Lesson 10: Intervals

In Lesson 7, you learned how to name "small" intervals. These were intervals that occupied the space of a "second" - the semitone, whole tone, and the tone-plus-semitone. Now we are going to learn how to name intervals that are larger than a second.

In fact, the method we use to name larger intervals actually applies to all intervals, big or small. There are two components to the name of an interval:

The first component, in this case the letter 'P', tells us the quality of the interval. The 'P' stands for 'perfect', but more on that a little later. The second component , the number, tells us the distance between the two notes. The number is very easy to determine. Assigning a '1' to the bottom note and counting upward until reaching the top note, you can see that the 'D' is five notes higher than the 'G'. Therefore, the interval shown above is a 5th. So much for the easy part!

There are several different kinds, or qualities, of intervals. You have heard these terms before in conversation with musicians: major this, diminished that, etc. But how do we actually determine the quality of an interval?

For our purposes here, all intervals will fall into two main categories: the perfect ones, and the non-perfect ones. Let's look at the perfect intervals first. There are four intervals that can be described as being perfect: 1, 4, 5, and 8. For example, we might say "perfect fifth" in describing a certain kind of fifth. Intervals that are perfect have a certain sound that is variously described by musicians as "pure", "hollow" or "bare". The other intervals, 2, 3, 6, and 7, are non-perfect ones. They are the ones described as being major or minor. Depending on the number, these intervals will be described as either "harsh" (2 or 7) or "sweet" (3 or 6).

Back to the perfect ones. If an interval is determined to be a fifth, like the one above, we need to ask ourselves an important question in order to determine what kind of fifth the interval is: "Is the top note in the major scale of the bottom note?" If the answer is "yes", then the interval will be perfect - a "perfect fifth". If you examine the example above, the question you would ask is "Is the top note ('D') found in a 'G' major scale? You know from the previous scale lesson that the answer to that is "yes". Therefore, it is a perfect 5th.

But what if the answer was 'No"? What if instead of the above example, we had one of the following:

Would the number of the interval be the same? Absolutely, because the top note is still five notes above the bottom note. But are they still perfect intervals? Well, ask yourself the question, "Is there a D# in a G-major scale?" No. "Is there a Db in a G-major scale?" No. So they're not perfect - they're something different.

With the perfect intervals (1,4,5 or 8), there are three possibilities:

This diagram shows those three possibilities. If the answer to the question is "yes", then the interval is perfect; this is why there is a rectangle drawn around the word "perfect". If it is "too large" to be yes (such as is the case with the D#), then the answer would be "Augmented 5th". That's because D# is one semitone higher than 'D', and so we go to the next larger interval. If it is "too small" to be yes (such as is the case with the Db), then the answer would be "Diminished 5th". That's because Db is one semitone lower than 'D', and so we go to the next smaller interval. Easy!

Now consider the following interval:

What number would be placed under it? A '3', of course, because if you consider the bottom note to be '1', and then count upward until reaching the top note, the 'A' would be three notes higher. But what kind of '3'?

This interval is a third, and so we know that it is not going to be a perfect interval. It's going to be given a name like "major" or "minor, or something else. But you still have to ask the same question: "Is the top note ('A') in the major scale of the bottom note ('F')"? Checking your Scale Reference Sheet, you can see that the answer is "yes". But what does that mean?

With the non-perfect intervals (2,3,6 or 7), there are four possibilities:

Notice the rectangle drawn around the word "major". That is there to remind us that if the answer to the question "Is the top note ('A') in the major scale of the bottom note ('F')" is yes, then the interval is major. Indeed, the answer to the question is yes, so the interval is a major 3rd. We can show that by writing either '+3' or 'M3'. What if the interval were different - say, an 'F' on the bottom and an 'Ab' on the top. That would be one semitone smaller than a major 3rd - it would be a minor 3rd ('m3', or '-3'). Here, then, are the four possibilities with the interval of a 3rd:

There are several things about this example that would actually require some in-depth explanations (the double flat, for example!) Do not be concerned about those issues at this point. Later lessons will deal with double flats (and double sharps as well). For now, it is important that you realize that all four of the intervals shown above are considered '3rds'. They are 3rds because the distance from the lowest note to the highest note is 3, no matter what accidental is in front of the note. But looking at those four intervals, if you ask yourself the question, "Is the top note in the major scale of the bottom note?", the only interval for which the answer is "yes" would be the one with the 'A' on top. Therefore, that's the one we would call the major 3rd. From left to right, the four intervals are: diminished 3rd, minor 3rd, major 3rd, and augmented 3rd.

What do you do if the bottom note is a note for which we don't have a major scale? For example what about this one: We don't have a B-sharp major scale. In this case, imagine in your mind that you just lowered both pitches by a semitone. That would result in an E-flat on top and a B on the bottom. Then the interval becomes easier to figure out: "Is there an E-flat in a B-major scale?" No, there's an E-natural. E-flat makes this a diminished 4th. Then, raise both notes the same amount to get back to the original notes. By raising both notes the same amount, the interval stays the same size. And so the answer to the above example is: Diminished 4th.

So to sum up, there are two steps to naming an interval. Here they are:

1) Starting with the number '1', count upward until you reach the top note. Write that number down underneath the interval.
2) Ask yourself "Is the top note in the major scale of the bottom note?"

IF YES: The interval will be PERFECT (if the number is 1,4,5 or 8), or MAJOR (if the number is 2,3,6 or 7)

IF NO: It will be one of the other words as described above, taking into consideration whether it is a [1,4,5 or 8], or [2,3,6 or 7]. For each semitone smaller, go one word to the left of the word in the rectangle; for each semitone larger, go one word to the right of the word in the rectangle.

Use the following guide for abbreviations:

Major:	+ or 'M'
Minor:	- or 'm'
Perfect:	P
Augmented:	Aug or 'X'
Diminished:	dim or 'o'

When it comes to writing a note that is a certain interval above a given note, just proceed in the manner described above: If you are given this: and told to write a note a minor 6th above it, simply count up six notes (the bottom note is '1'). You'll get this: Then ask yourself the question, "Is there a 'G' in a B-flat major scale?" The answer is "Yes", and so this is a major sixth. We want a minor sixth. So what do we do? We lower the 'G' to a 'G-flat', and now the interval is a minor 6th:

If you are asked to write a note that is a certain interval below a given note, the process is similar. Simply count down from the given note, starting on the number of the interval. If you are given a 'G,' and told to write a note that is a diminished fifth below it, start on that 'G' and count down from 5 until you reach 1. You'll now be on the note 'C'. Ask yourself the question, 'Is there a 'G' in a 'C' major scale"? The answer is "Yes", so this is a perfect fifth. We want to make the interval smaller(to make it diminished), so we raise the 'C' to a 'C-sharp'. (In this case, we raise the 'C', because the 'G' was the note you were given. Do not change the given note.)

Here are several intervals all correctly labeled*. Study each one and be sure you fully understand the process involved in naming intervals before doing the test.

Remember to follow the two steps:

1) Start on 1, and count upward until you reach the top note.
2) Ask yourself, "Is the top note in the major scale of the bottom note?"

*Two of the intervals shown above, Aug.4 and dim.5, are also known by the term "tritone". Historically, the tritone was known as the "interval of the devil"; its position between the perfect 4th and perfect 5th made it quite difficult to sing in tune.

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