[This post is the third in a series on Introductory Music Theory. The series begins with A Musical Theory. The previous post in this series is Stepping Into Numbers.]

The interval of an octave is a pretty amazing thing. When we sing the Do-Re-Mi scale it seems perfectly reasonable that the eighth note is called “Do” again because, as one could say, “it sounds just like the first Do only higher”. (By the way, if an octave doesn’t sound this way to you, it’s may be time to consider poetry or painting as your artistic endeavor instead of music.) Of course you can sing Do-Re-Mi past the second Do, ever higher to the third Do, and as you do so each successive note is exactly an octave above the earlier one of the same name. So Mi to Mi (3 to 10) is called an octave just like Do to Do (1 to 8). As I mentioned in the last post, all of the interval names – 2nd, 3rd 4th, 5th, etc, refer to a specific number of half-steps no matter what the starting point is. The interval of a 2nd gets its name from the distance between 1 and 2 on the Major scale (1 step). Since the interval from 6 to 7 is also 1 step, we can also call it a 2nd.

Now let’s consider the interval from 2 to 4 (Re to Fa). From the definition of the Major scale we know that this distance is a whole step (2 to 3) followed by a half-step (3 to 4), or 1½ steps. This distance is a half-step larger than a 2nd, and also a half-step smaller than a 3rd. In other words if I started at Do and sang or played the note that is 1½ steps higher, I would end up at the note that is in-between Re and Mi! So one might want to call this interval a “2nd and a half” or a “third minus a half”. As it turns out this interval does have two names and they sound a bit like that. The 1½ step interval is called either an “augmented 2nd”, or, a “minor 3rd”.

We want to make sure that there is no confusion between a minor 3rd (1½ steps) and a “regular” 3rd (2 steps). In fact, the “regular” third we first learned about has a more complete name that can be used to avoid any ambiguity; it is properly called a Major 3rd. This makes sense because a Major 3rd is the kind of third that occurs between 1 and 3 on the Major scale. If we refer to a 3rd without any qualifier (no “first name”, so to speak) we can usually safely assume that we mean a Major 3rd. A minor 3rd always carries the qualifier “minor” with it.

Each of the intervals that we first learned about (from the Major Scale) have a proper “full name”. These names are Major 2nd, Major 3rd, Perfect 4th, Perfect 5th, Major 6th, and Major 7th. We will discuss why the 4th and 5th are called Perfect instead of Major in a future post. (We should also note that the unison and octave intervals are also considered perfect, but in practice they are never described with the qualifier on their name.)

It is clear that when we play the Major Scale, we skip over a lot of notes (such as the note that is halfway between Re and Mi). The intervals from Do to each of these “in-between” notes usually have two names depending on whether we think of them as the next larger interval minus a little or as the next smaller interval plus a little. The table below shows the names of all of the intervals to the 13th from the Major scale as well as the names of the intervals of all neighboring “in-between” notes.

In the above table terms that are optional are in parenthesis. Terms in lighter typeface are less commonly heard.

It may seem confusing that there can be more than one name for the same interval, but it turns out that there are often good reasons to choose one name over the other depending on the situation. We’ll pursue this idea further in an upcoming post. You may also notice that the table contains some syllable names that may be unfamiliar to you. These exist simply to allow someone to sing a unique syllable for any note even if it is not on the major scale. As with the intervals, positions not on the major scale tend to have two syllable names.

Using the table above we can figure out the name of the interval between any two notes on the Major scale. For example if we want to know the name of the interval that goes from Re to Do (2 to 8), we can count the steps between these notes and find that it is 5 steps. Then from the table we can see that the 5-step interval is called a minor 7th.

All the different interval names may seem a bit confusing at first. However, the rules for understanding the size of an interval based on its name are fairly straightforward and should be committed to memory. First, as we learned, the basic interval names come from the distance from Do (or 1) on the Major scale to any note on that scale. That gives us the intervals called unison, a 2nd, a 3rd, a 4th, a 5th, a 6th, a 7th, and an octave. To know the distance (in steps) that these interval names represent, one need only remember that the Major Scale is the progression of distances: whole, whole, half, whole, whole, whole, half. This progression of distances as numeric values is: 1, 1, ½, 1, 1, 1, ½. Remember that these are the distances between the notes, they are not a reference to the notes themselves. Let’s take it step by step (pun intended) going from the position 1 (Do) to the position 4 (Fa). We start at position 1 and to get to the second note of the scale we travel the first distance which is 1 step. To get to the third note we then travel 1 more (for a total of 2). To get to the fourth note we then travel ½ step further for a total distance of 2½ steps from Do. Therefore the interval called a 4th is 2½ steps. Remember that from our starting point we cross three distances to get to the fourth note. These distances where whole, whole, half, or 1 + 1 + ½, which is 2½ steps.

The next thing to remember is that these intervals from the Major scale are also known as, unison, a Major 2nd, a Major 3rd, a perfect 4th, a perfect 5th, a Major 6th, a Major 7th, and an octave. The shorthand for this is that unison and octave have no other name, the 4th and 5th are the only ones called “perfect”, and the rest are call “Major”. I’ve referred to the terms “Major” and “perfect” as the qualifier terms for the interval. Different qualifiers are used when the interval is from Do to one of the in-between notes that isn’t exactly on the Major scale. These other qualifiers are “augmented”, “diminished”, and “minor”. The qualifier “augmented” always means “½-step more than”. The qualifiers “diminished”, and “minor” always mean “½-step less than”. From this we can see that an augmented 4th is a 4th plus a half-step, or 3 steps.

Armed with this info you should be able to work out the size of any named interval. A minor 7th is a 7th minus a half step. From the progression of distances that make the Major Scale we can see that a 7th is 5½ steps and therefore a minor 7th is 5 steps. But what about the reverse process? If we have an interval of say, 4 steps, how do we figure out what to call it? That we will cover in the next post.