and valuable idea to the discussion.

  • Thanks Eric,
    Really enjoyed this article. It’s so fascinating how certain intervals cause certain associations in you (sad, happy, evil, etc), it’s actually pretty magical because there is no logical explanation.

    • Jaanis-
      Glad you enjoyed the article.
      I agree, sometimes I listen to a song with a certain chord progression or melody and there is that feeling you get….. We can analyze it from a music theory perspective, but at the end of the day, sometimes it feels like there is just no logical explanation.

  • So, I came here looking for a way to analyze a pop song for an introductory music class at the college level. You certainly write in a manner that I can understand but I don’t know if I’ll make it through all your lessons in time to finish the assignment on time. I need to write 250 words on instruments/voices used, the function of pitch, dynamics, harmony, melody, texture, as well as the form/structure of the song. Unfortunately, I’m in an online class so hearing these ideas is not happening though I reckon it should occur as supplements? However, I will return so, thanks, for making this blog. I am sure it’s going to help!

    • Daniel,
      Glad you liked the article.
      I don’t know exactly when the next installment of the Fundamentals Series will be coming out, but likely in the next couple months. They take many hours of research, writing and editing to prepare! Thanks for your comment.

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