First published in Victory Review, May 1999.
This is the first of four articles on harmony, examining how intervals and chords work, what their names mean, voicings and inversions, etc. We'll start with intervals, the basic building blocks of harmony.
When two notes are played together, the distance between them in pitch (and the sound they make together) is called an interval. When three or mores notes are played together, they make a chord. You can think of a chord as several intervals combined, i.e. each note is some distance away from every other note. For example, in a three-note chord, there's a low note, a middle note, and a high note. The low and middle notes form one interval, the middle and high notes form another, and the low and high notes form another. Think of chords, then, as being made of intervals.
Intervals are named using numbers, i.e. "second," "third," "fifth," etc. These names often sound like fractions but they're really ordinal numbers, i.e. "fifth"; means "the fifth note in line." For example, a fifth is made of two notes that are each the "fifth note in line" relative to each other. To name the interval between two notes, we count how far apart they are. But what do we count? The basic units for counting intervals are the letters of the musical alphabet: A, B, C, D, E, F, and G. To name an interval, we count how many letters apart the two notes are.
IMPORTANT: Intervals are always inclusive, i.e. when you count, the starting note is always "one." To count the interval A-E, count from A up to E, starting with A as "1": 1, 2, 3, 4, and 5 is E. Therefore, A-E is a fifth. In other words, E isn't the fifth note "away from A," it's the fifth note "starting on A." Similarly, A-B is a second, A-C is a third, A-D is a fourth, A-F is a sixth, A-G is a seventh, and A up to the next A is an octave ("oct" = eight).
Let's count other intervals that don't start on A, for example D-E. That's a second. F-A is a third. D-G is a fourth.
You can also count down from letter to letter: C down to A is a third, G down to D is a fourth, etc. Count these intervals in your head and on your instrument, then play them. For each interval, say its name, play both notes together, and listen to the sound.
Notice that some intervals share the same interval name but aren't the same distance on the fretboard/keyboard. For example, A-B and B-C are both seconds, but while B and C are adjacent frets/keys, A-B skips over B-flat. Both intervals are called seconds because, in both cases, the letters are adjacent in the alphabet. Similarly, A-C and C-E are both thirds, but they're not the same number of frets/keys apart: A-C skips two frets/keys (B-flat and B-natural), but C-E skips three (D-flat, D-natural, and E-flat). But both are called thirds because they're thirds apart in the alphabet.
So, some seconds are bigger than other seconds by a difference of one fret/key, and some thirds are bigger than other thirds by a difference of one fret/key. This can be confusing, but there is a method to the madness. Let's look again at the seconds, A-B, and B-C — of the two, A-B is larger, and B-C is smaller. In music, larger is called "Major," and smaller is called "minor." We call A-B a "Major second" and B-C a "minor second," so that we know the specific distance between the two notes in each interval. The Major second, A-B, is two notes with another note between; the minor second, B-C, is two notes that are directly adjacent to each other.
Let's look again at our two thirds, A-C and C-E. A-C, being the smaller of the two, is a "minor third," and C-E is a "Major third."
As we saw before, there's a difference of only one fret/key between the Major and minor second and the Major and minor third. This is true of all Major and minor intervals: a Major second is always one fret/key wider than a minor second; a Major third is always one fret/key wider than a minor third; a Major sixth is always one fret/key wider than a minor sixth; and a Major seventh is always one fret/key wider than a minor seventh.
There is another way of naming Major and minor seconds that is used quite often in music. Major seconds (e.g. A-B) are also called "whole steps," and minor seconds (e.g. B-C) are also called "half steps." Whole steps and half steps are often used to "measure" intervals, in the following way: a minor second is one half step, a Major second is one whole step; a minor third is 1.5 whole steps, a Major third is two whole steps (or "two steps" for short); a minor sixth is four steps, a Major sixth is 4.5 steps; a minor seventh is 5 steps, a Major seventh is 5.5 steps.
Thus we get the following rule: the Major and minor form of each interval are always one half step apart; Major is bigger, minor is smaller.
Notice that we haven't done anything with the fourths and fifths. Fourths and fifths are not called Major or minor; they use a different naming scheme, which we'll look at in a later article. Of the intervals we've seen so far, only seconds, thirds, sixths, and sevenths can be called Major or minor.
Here's food for thought until next time... If C is a minor third up from A, what pitch is a Major third up from A? Remember, a Major third is one half step bigger than a minor third. This means the top note, C, needs to rise up to C-sharp: C-sharp is a Major third up from A. Try to figure these out on your own: a minor third up from C; a Major second up from B; a minor second up from A. Good luck!
© Copyright 1999 by Richard Middleton.
All rights reserved.
Richard Middleton is a musician, songwriter, producer, educator, and writer based in Seattle. He is the author of "Rhythm Guitar Secrets" (Countersine), and his music writing has also appeared in Smithsonian magazine, Victory Review, and SingOut! magazine.
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