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"Beginning Harmony (Part 2)"
by Richard Middleton

First published in Victory Review, June 1999.

This is the second article in a series on harmony. In Part 1, we began by exploring intervals; you may want to refer to that article. To recap briefly, an interval is made of two pitches that are a specific "distance" apart on your instrument. An interval is named according to the distance between the pitches in the musical alphabet. For example, A and B are a second apart because if you start counting on A, B is the second pitch in line. To name an interval, just count from one pitch to the other in the alphabet.

We also learned about "Major" and "minor," which in music mean "bigger" and "smaller." We found that some intervals are the same distance apart in the alphabet, yet different distances on an instrument. For example, A-B and B-C are both seconds, but A-B is one guitar fret or one piano key "wider" than B-C (i.e. there's a B-flat between A and B, but nothing between B and C). Therefore, A-B, being bigger, is called a "Major second," and B-C, being smaller, is called a "minor second." The Major form of an interval is always one fret/key bigger than the minor form (this distance of one fret/key is called a "half step").

Let's apply these concepts to the questions at the end of the previous article. If C-E is a Major third (i.e. E is a Major third up from C), what pitch is a minor third up from C? A minor third is a half step (one fret/key) smaller than a Major third, so the pitch we want is a half step lower than E, or E-flat. Therefore, C and E-flat are a minor third apart. Here's another: If B-C is a minor second (i.e. C is a minor second up from B), what pitch is a Major second up from B? A major second is a half step (one fret/key) bigger than a minor second, so we go a half step higher than C to C-sharp. Therefore, B and C-sharp are a Major second apart.

Why did we call that pitch a C-sharp rather than a D-flat? It's the same pitch, right? Yes, it's the same fret/key and the same sound, but in interval terms, it's not the same at all. Since we use the alphabet to count how big an interval is, the numerical distance (i.e. second, third, fourth, etc.) depends on what letters we use to name the pitches. It doesn't matter whether the pitches are naturals, flats, or sharps — it's the letters that determine what number we assign to the interval. Therefore, if we want to go up a second from B, we must use some kind of C because B and C are adjacent in the alphabet. If we'd named that note a D-flat in the earlier example, that would have made our interval some kind of third, because any kind of B to any kind of D equals some kind of third. And in our minor third on C example (C and E-flat), we can't call the E-flat a D-sharp because that would make the interval some kind of second (because any kind of C to any kind of D equals some kind of second). Because we were forming a minor third starting on C, we had to call the second pitch E-flat.

So far, we've defined intervals only in relative terms, i.e. by comparing their relative sizes, Major vs. minor. But how do we know what to call a interval if we don't have another interval to compare it to? The number (second, third, fourth, etc.) is easy — all we do is count how far apart the two pitches are in the alphabet. But how do we know whether it's Major or minor? To do this, we count the half steps (two pitches that are directly adjacent on your instrument are a half step apart, e.g. B and C, E and F, A and B-flat). Every interval is made of two pitches that are a specific number of half steps apart:

minor second

1 half step

Major second

2 half steps (or 1 step)

minor third

3 half steps (1.5 steps)

Major third

2 steps

Perfect * fourth    

2.5 steps

Perfect * fifth    

3.5 steps

minor sixth

4 steps

Major sixth

4.5 steps

minor seventh

5 steps

Major seventh

5.5 steps


6 steps

* "Major" and "minor" don't apply to fourths and fifths. Also, notice that there is no interval shown that has a distance of 3 steps. There are fourths and fifths that are not "perfect," however that topic is beyond the scope of this series on beginning harmony — it will be covered in a later series dealing with more advanced harmony.

Until next time, try finding all of these intervals on your instrument. Consider: how does each interval's name (fifth, sixth, etc.) determine which letters you use to name the pitches (e.g. E-flat vs. D-sharp)?

Copyright 1999 by Richard Middleton.
All rights reserved.

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Richard Middleton is a songwriter, musician, teacher, and writer based in Seattle. He is the author of "Reading Rhythm" (Countersine 2018).