Welcome to the official tonebase guide to music theory!

This post will walk you through all of the basics of Western music theory so that you can better understand the repertoire you’re working on with your instrument, or so you can just understand a bit more about the music you enjoy.

I'm going to hand it over to our Head of Piano Ben Laude to introduce this course on music theory, which is available to all tonebase subscribers:

Where do we get our notes?

In order to understand music theory, you have to understand the notes that we use.

In western music, we use a system called equal temperament.

While on a piano it may look like we have lots of notes, we really only have 12.

This is because we derive our notes from dividing an octave into 12 equal parts.

So what’s an octave?

In scientific terms, an octave is one wavelength frequency/note, plus another note that is either 2x the wavelength frequency (for an octave higher) or ½ the wavelength frequency (for an octave lower).

This makes it sound like each note in the various octaves are the same note, just higher or lower.

Whole steps and half steps

Now when we take our 12 notes and put them next to each other, we get intervals.

The first interval to know is the half step.

Every note is 1 half step away from the next note, so C is one half step below C# and E is one half step below F.

However, in almost all of our scales we don’t just use half steps, but we use a lot of whole steps.

A whole step is the interval between a note, and another note 2 half steps up or down, so C is one whole step below D and B is one whole step below C#.

Here is an example of the C major scale with all of the whole and half steps indicated:

Ben Laude explains this well in this tonebase lesson on whole and half steps.

The major scale

When we put a bunch of whole and half steps together, we get a scale.

The most common scale you’ll encounter in music theory is the major scale, as it’s deeply embedded in every popular genre and most of the pieces you’ll play as a musician.

Thinking back to the C major scale above, here are a few other examples of different major scales (there are only 12, since each one starts on one of the 12 notes):

Notice how the whole/half step combinations are all the same?

This is the “DNA” of the major scale, this WWHWWWH string.

Other scales can be derived from incorporating different combinations of these intervals, which we will cover in a later section.

For now, be sure to check out this hour long deep-dive into the major scale for a better understanding of its purposes.

The fifth interval

Before we can talk about anything else, it’s important to understand the core interval behind all of our Western music: the fifth. 

In music theory terms, the fifth is just a note, plus the note 7 half steps above (so C and G, or D# and A#).

But the fifth is actually rooted deep in science, which we will attempt to very briefly explain here before we proceed:

The overtone series

I’m gonna tell you something that might seem crazy at first, but hopefully after some further reading it will start to make more sense.

Whenever you hear a note, or a pitched frequency, you’re actually hearing lots of notes at once, not just one note.

Check this out - When you play a C2 on the piano, or low C, here are all of the notes you’re actually hearing:

Pretty crazy right?

Well guess what, the first note you hear (or the most prominent of the “overtones”) is actually the fifth (plus and octave) above the note you played!

Check out the image above again, you’ll see the first note that isn’t C is G, which is a fifth above C.

Keep in mind that I’m just barely scratching the surface on the overtone series and the science behind frequencies, so if you’re interested feel free to pursue more independent research because there are lots of interesting things to discover.

Now that you have a general understanding of why the fifth is so important, let’s dive into the singular concept from which we derive almost all of our chords from: the circle of fifths.

The circle of fifths

Here’s another concept that might seem daunting at first but comes easy the more you spend time with it:

If you take a note, say C, then add a fifth above that, you get G, right? 

Now what happens if I keep adding fifths above the fifths, would it go on forever?

Well you would actually just cycle through all 12 notes until you got back to your starting note. Here’s an image of the circle of fifths:

Now I want you to consider that there is an inherent “distance” between the notes in the circle of fifths. You’ll see that F# is farther from D than G is from D.

This is where we derive all of our harmony in Western music from.

If I play a D major chord (we’ll get more into chords in a bit), then I play a G major chord, they will sound pretty connected. This is because they are close to each other on the circle of fifths.

Now if I play a D major chord, and an Ab major chord, they are going to sound quite odd next to each other. This is because they are far apart from each other on the circle of fifths.

But there is something deeper behind all of this, and that is our concept of harmonic tension and resolution. If there is one “most important” concept from this entire post I would argue it’s this one.

The “five-one”

Listen to this chord progression, and I want you to pay close attention to the last 2 chords.

The 2 chords at the end are referred to as a cadence, and this cadence in particular is an “authentic cadence”, otherwise known as a five-one. The V-I (we always use roman numerals for chords in music theory) is the core harmonic function behind all Western music.

In the chord progression above, The “V” is the G chord, and the “I” is the C chord, which if you remember are a fifth apart.

All chords have an inherent musical “gravity”, where they always want to resolve to the “one” (I) chord. And the single chord that tips that resolution is the five (V) chord.

Click here to watch Ben Laude’s tonebase lesson on the circle of fifths to get a better understanding of this concept, as well as the whole V-I concept.

Now, let’s keep this whole concept of the circle of fifths in the back of our head as we talk more about intervals.

Intervals, continued

So far we’ve discussed 3 intervals: the half step, the whole step, and the fifth.

Well as one can assume, you can create an interval out of any combination of two notes.

Going back to the circle of fifths, we can see intervals between all notes:

You can see that we define an interval as the distance from one note to another note.

Inverting intervals

What if we, assuming we’re going the same direction, swap the order of the notes?

Well, any interval is the difference between the full octave and its inversion.

So octave = interval 1 (ex. Major 3rd) - interval 2 (minor 6th)

Here is a notated example of how these inversions play out:

As you can see, the inversion of the interval stays within the octave.

Check out this chart that sums up the inversions of our intervals:

Lastly, here are a list of all intervals defined by their relation to the note C:

Now what are intervals used for?

Well, aside from the fact that they exist in all music, we use intervals to craft melodies.

Take this familiar melody:

You can see how a clever combination of different intervals lends itself to a pleasant melody.

Click here for the associated tonebase lesson if you want more clarification on this topic.

What are chords?

Think back to when we discussed how chords can be more “distant” from each other due to their place on the circle of fifths.

Basic chords, or triads as they’re referred to, have a basic structure:

They’re made of 3 notes, and each note is separated by the interval of a third.

Now thinking back to the section on intervals, we can remember that there are different types of thirds.

Similar to how we can find new scales by putting together different combinations of step-based intervals (whole and half), we can find new chords by putting together different combinations of thirds.

Here is the C major triad, the C minor triad, the C diminished triad, and the C augmented triad back to back:

You’ll see that each chord has a unique combination, or “DNA”, of stacked intervals that give it its defining harmonic characteristics.

I recommend spending time familiarizing yourself with these 4 chords, as they are the most common basic chords you will see in any music you encounter. Click here to check out Ben Laude’s music theory lesson on triads and 7th chords.

On the subject of 7th chords, what are they?

Well so far we’ve seen chords with 3 notes, each separated by the third interval. Let’s see what happens when we add a fourth note, also separated by a third:

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These chords are 7th chords, because they include the “7th” interval relative to the root. They’re quite colorful and show up in lots of music after the 19th century, sometimes even before then. Jazz had a huge impact on the popularity of these sounds and helped propel them into mainstream music across all genres.

Inverting chords

Earlier we inverted intervals, what if we change the order of notes in a chord?

This is what musicians refer to simply as inversions.

Inverting common triads and 7th chords reveals some very interesting musical characteristics, and can be used in a composition to play with tension and resolution.

Here is a notated example of a C major 7 chord in its 4 inversions:

Minor and other modes

Congratulations for making it this far in our music theory guide, this isn’t easy stuff!

Earlier we looked at the major scale, now let’s look at the minor scale and another important concept to help you understand the architecture of scales: modes.

Here is the “natural” C minor scale, with its “DNA” of intervals: 

Now, when we refer to something being “in C minor”, this is the scale we’re referring to:

We use the harmonic minor scale to create “minor keys” because with the raised 7th, or the B natural in C minor (revisit the scale above), we can create a major V chord with the notes, giving us a nice V-I resolution.

Let’s go back to natural minor for a second.

Here is the C natural minor scale:

And here is the Eb major scale:

Notice something similar?

They both have all of the same notes!

C natural minor is basically Eb major just starting on C.

Now what if you take any major scale, say C major, and start on different notes of the scale?

These new scales that result from this are called modes.

From the major scale, we have 7 modes, each corresponding to each of the 7 notes in the scale: Ionian (this is just a fancy way to say major), dorian, phrygian, lydian, mixolydian, aeolian (also a fancy way to say natural minor) and locrian.

There you go, that’s an overview of modes for you.

Conclusion

So far we’ve learned about our notes, intervals, chords, inversions, the circle of fifths, V-I progressions, and more.

Congrats on making it to the end of our complete music theory overview! Feel free to revisit sections as you need to refresh on concepts.

If you’re looking for any further instruction on these topics, refer to the tonebase lessons listed at the end of each section where you can watch them for free.

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