Two Simultaneous Notes
So, what happens when more than one pitch is played at the same
time? In music, we call two notes being played at the same
time an interval, and three ore more notes (2+
intervals) a chord. But, sound waves travel pretty
fast, so that they effectively occupy the whole volume of air
around us all at once, so how can more sound wave exist in the
same space? What happens is that the waves overlap with
one another and effect each other, resulting in a new wave: this
process is known as Interference, and is demonstrated in
Figure 7 (SLH-PAP).
| In some places, the two
waves compress and rarefract the same regions of air,
increasing the amplitude of the wave at this point, which
is known as constructive interference. In
other places, one wave tries to compress the air while the
other tries to rarefract it, resulting in no net change,
known as destructive interference. The
result is a composite wave that has a more complex
waveform; two of these can be seen in Figure 7 (C and D). Even though your brain is only receiving one composite wave, it can piece out the the constituent parts that correspond to different sources, allowing you to comprehend more than one sound at the same time. The way our brains do this is complicated and variable, but the fact that we can is the key to being able to hear harmony in the first place. |
![[image
describing interference]](figures\figure7.jpg) Fig 7: Interference described (SLH-PAP) |
Consonance and Dissonance
| So, you can hear different sounds at the same time. However, it's not like we hear sounds in discrete, separate bubbles; for example, listen to this clip: | |
| You can hopefully hear that I'm playing 3
notes here, but notice how they sort of blend agreeably
together. Now, compare this to this: |
|
Again, there are 3 notes, but now they don't blend so well. This quality of "agreeable blending" in harmony is known as consonance, and the quality of clashing harmony is known as dissonance, and they are what makes harmony sound the way it does: beautiful, scary, wistful, empty, whatever. So what causes consonance and dissonance? It's actually the result of your brain dividing the frequencies of the notes it hears at the same time. All harmony is, on a physical level, is mathematical ratios.
Harmony is Just Math
Much like a grade school student, your subconsciousness likes
simple fractions; the simpler the frequency ratio, the more
consonant the harmony; the less simple, the more dissonant.
The simplest ratio is 2/1 (doubling the frequency) and 1/2
(halving the frequency) so we would expect these to be the
simplest intervals. As it turns out, they are:| The first interval has a note with
frequency 440 Hz (A4) and another at 880 (A5):
880/440 = 2/1 The second interval has notes with frequency 440 Hz and 220 Hz (A3): 220/440 = 1/2 |
From here we can see that to get the next most consonant interval, we just use the next simplest fraction: 3/2, and then 4/3, and then 5/4, 6/5, etc. Here's what this sounds like:
| The first interval is 3/2, known as a fifth, followed by 4/3, known as a fourth, then 5/4, a major third, and finally 6/5, a minor third (Suits). |
The peculiar names of these intervals come out of the Western music tradition: what's important is that you can hear that as the ratio get more complex, the sound gets more colorful, but since all these ratios are still quite simple the harmony still sounds quite consonant. If I use intervals like 22/24, 15/8 or 45/32, the result is much more dissonant:
| First is 22/24, a minor second,
next is 15/8, a major seventh, and then 45/32,
often called a tritone (Suits). |
For more than two notes, our brains do the same thing, making a compound ratio - the first audio clip on this page was a major chord, and had the ratio 5/4/3. Actually, its not exactly 5/4/3: I should probably mention that for every one of these ratios except the octaves my piano was slightly off. The reason for this has to do with what's known as Equal Temperament, which is an entire website on it's own.