Intervals and Basic Triads

In this post we'll learn about intervals and start building sounds with three-note chords. We'll also get into roman numeral analysis so that you can see how to use chords in a variety of ways.

What is an Interval?

An interval is the distance from one note to another note. The twelve-tone system uses the notes A, A#, B, C, C#, D, D#, E, F, F#, G, and G# ascending (or A, Ab, G, Gb, F, E, Eb, D, Db, C, B, and Bb descending). When we talk about the distance from any of these notes to the next one in either direction, we describe them in “steps” in western cultures and “tones” in eastern cultures. They’re the exact same thing. What you need to know is that the distance from A to A# is a half-step or semi-tone and the distance from A to B is a whole step or tone. I’ll discuss topics using steps, so if you are used to tones then just know that they are the same thing as steps.

When we talk about scales, we are usually using half-steps and whole steps. There are some scales out there that use one and a half-step intervals, which are also known as a minor third. We’ll discuss the minor third soon, but for now let’s focus on the C major scale, half-steps, whole steps and just flat notes to keep things simple.

Major Scale Intervals

The C major scale starts on the note C and is constructed using the follow intervals, which will be listed as “h” half-step and “W” for whole step: W, W, h, W, W, W, h. A simple way to remember this is 2 & ½ and 3 & 1/3. This pattern repeats itself over and over. Let’s use this to find our notes of the C major scale. Starting at C, all the notes are C, Db, D, Eb, E, F, Gb, G, Ab, A, Bb, and B. Applying our formula of W, W, h, W, W, W, h we get C, D, E, F, G, A, and B. Notice how we have skipped all the flat notes. This is because the C major scale is the only scale to have no sharps or flats, which makes it easier to understand intervals of other scales.

The way we understand other scales through the major scale is by intervals. Let’s look at C major scale’s note again: C, D, E, F, G, A, and B. If we think of these notes as numbered degrees of the scale then we would have 1, 2, 3, 4, 5, 6, and 7. The intervals from 1 to any of these other degrees have names, which are:

1 to 1: Unison

1 to 2: Major Second

1 to 3: Major Third

1 to 4: Perfect Fourth

1 to 5: Perfect Fifth

1 to 6: Major Sixth

1 to 7: Major Seventh

There are also interval names that use the altered notes relative to the C major scale, which are notes that are sharpened or flattened. Starting at C we would have Db, Eb, Gb, Ab, and Bb as our altered notes and would have the numbered degrees of b2, b3, b5, b6, and b7. These intervals are names as follows:

1 to b2: Minor Second

1 to b3: Minor Third

1 to b4: Diminished Fourth

1 to b5: Diminished Fifth

1 to b6: Minor Sixth

1 to b7: Dominant Seventh

Basic Interval Functions

Notice how all the intervals have specific names. Each one helps you to understand the function of that interval. To better understand this, let’s build some basic triads. Starting with one note we simply skip notes until we have a chord made of three notes since a three-note chord is a triad. Begin with C, skip D, use E, skip F, and use G. C – E – G is the C major chord. Now look at the distance from C to E. That is a major third: it goes from the first degree of the scale to the third degree of the scale.

Continuing with E to G we get a minor third. This is because if we start at E as our first degree, we have E as 1, F is b2, Gb is 2, and G is b3. This means that the C major chord is a major third interval followed by a minor third interval. You can use this formula of a major third followed by a minor third to create all major chords. Let’s try it with the F major and G major chords: F – A – C and G – B – D. The first interval for these chords is a major third and the second intervals is a minor third.

But what about our minor chords? Starting with the Dm (or D minor) chord we have the notes D – F – A. The interval from D to F is a minor third and interval from F to A is a major third. This is the opposite order of intervals found in a major chord, but both chords have some similarities. Both chord types start on the root note as all chords do and their intervals both add up to a perfect fifth. This is one of the many reasons why a fifth is perfect. Since it works so well with so many major or minor chords it can be thought of as perfect in its use. The difference is the degree of b3 or 3.

So far, we have only used minor thirds & major thirds and added them together to create perfect fifths. Only three of the of the thirteen intervals mentioned above are needed to create the sound of major and minor chords. There are plenty of other chord structures that we can create with these intervals with each having their own flavors of sound. For now, let’s continue to build chords in thirds.

A Pattern of Thirds

The major and minor thirds are intervals that give you the quality of your chord. The quality being whether a chord is major or minor as the first interval used in a chord structure. What is even more important is how the quality of a chord sets up the notes in a pattern. The pattern is a major third followed by a minor third over and over. However, if you start on a minor third followed by a major third then you have the same pattern, but you start one step in compared to the major pattern.

So, let’s use this pattern on a C major chord structure, which will be major third follow by a minor third repeated, and see what happens as we add intervals.

C: 1, 3, 5 – C, E, G

CMaj7: 1, 3, 5, 7 – C, E, G, B

CMaj9: 1, 3, 5, 7, 9 – C, E, G, B, D

CMaj#11: 1, 3, 5, 7, 9 – C, E, G, B, D, F#

Now let’s use the pattern starting with a D minor chord.

Dm: 1, b3, 5 – D, F, A

Dm7: 1, b3, 5, b7 – D, F, A, C

Dm9: 1, b3, 5, b7, 9 – D, F, A, C, E

Dm11: 1, b3, 5, b7, 9, 11 – D, F, A, C, E, G

Dm13: 1, b3, 5, b7, 9, 11, 13 – D, F, A, C, E, G, B

Using these chord structures that are built in thirds are just the same basic triads built on top of themselves. Notice how the CMaj#11 uses an F# as the last note. It does not match the major scale. Instead, it uses the Lydian scale, which can be though of as the major scale with a sharpened fourth degree. Because this even numbered interval is in the next octave (meaning that we started at C, passed C, and are in the next set of notes), we keep counting as if the second octave’s C is the eighth degree.

This can be a bit advanced for people who are just learning music and I don’t want to oversimplify this. Instead, think of this pattern as the backbone structure of all major or minor chords. If you need a visual example, then check out the image below, which has the C major chords using the blue intervals and the D minor chords using the red intervals. We can modify that structure and come up with all kinds of unique sounds. As you play chords with more than three notes, try to look for breaks in the pattern. Those breaks can cause tension that can be released by going back to this pattern of stacking thirds. It’s up to you to decide when to break the pattern and why it should be restored.

Diminished Chords

There seems to be a lot of disputes as to how many diminished chords there are. These differences in count come from where someone learns about diminished from. I like to use any version of what a diminished chord is if it makes sense and functions in a specific way. With that said, there are three diminished chords. Hopefully that doesn’t strike nerve with anyone.

The first is the diminished triad. This is two minor intervals stacked on top of each other. In the C major scale, we have B diminished (written as B°), which is B – D – F or 1 - b3 - b5. We also have B half-diminished (written as Bø), which is B – D – F – A, or 1 – b3 – b5 – b7. The half-diminished chord can also be written as m7b5 because we took the m7 structure of stacked thirds (1 – b3 – 5 – b7) and modified the fifth degree to be a diminished fifth. It is named so because it breaks the pattern of using only minor third intervals. If we did use only minor third intervals starting at B, then we could use a fully diminished chord (written as B°7). This would use the notes B – D – F – Ab, or 1 – b3 – b5 – bb7.

You’re probably wondering what in the world a bb7 is. It’s the b7 that is flattened again and happens to be the sixth degree as well. We call it a bb7 and not 6 because we are once again modifying the m7 structure. This time we have flattened the fifth degree and “double flattened” the seventh degree. Ab does not belong to the C major scale, but we can still use a fully diminished chord as a borrowed chord. I’ll discuss much more on diminished chords and borrowed structures in another post since there is a lot to talk about.

The reason why I say there are three diminished chords is because while the half diminished chord and fully diminished chords have unique notes, the diminished triad does not have a b7 or bb7. Because of this you could think of the triad as potentially being half or fully diminished. It would be like playing a major chord and not the 7 or b7. This allows the major chord to be either version until you pick one. Once a 7, b7, or bb7 is used your listener will hear the triad version as something that belongs to the four note structure used.

Try playing these three progressions. They all work on their own, but once you use the half or fully diminished chord you commit to that b7 or bb7. Only the diminished triad lets you be ambiguous so your listener is fine with hearing the half or fully diminished chord later on in a song.

Progression 1: Dm, G7, B°, C. (Does not use the note A or Ab in B°.)

Progression 2: Dm, G7, Bø, C. (Uses the note A in Bø.)

Progression 3: Dm, G7, B°7, C. (Uses the note Ab in B°7.)

Augmented Chords

The augmented chord is the opposite of the diminished chord. It is a major third followed by a major third and is written with a plus next to it. The C Major scale does not have an augmented chord in it because it is impossible to build such a chord with the third intervals that are available. You would have to use a scale like melodic minor or harmonic major, which we’ll get to another time so that we are just talking about the major scale for now.

The other unique part of these chords is that they have three notes and can only have three notes. For C+ you must have two major intervals, so that’s three notes used: C – E – G#. If we go a major third up from G# we will land on C. This means that an augmented chord is already complete. The only thing we could do is modify it with something like a major seventh interval. C+Maj7, or CMa7 #5, would be C – E – G# - B, or 1 – 3 - #5 – 7. Yes, the #5 is the same note as the b6, but since we modified a Maj7 structure of 1 – 3 – 5 – 7, we sharpen the fifth degree rather than use a flattened sixth degree.

Augmented chords can be hard to use if they’re a new concept to you. I’ll have another post for this chord structure. While you are using the C major scale try these two progressions and see if they work for you. The idea here is that the root note is moving down through the three chords. Both work in the C major scale because the first and third chords are part of the scale.

Progression 1: Am, Ab+, G.

Progression 2: Dm, Db+, C.

Roman Numeral Analysis

When we are using basic triads in a scale, we can reference them by number. There is a concept known as the Nashville Numbering System, which is essentially the same thing as using roman numerals to count the degree of a scale your triad starts on. I’ve seen both ways used and prefer to use roman numerals in practice so that I can work with people who use either method.

The way this works is the major & augment chords get upper case letters and minor & diminished chords get lower case letters. That’s it. Now let’s write out the chords of the C major scale and see how this is helpful when we start looking at other scales. C major scale is:

I, ii, iii, IV, V, vi, vii° or C, Dm, Em, F, G, Am, B°.

If someone says they are playing a 2-5-1 progression, then they are playing ii, V, I or Dm, G, C. If I’m told to play a plagal cadence, then I will play IV, I or F, C. If I’m then told to try a minor plagal cadence, then I know to use a minor four chord and play iv, I or Fm, C. There’s a lot of use to this because you can use this to describe parts of a song.

Consider a song that goes Am, Dm, G, C three times and then Em, G, G7, C once before repeating. You could write this as vi, ii, V, I for the first part and then iii, V, V7, I to notate that one of the chords is a dominant seventh form.

Another great use is in comparing two scales. Let’s look at A Aeolian. This is A, B, C, D, E, F and G so it uses the same notes as the C major scale. It just starts on A rather than C. To be honest, I picked A Aeolian because it is a mode of the C major scale and will make this easier to understand.

Because we are using the same notes and pattern of intervals, we have the same chords as well. The difference is starting on A. This gives us the degrees 1, 2, b3, 4, 5, b6 and b7. Notice how three degrees of the scale are flattened. Now we can write out the chords of A Aeolian as this:

i, ii°, bIII, iv, v, bVI, bVII or Am, B°, C, Dm, Em, F, G.

Notice how the roman numerals represent the degrees that each chord starts on as well as the quality of the chord and its form. You get all the information you need from the roman numerals as long as you know what the first note is. Now let’s try this out with C Aeolian. We still have 1, 2, b3, 4, 5, b6 and b7 as our degrees. That’s what Aeolian is. We’ll just start on C. I’ll notate C major scale as well and call it Ionian since that is the mode of the major scale we are using.

C Ionian: I, ii, iii, IV, V, vi, vii° or C, Dm, Em, F, G, Am, B°.

C Aeolian: i, ii°, bIII, iv, v, bVI, bVII or Cm, D°, Eb, Fm, Gm, Ab, Bb.

Our first look at these two modes is that they are very different. And that’s the point. By using roman numerals, we can see that we have different chords and some differences in degrees. If you try to play C Aeolian the same way as C Ionian, then you’ll be in for a treat. Or a shock. That may depend on your point of view. What I want to show you is that people use different modes or the same scale (or set of chords) to create new flavors of sound. This sounds can in turn be described as roman numerals.

Now you might be thinking that you need to know every scale to understand this. You don’t. You just need to know what your triads sound like and what your intervals can do for you. Let’s use that idea to build a song. Let’s use C Ionian and start with a |vi |ii |V |I |progression using the vertical lines to separate measures of our song. We’ll play that a few times and then play |iii |iii |IV |I |. Sounds good, but it needs some spicing up. Let’s add some tension with our dominant and diminished chords and play |vi |ii |V7 vii° |I |. Now let’s add some mood to our second progression. This time we’ll borrow the minor four chord from C Aeolian and play |iii |iii |IV iv |I|.

So far, our song’s measures use the format of one chord, one chord, two chord, one chord for both parts. To keep our song from sounding too repetitive, let’s work on the second progression some more. First let’s drop the second iii chord and use a ii. Then let’s add our dominant chord just before we finish. Now our second progression is |iii |ii |IV iv |V7 I |.

Here’s the whole song in the keys of C and G, but with only one set of roman numerals. Try it out and try out your own variation. Be sure to listen to the sounds that your intervals make within each chord as well as the way moving through a progression feels.

|vi |ii |V |I |

|vi |ii |V |I |

|vi |ii |V |I |

|iii |ii |IV iv |V7 I |

Key of C: C, D, E, F, G, A, B.

|Am |Dm |G |C |

|Am |Dm |G |C |

|Am |Dm |G |C |

|Em |Dm |F Fm |G7 C |

Key of G: G, A, B, C, D, E, F#.

|Em |Am |D |G |

|Em |Am |D |G |

|Em |Am |D |G |

|Bm |Am |C Cm |D7 G |