The art of arranging sounds in time so as to produce a continuous, unified, and evocative composition. – Definition of Music from thefreedictionary.com
Music is the art of arranging sounds in time. To me, I think of music in two ways: vertical music and horizontal music.
Today we start our multi-part music theory series with the vertical axis of music: pitch.
Pitches and Frequencies
If music is the art of arranging sounds, what is sound? Our ears hear sound by sensing vibrations through the air. The frequency of those vibrations are what we perceive as pitch. When in tune, the A string on an acoustic guitar vibrates, cycling back and forth 110 times per second (or 110 Hz).
Humans have the capacity to hear from 15Hz to 18kHz, although our hearing diminishes over the course of life, particularly the high end.
Our ears are marvelous, but so is our brain. While our brain cannot distinguish individual frequencies, it will interpret those frequencies and create order. For example, your brain will not know you are hearing 220Hz and 440Hz, but it will perceive that you are hearing a frequency two times greater than the previous.
We don't hear individual frequencies as raw numbers; we hear ratios.
The most consonant interval in music – outside of unison – is the octave.
Octaves are created by doubling the frequency. The bottom A is 110Hz, followed by 220Hz, 440Hz and 880Hz.
Our ears perceive the 2:1 relationship as the same pitch. This is very similar to elementary math class and least common denominators.
- 2/1 = 2
- 4/2 = 2
- 8/4 = 2
In the same way, frequencies and pitches:
- 110Hz = A
- 220Hz = A
- 440Hz = A
Intervals like the octave are called "perfect" because of the relationship between the notes. There are four perfect intervals:
- Perfect unison – 1:1
- Perfect octave – 2:1
- Perfect fifth – 3:2
- Perfect fourth – 4:3
The perfect fifth is a 3:2 ratio, or 1.5. Let's take A 440Hz and multiply it by 1.5, that gives us 660Hz, also known as E. We will talk more about intervals in future posts.
Why All the Talk of Ratios?
I could have started this way: music has seven notes: A, B, C, D, E, F, G. You write these using little ovals on a staff that has five lines....
But that's not how we operate in modern bands. For one, we don't use a lot of music with lines and spaces, ovals and dots. The most successful modern musician uses their ear.
We play songs that follow predictable patterns. These patterns are found in how the notes and chords relate to each other. Understanding these relationships is key to being an effective worship musician. And these relationships are built on the foundation of how our brain perceives vibrations in the air.
Music is the art of arranging sounds in time: vertical music and horizontal music. Where the sound falls on the vertical axis is called pitches. Pitches are names given to frequencies.
While it is super interesting to look at the physics of music and why it all works mathematically, keeping up with 18,000 frequencies and working out ratios isn't exactly practical. That's why western music has broken down the octave into 12 notes. That's where we start next week.
Special thanks to the following websites:
Jim Aikin has written over the years for magazines like Keyboard, Electronic Musician, and Mix. He has a great series on his website call “Just Intonation".
Great article on the workings of the ear.
[UPDATE 2012-09-21: This article has been revised changing the second-to-last sentence to say "12 notes" instead of "seven notes". My first thought was of the scales that frame western music, but the 12 notes of the octave is a better starting point.]