Intervals from Scales
You may be wondering why a discussion of the C major scale appears in the interval chapter, when, according to the plan of the book, scales appear in the next chapter. Simply put, once you know whole and half steps, you can spell any scale, but more important, the other intervals are much easier to see and learn through the use of a scale.
Usually when musicians name a large interval, they don't count the numbers of half steps they need to figure out the answer. They are so familiar with scales that they use that information to solve their puzzle. Scales are such useful bits of information, and they are, of course, made up of simple intervals!
Consider this a sneak peek at scales; you will get the full scoop in the next chapter.
Intervals in the C Major Scale
Forming a C major scale is pretty simple: You start and end on C, use every note in the musical alphabet, and use no sharps or flats. Because the C major scale contains no sharps or flats, it's very easy to spell and understand. It's the scale you get if you play from C to C on just the white keys of a piano. FIGURE 2.5 shows the scale.
FIGURE 2.5 The C Major Scale
Look at the distance between any two adjacent notes in the scale, and you will see that this is simply a collection of half and whole steps. Now try skipping around the scale and see what intervals you come up with. Start with C as a basis for your work for now. Every interval will be the distance from C to some other note in the C scale.
To start simply, measure the distance where there is no distance at all. An interval of no distance is called unison. See FIGURE 2.6.
FIGURE 2.6 Unison Interval, C to C
Unison is more important than you think. While you won't see it in a solo piano score—you couldn't play the same key twice at the same time—when you learn to analyze a full score of music, it's handy to be able to tell when instruments are playing exactly the same notes and not other intervals, like octaves.
The movement from C to D is a whole step, but the interval is more formally called a major second. Every major second comprises two half steps’ distance. See FIGURE 2.7.
FIGURE 2.7 Major Second, C to D
The next interval is from C to E, which is four half steps’ distance. It is more formally called a major third (figure 2.8).
FIGURE 2.8 Major Third, C to E
Next up is the distance from C to F, which is five half steps. It is formally called a perfect fourth, as seen in FIGURE 2.9.
FIGURE 2.9 Perfect Fourth, C to F
Perfect fourth? Are you confused yet with the naming of these intervals? Hang in there! Before you get to why this is so and the logic behind it, finish the scale. You have only begun to chip away at intervals.
The next interval is the distance from C to G. It is seven half steps and is formally called a perfect fifth (figure 2.10).
FIGURE 2.10 Perfect Fifth, C to G
The interval from C to A, which is nine half steps, is formally called a major sixth. FIGURE 2.11 presents a major sixth.
FIGURE 2.11 Major Sixth, C to A
The next interval, from C to B, is eleven half steps. It is formally called a major seventh (see figure 2.12).
FIGURE 2.12 Major Seventh, C to B
To complete this scale, the last interval will be C to C. This interval is a distance of twelve half steps, or an octave (see figure 2.13).
FIGURE 2.13 Octave, C to C
Intervals in the C Minor Scale
Now that you've seen the intervals in the C major scale, here is the whole C minor scale and all of its intervals. Look at FIGURE 2.14. What do you see?
FIGURE 2.14 Minor Scale Intervals
For starters, the third, sixth, and seventh intervals are now minor. That makes sense because those are the three notes that are different when you compare a C major and a C minor scale side by side, as in FIGURE 2.15.
The intervals that were perfect in the major scale remain the same between both scales. However, the second note of the scale (C to D) remains the same in both scales, yet that interval is called a major second.
Why are scales so important when dealing with intervals? Can't intervals be measured on their own, separately from a scale? Of course, that's right, but most musicians become very comfortable with scales and use them to figure out intervals because scales are a point of reference. If you ask a musician what the interval is between A and F, it's likely that he will think first of an A major scale and then determine if F# is in the A scale. Since it is, he will quickly lower the F# from a major sixth down to a minor sixth, and that's the answer. Otherwise, he would have to count half steps (a tedious process), or memorize every possible interval combination in music, and that has its own obvious disadvantages. (It might happen naturally over time but not overnight.) Certain intervals are easy to memorize, but most musicians remember scales since they know them so well. What you don't see in either the major or minor scale is diminished or augmented intervals. That's not to say they aren't there; it just depends on how you look at it. Suffice it to say that major, minor, and perfect intervals are the most basic intervals, and they are the easiest to spell and understand because they naturally occur in the major and minor scales that you play so much. Augmented and diminished intervals are less common but are equally important to know and understand.
FIGURE 2.15 Major and Minor Scale Comparison
When you measure a musical interval, always count the first note as one step. For example, C to G is a fifth because you have to count C as one. This is the most common mistake students make when they are working with musical intervals. They often come up one short because they forget to count the starting spot as one.
Quality and Distance
Intervals have two distinct parts: quality and distance. Quality refers to the first part of an interval, either major or perfect, as you saw from the C major scale intervals. Now, these are not the only intervals in music, these are just the intervals in the C scale; you will see the rest of the intervals shortly. Distance is the simplest part—designations such as second, third, and fourth refer to the absolute distance of the letters. For example, C to E will always be a third apart, because there are three letters (C, D, and E) from C to E.
The numerical distance is the easiest part of intervals: Simply count the letters! Determining the quality of an interval is a different story. In the C major scale, there are two different qualities of intervals: major and perfect. Why were some of them major and what's so perfect about the fourth and the fifth? At first, learning all of these rules is challenging, but when you understand the basics, you can do so much. As for interval quality, it's only when you understand all of the different qualities that you can name any interval.
An interval has to determine the distance from any note to another note. As you can see in the C major scale, every interval has a distance and a quality to it. Confusion arises because notes can have more than one name. You might recall enharmonics (it was mentioned at the beginning of the chapter), where C# and D sound the same yet are different notes when written.
In analyzing written music, you have to deal with what you are given. When you listen to any interval, you hear the sound—you don't listen to the spelling—so the distance from C to D# will sound just like C to E What you hear is the sound of those notes ringing together, but if you had to analyze it on paper, you'd be looking at two different intervals (one is a minor third and the other is an augmented second) with two different names. The system of intervals has evolved somewhat strangely and with a certain amount of ambiguity because enharmonics is built into written music.
Many modern theorists and composers don't use the traditional intervallic system. Instead, they use a more numerically based system of organization, called set or set theory, which bases intervallic measurements on pure distance-based relationships in half steps. This system solves the ambiguity with enharmonic intervals. So, instead of a major third, it would be a five because a major third is five half steps.