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Triad Inversions

The Basics

Intervals are the units by which music can be measured. You could say that intervals are to music what inches (or centimeters) are to carpentry. If a carpenter wants to know how “things” fit together, he needs to understand how to measure those “things”. If a musician wants to know how music is put together, that musician needs to understand intervals.

Intervals are defined by the Major scale. In other words, every aspect of music is compared to the major scale to see how “things line up”.

Simply put, an interval is the distance between two notes and the distances between the notes of the major scale provide us with a reference point.

Let’s look at the C major Scale:

C – D – E – F – G – A – B – C

The C note functions as the root or 1, and the rest of the notes are numbered 2 through 8. In other words, D = 2, E = 3, F = 4, G =5, A = 6, B = 7 and the octave C = 8. (This is where the name octave comes from. Octo = 8, as in octopus.)

Before we continue, you need to fully understand a couple of points about the major scale:

  1. The major scale is derived by following the whole-step half-step pattern: w – w – h – w – w – w – h. This w/h-step pattern is what “really” dictates where the intervals lit on the fingerboard.
  2. The major scale can start on any note of the chromatic scale. I’m only using the key of C as an example. Everything that applies to the C major scale applies to any and all other major scales.

If you are not clear on how major scales are built and how they cover the fretboard in every key, you need to check out the Major Scale before continuing with this lesson.

The major scale is the only musical element that has the intervals 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8. Everything else has a different interval structure. You see, intervals are just like notes in that they can be sharp or flat. For example, you will run into such things as b3, #5 and b7.

This numbering of the notes is called the FORMULA. Scales, chords, chord progressions, and even entire songs can analyzed by their underlying formula. All other musical structures can be learned on the guitar by understanding the formula ie., how that structure is different from the major scale.

Let’s take a look at the Harmonic Minor Scale. The harmonic minor scale, when compared to the major scale, has the intervals: 1 – 2 – b3 – 4 – 5 – b6 – 7 – 8. This means that the harmonic minor scale is exactly like the major scale except that the 3rd and 6th intervals are flattened (lowered by one fret).

C Major: C – D – E – F – G – A – B – C

C Harmonic Minor: C – D – Eb – F – G – Ab – B – C

Now, understand that the notes and the intervals are one and the same, but just because a note is sharp or flat, that doesn’t mean that the interval is sharp or flat and vice versa. You have to know the major scale absolutely well in order to understand how this interval stuff works.

Once and for all, the intervals are dictated by the major scale. Depending on what key the major scale is in, you will have sharp or flat notes in the scale.

Take the E major scale for example: E – F# – G# – A – B – C# – D# – E. In this case, E =1, F# = 2, G# = 3 etc… You have to know the notes that are already in the key before you can determine what the b3 (or any other interval) might be. In the key of E, the b3 would be G (3 = G#).

Intervals are the distance (how many frets) between the notes. If you put your index finger on any note on any string, and call that note the root (or 1), 2 will ALWAYS be a whole-step higher, no matter the name of the note you are playing. That is how intervals work. They follow the w/h-step pattern without exception.

So, the harmonic minor scale (1 – 2 – b3 – 4 – 5 – b6 – 7 – 8) starting on E would look like this:

E Major: E – F# – G# – A – B – C# – D# – E

E Harmonic Minor: E – F# – G – A – B – C – D# – E

Every aspect of music theory is discussed in terms of this interval formula. This is why I often say that the major scale is the single most important element of music theory – every thing else is compared to the major scale.

Now, for the sake of clarity, I usually just refer to intervals by number and throw in sharp or flat if it’s needed, but there is an old system for naming intervals that a lot of overly educated people insist on using. I figure I better go over this with you, so you won’t think I ripped you off or I don’t know what I am talking about.

If you haven’t already, you are bound to run into people saying things like minor 3rd, perfect 5th, and major 7th. The reason that I don’t use these names in conjunction with intervals is that these names are also used to name chords. Most people that I have taught just find it confusing. I say, “If there is a simpler way to understand something, why not use the simpler way?”

So here goes:

The 2nd, 3rd, 6th, and 7th are considered major intervals. If you lower (flat) a major interval it becomes minor. So 3 = major 3rd, and b3 = minor third etc… When this system was invented (back in the days when you had to wear a powdered wig if you wanted to be taken as a serious rock star), there was no such thing as sharping the 2, 3, 6 or 7. More on this in a moment.

The unison (playing the same note), 4th, 5th, and octave are considered perfect intervals. If you lower a perfect interval, it becomes diminished. So 5 = perfect 5th, and b5 = diminished 5th. If you raise (sharp) a perfect interval it becomes augmented. So 4 = perfect 4th, and #4 = augmented 4th. (I hope your getting all this.)

In more recent times, it has become necessary to account for raising (sharping) the major intervals. Rather than come up with a unique name for this, the powers that be decided to just call these intervals augmented as well. So, a person is stuck trying to remember which names fit which intervals and when to use a unique name for the interval as opposed to the same name…. “no…wait…don’t tell me… that must be the augmented 3rd from the perfect 5th…. or was that a diminished 5th?”

As far as I’m concerned, it’s much easier to call ’em by number and say sharp or flat.

The Fingerboard

Up and down the strings:

Major Scale

Harmonic Minor Scale

Across the strings:

Major Scale

Harmonic Minor Scale

The Practice

Learning intervals is just like learning the notes on the fingerboard. All it really takes is the willingness to stop yourself once in a while and ask a couple of questions. “What key am I in?” “What interval am I playing relative to the root note of the key?” Ask those questions a few times and you will start getting the hang of this stuff.

Here are a couple of exercises to work on:

Both exercises are based on the same idea: moving the 3rd interval through the scale. Notice that as you move the interval through the scale that sometimes the interval is normal and other times the interval is flat. Study this carefully, it is very important to understanding how chord progressions work.

Also, you need to work these exercises out in all possible positions on the fingerboard for all keys. Lots of work to do there 🙂

Then you need to do the same thing starting with each of the other possible intervals. Work them through the scale and pay close attention to the spots where the interval changes from normal to sharp or flat.

Have fun.

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