Major and Minor Triads, Sevenths, Ninths and More…

This article was originally published back in 2014. As with other well-read posts on this site, I’m trying to revisit some to tidy up some of the writing and audio and generally make them a little more professional.

This article is part of a wider series on music theory fundamentals, so there will be some gaps in knowledge here if you don’t read the whole series, but this is part 1 on harmony. I want to cover four topics in this article:

• How to figure out major and minor chords
• How to figure out the chords related to a scale
• How inversions work
• How to go beyond triads

I feel the need to caveat this by saying this is by no means a “this is how you should write music” post, or anything instructive about how harmony should be understood, heard or used – it’s merely a recap for students who are taking music theory classes or anyone who wants to understand more about chords and use them in your own music. Today we’re just looking at diatonic harmony. I have written extensively about non functional harmony including jazz and contemporary music elsewhere on this blog. If that’s something that interests you but you’re unfamiliar, this is a great primer.

Western music has keys and scales that broadly govern how we organise our sounds. Without delving too far into the Harmonic series or Equal temperament there are chiefly a finite number of chords that will work ‘well’ together, both sounding ‘pleasing’ and working on deep mathematical levels. I’m adding quitting marks because this article is being both written and assumed to be read through Eurocentric western ears, I understand harmony is subjective and different sounds, scales, modes, tetrachords, inflections and articulations can sound different to different ears depending on cultural exposure. Hopefully that is enough of the caveats out of the way. Let’s get started.

Basics

We are going to need four intervals to follow along with this article. All these intervals are measured in semitones, the smallest discrete pitch leap on a keyboard or guitar. This is the space between a note and the note directly adjacent to it, regardless of weather or not it’s black or white. With intervals it’s important to remember to count from zero:

• Semitone – one discrete step
• Minor third – three semitones from the root
• Major third – four semitones from the root
• Perfect fifth –  seven semitones from the root
• Octave – twelve semitones from the root

Below we see a keyboard displaying two octaves. An octave is twelve semitones and we could count 25 notes here (two octave is 24 notes plus the beginning of the next octave). We’re going to focus all of our chords around C for simplicity.

The white notes on the keyboard are simple enough: the notes A through to G and then they restart again. This image is cropped with C as the lowest note, but the principle is the same.

The black notes can either be thought about as relative to the note above or below. For example the black note between C and D can be C# or Db depending on context. For today I’m going to dive too deep into this context, but a general rule of thumb is within a scale you don’t tend to mix sharps and flats. Additionally each diatonic scale contains the notes A through G, with some either sharp or flat. For example, you wouldn’t have both D and D#, because there would be no “E”.

Tertian Chords, Major and Minor

There are many different types of chords, but two of the most common are major and minor chords. These chords, along with some others we’ll look at further down the article, can be constructed with just thirds. Let’s look at C major and C minor.

Major chord

To build a major chord we start with our root, go up a major third and then up a minor third. Major chords are just written with a capital letter, so C major wold be written as “C” on a chord chart.

Minor Chord

To build a minor chord we start with our root, go up a minor third and then up a major third. Minor chords are typically written with a lowercase “m” after the chord root, so C minor would be written as “Cm”. Sometimes on jazz chord charts you might see a minus symbol “C-“.

Hopefully you should be able to recognise that aside form sharing a root note, these chords also share the top note of the chord; G. This G is a perfect fifth away from he root. In-fact, the note determining the quality of this chord is the middle note, which confusingly you might see referred to as “the third” (more on this later).

Diatonic Chords – How Chords fit in a Scale

Once we know conceptually what major and minor chords are, how can we fit this into a wider understanding of working with scale? For this article we are only going to look at the major scale and we’re going to stick with C. First let’s write our scale out:

C D E F G A B C

It’s useful to mentally number each scale degree 1 to 7 (some people use roman numerals for this). As you can see there are 7 unique notes in the scale, and we can build a chord on each scale degree. Next write the scale out in two octave. Our first chord is build from scale degree 1, C in our case. Then, skip the next adjacent scale degree (D) and take the E, from the E skip the F and take the G, that gives us our first chord.

Using this method (I’ve always called it the “leapfrogging method”) move to scale degree 2 and do the same thing, (D, F, A) and so on. Once you’ve done it for each scale degree you will have 7 chords. Some of these chords are major (1, 4 and 5) some are minor (2, 3 and 6) and chord 7 is diminished. This is like a minor chord only with a flattened 5th degree. Normally we denote this with a º or ø symbol (more on these later).

You can do this with any major scale and the pattern of chords is always the same: major, minor, minor, major, major, minor, diminished. This isn’t to say you can’t use a major chord 2 or chord 5 can’t be minor – this is just the guideline of how these chords appear naturally in this scale.

Inversions

Let’s say with C major for a moment. Inversion are play a chord with the notes in a different order. There are numerous reasons you might use an inversion; as a pianist inversions make it simpler to move between chords in a progression, harmonise a melody or keep the harmony moving while hanging on a chord.

Let’s start with C major in root position. This is as we learnt it above, with C as the lowest note of the chord, followed by E and then G.

If we transpose that C up an octave, so the chord reads E, G, C, we have C 1st inversion. This is generally understood to sound more unstable than root position – by that it is generally used to transition. This is absolutely not a robust rule, it’s just an observation.

Lastly if wet then also move the E up an octave so the chord reads G C E we have 2nd inversion. In terms of stability this sits somewhere between root position and 1st inversion. Compare all three audio clips of these inversions to see if you can hear a difference.

Inversion can be applied to any chord type, not just majors, so familiarise yourself with inversion of minor chords as well as whatever other voicings you are learning/writing with.

Going beyond Triads

If we continue our leapfrogging method of skipping adjacent scale steps we can get some richer, more colourful chord voicings. Adding the 7th note of the relative scale to each chord is normally the first step.

• For chord 1 and 4 we get a major 7 chord. This is as major chord with a major 7th interval on top (11 semitones from root). Sometimes on chord charts you’ll see maj7 or the greek “delta” ∆7 used to denote this chord voicing.
• For chord 5 we get a dominant 7 chord, which is just abbreviated to “7”. This is a major chord with a minor 7th interval on top (10 semitones above the root).
• Chords 2, 3 and 6 are minor and we add a minor 7th on top giving us a minor 7 chord.
• Lastly our diminished chord also has a minor 7 on top. When we have a diminished triad with a minor 7 on top we get what’s called a diminished chord. This can also be called minor 7 flat 5 or have the ø symbol used.

Diminished and Augmented

When we built chords using thirds there were two chord voicings I omitted earlier on, diminished and augmented chords. These are like x and z in the alphabet, uncommon but they certainly have their usage. They tend to appear more in minor key compositions and they can appear in pop, jazz, blues, musical, theatre and classical music in equal proportion.

Diminished chords

To build a diminished chord we start with our root, go up a minor third and then up another minor third. Diminished triads are typically denoted with the degree symbol, so a C diminished triad would be Cº.

This gets complicated when we adds 7ths on top, as discussed above we get Cø7 when we add a minor 7th intervals on top of a diminished triad. There are such things as full diminished chords too, which is a series of stacked minor thirds (C Eb Gb Bbb (yes, double flat)), this would be written “Cº7”.

Functionally, diminished chords can be used as passing chords between two adjacent scale degrees (C, C#ø7, Dm), or they can be used in place of chord 5, as chord 7 or in a minor key chord 2 is diminished.

Augmented chords

To build an augmented chord we start with our root, go up a major third and then up another major third. Augmented chords are typically either denoted with “aug” or more commonly an plus symbol, so C augmented would be “C+”.

Augmented chords are typically used in place of chord 5 and are more customary in minor scale than major scale compositions.

9ths, 11ths and 13ths

We can continue our leapfrogging up another scale degree. You might wonder why we have 9ths, 11ths and 13th when there are only 7 notes in a scale. These are called compound intervals and they are greater than an octave. If you want to figure out what a 9th, 11th or 13th is terms of scale degree then just subtract 7. A 9th is scale degree 2, 11 is 4 and 13 is 6. The nomenclature might seem strange but the extensions are usually appearing one octave above the root so that’s why the names have stuck.

It’s normally a formality to keep the 7th as part of the chord when using these voicings too, so a Cmaj9 would be the same as Cmaj7 with an added 9th above the root (D). Dm9 would be the same as Dm7 with a 9th added above the D, and so on.

There are a few quirks here, firstly the Em7 and Bø7 chords have flat 9th degrees. This is because the respective 9th intervals in E minor and B minor would be outside of the key of C major. A 9th above E is F# and a 9th above B is C#, both outside of the key. Aside form that note that our G7 chord with an added 9th still retains the same naming convention as G7.

I wont exhaustively write out every 11th and 13th for the scale because many of these chords are impractical. Here are a few minor 11th chords. These voicings are verbatim certainly not how a pianist might play them, where the notes might be grouped in clusters or a series of stacked fourths or fifths, depending on the idiosyncrasies of the player.

Lastly there are some 13ths below, two major 13ths and one dominant 13th. Again these voicings might seem a bit clunky, you’ll need to find our own way of using these.