The Ingredients of Melody: Intervals
I can be a cerebral sort of guy. When I was a kid, I’d sometimes spend more time reading about a new toy than playing with it. As much as I’m embarrassed to admit it, it’s true.
So when I started to learn music around the age of twenty, I thought that understanding music would help me play it better. I started looking around for a book that explained how music worked. Although I did finally find my music “Bible” (Making Music compiled by George Martin, which I may talk about in a future post), there is no book that can explain music in the way that I wanted. I discovered that in many ways music is arbitrary and man-made.
So I kept on practicing my scales, learning how to read music, working out how synthesizers worked, and bought a portastudio. I got to know the ingredients of music, how to put them together, and how they related to each other.
And I learned about one of the ingredients of melody: intervals.
The Theory of Intervals
Not everything in music is man-made. There are physical laws that describe how sound is made, and how sound waves interact with each other. The physics of sound is the foundation that we built music on top of.
Take the concept of an octave, for example. When we hear two notes that are one octave apart, they sound similar – like the same note, only one sounds higher than the other. And when we play the two notes together, they sound good. They harmonize.
A scientist would tell you that sound is made up of waves. Waves of differing air pressure. Although the waves aren’t made of water, they are a lot like the waves we see at the beach. I’ve often watched patterns in the surf, and the way the waves interact. Sometimes the waves move together in an orderly fashion, in the same direction at the same speed. Sometimes one wave will catch up to another, and become one huge wave. Other times they will collide violently. And once or twice I’ve been in the middle of them when they collided.
Notes that sound good together are like the orderly waves flowing in the same direction at the same time. In fact, there is a mathematical way of describing how they interact.
Imagine Middle C as a wave. Picture its crests and troughs as it flows through the air. Mathematically, the note one octave higher (C above Middle C) has exactly two times as many peaks and troughs. So as those two waves traveled together, every second peak would coincide. The notes would harmonize rather than clash.
Other important intervals have similar mathematical descriptions. For example a perfect fifth (in this case G above Middle C) has one and a half times as many peaks and troughs, so every third peak coincides. And a major third (in this case E above Middle C) has one and a quarter times as many peaks and troughs, so every fifth peak coincides. The notes still harmonize, but no longer sound like the same note.
So there is a scientific reason some notes sound good together. These intervals form the basis of our music. From that basis Westerners have developed a set of scales built on an octave of twelve distinct notes. That came more from culture than science. Other cultures break up the octave differently.
The Flavors of Intervals
Because of the mathematical way that notes interact, some notes harmonize with each other and some clash. This is important to understand when playing chords. But when we play melody we are not playing the notes together, so we’re not as aware of whether the notes harmonize as much as the size of the step between notes, and the concept of tonality – that every scale has a starting or “resting” note.
Here is the list of all intervals in Western music. I’ll use the key of C major as an example, and give all occurrences of the interval in that key.
| Interval | Step | Flavor |
| Unison | 0 semitones | The same note is played twice. There is no sense of movement. |
| Semitone, or minor second | 1 semitone | e.g. E-F and B-C. The smallest interval – there is no black key between these notes. The notes very discordant when played together, and can sound spooky. This interval is used a lot in Jaws, Batman (the 60’s series) and Fur Elise. |
| Whole tone, or major second | 2 semitones | e.g. C-D, D-E, F-G, G-A and A-B. There is a black key between these notes, so it sounds like a bigger step than a minor second. Most of the steps in a major scale are major seconds. |
| Minor third | 3 semitones | e.g. D-F, E-G, A-C and B-D. A third with only one black key between the notes. Has a more emotional quality than a major third. |
| Major third | 4 semitones | e.g. C-E, F-A, and G-B. A third with two black keys between the notes. Thirds are normally steps within a chord, while seconds (momentarily) step out of a chord and add more color. |
| Perfect fourth | 5 semitones | e.g. C-F, D-G, E-A, G-C, A-D and B-E. A fairly big jump with a somewhat completed feel. |
| Augmented fourth, or diminished fifth | 6 semitones | e.g. F-B, B-F. Exactly half an octave, sometimes called a “tritone”, the interval between B and F is the same whether B or F is the higher note. The only occurrence in the scale. All other fourths and fifths are perfect. This interval has a less complete feel than perfect fourths and fifths. |
| Perfect fifth | 7 semitones | e.g. C-G, D-A, E-B, F-C, G-D, A-E. A big jump with a completed feel. |
| Minor sixth | 8 semitones | e.g. E-C, A-F, and B-G. A perfect fifth plus a minor second. |
| Major sixth | 9 semitones | e.g. C-A, D-B, F-D and G-E. A perfect fifth plus a major second. |
| Minor seventh | 10 semitones | e.g. D-C, E-D, G-F, A-G and G-F. A major second less than an octave. |
| Major seventh | 11 semitones | e.g. C-B, and F-E. A minor second less than an octave. A very big jump that doesn’t quite feel completed. |
| Octave | 12 semitones | Jumping to the same note one octave higher. Even though it’s a big jump, there isn’t a sense of movement, because the notes sound the same in the context of the scale. |
Next time you’re playing or composing a melody, try to be more aware of the intervals you are playing. Over time your appreciation for the roles and flavors of different intervals will grow.
I know that a lot of you would prefer to play with the toy than read the description on the box, so I hope you haven’t minded me indulging in some theory. It can very helpful to think about how and why things work. If you’d like to explore more about intervals, you might like to read Joel’s article, “Boot Camp for Your Ear: Detecting Intervals with Song Associations“.
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Comments
Adrian
Adrian is writer and editor for Audiotuts+ and the AudioJungle blog. He has been playing keys and acoustic guitar for three decades, and has six kids. Follow him on Twitter at @audiotuts.
Hi Adrian, great article. I think it would help if you insert sound clip examples in your flavor listing instead of providing a link to Joels’ article, as this is all VERY theoretical.
Hi Clublime. Thanks for your comments and your feedback.
I agree that the article became very theoretical – it seemed to have a mind of its own! I’m not aiming to do any more like that, but a minority of people do seem to enjoy that type of article.
I appreciate your suggestion about including sound clips. I hadn’t thought of doing that, and it would have been helpful.
Good helpful look at intervals!
One tiny issue: I think you’ll find that a “tritone” is an aug4 or flat5, not a P4th. The term also (and in some cases more commonly) applies to a triadic combination of two sets of 6 semitone intervals played together, making a diminished triad.
Otherwise, great work! I’m sure it will be useful.
Hi Ben, you’re absolutely correct about the tritone. Three tones is six semitones, and I had put it in the table under five semitones.
Your comment prompted me to do a bit of reading about the tritone, and I discovered that in the Middle Ages this interval was known as “the devil in music”, and was absolutely prohibited from being used in melodies. Amazing!
Clublime, your idea of being able to listen to the intervals really appealed to me. I figured that someone else may have already had that idea, and sure enough, I found a “Listen to Musical Intervals” page on the Musical Intervals Tutor site.
You can listen to the intervals at
http://www.musicalintervalstutor.info/listenpg.html
I hope you enjoy it.