So we’ve established in the last post roughly what we mean by music, and we’ve also established that from now on I’m going to narrow down my meanings quite a bit, but that it’s worth bearing the broader definition in mind.
So let’s look at melody and harmony. The two are rather interlinked, and what they have in common is the idea of a scale. But to get to what a scale is, we have to look at what a note is, because scales are made up of notes.
Sound, as you may have learned in school, comes in waves — pulses in the air. When you hit something, or pluck it, or force air through it (the only three ways of making music up until the mid twentieth century, and still among the most popular), the thing you’re hitting or plucking or blowing moves, and that in turn shakes — vibrates — the air. Those vibrations are what we hear.
The particular type of vibration we’re interested in is called a sine wave. That wikipedia link goes into far more mathematical detail than we need, but what you need to know is that a sine wave looks like this (pinched from Wikipedia):
What you can see from that picture is that a sine wave is made up of regularly repeating peaks and troughs. This regular repetition is very important. Every pure musical note is a sine wave, and we know what note is what by the number of peaks per second. This number is known as the frequency — meaning how frequently there’s a peak — and it’s measured in hertz (written Hz), which is just a label meaning “number of oscillations per second”.
The higher the frequency of the sound, the higher the note sounds, and the lower the frequency, the lower the note. For an example of this, let’s look at a piano keyboard (again pinched from Wikipedia):
The note highlighted there is called “middle C”, and it’s about in the middle of the range in which music is generally played. Its frequency is 261.626Hz, which means that there are 261.626 waves every second when someone plays a middle C.
Let’s look at the C note above that:
. You can see from looking at the keyboard that these keys look similar, and from my writing that they’re both called “C”, but this one is 523.251Hz — almost exactly double the frequency of the previous note. And it’s higher as a result.
If you want to know how much higher, think of the first two notes of the verse to “Somewhere Over the Rainbow” — “Some… where“. That leap is the leap between those two notes.
Now we’ve said that those two notes have the same name, and they certainly sound OK together, one after another. So what’s the reason for that?
Well, in nature, one very rarely gets something that vibrates at only one frequency. Most things vibrate at multiple frequencies at once, and pure sine waves on their own sound very strange as a result.
Now, when two waves have their peaks and troughs at the same time, those peaks and troughs go together and reinforce each other. When they happen at different times, they can cancel each other out, partly or wholly. In sound, we call the reinforcement harmony, and the cancellation dissonance. (More precisely, dissonance is when you get partial cancellation that sounds irregular because the two frequencies constantly shift in and out of phase with each other. We call *total* cancellation silence…)
Generally speaking, people like sounds that are in harmony, rather than dissonant. This is not always the case — some people like dissonance in music a lot, myself included — but generally speaking, when we use dissonance in music, it’s to provide a little tension, so the listener is thinking “I hope it becomes harmonic again soon, I wonder how they’re going to do that” — at least on a subconscious level. When the average listener hears dissonance, they want it to become harmony again, and get very annoyed if it doesn’t.
Now the most harmonic you can get is to be at exactly the same frequency, because then all the peaks and troughs will line up previously. This is called unison, and it’s boring to talk about musically, because it’s just two things being the same as each other.
The next most harmonic you can get is to have frequencies that are integer multiples of each other. If you have two frequencies, and one of them is double the other, then when you play them together you will get the peaks matching half the time. These notes match so well that we give them the same name — double the frequency of a C note is another C note, double the frequency of an A is another A, and so forth.
The distance between one C and another (or between one A and another, and so on) is called an octave. If you look at the piano key diagrams above, you’ll see that there are eight white keys on the piano between the two Cs, and that’s where the “oct” part of an octave comes from. We’ll look at why that is in a future post, but for now, just accept that that’s the name.
And finally, for today, we’ll look at the next most harmonic note. That’s when the frequency of the higher note is one and a half times that of the lower, so every third peak of the higher note reinforces every second peak of the lower note. This note (for reasons we’ll again come to in a future post) is known as the fifth or the dominant, and if the low note (or tonic) is C, then the high note will be G. (You can count C-1, D-2, E-3, F-4, G-5 along the white notes on the keyboard).
When you play two or more notes together, you have what is known as a chord. If you play C and G together — with or without a higher C played at the octave — then what you have is the single simplest type of chord, the power chord. Lots of rock music is based around power chords — the guitar intro to “You Really Got Me” by the Kinks, for example, is just made up of two power chords, with the tonics being F and G.
We’ll look at more of this soon, but I think that’s enough for this post. Please let me know in the comments if I’ve not explained anything thoroughly enough, and I’ll try to explain better.
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If two things are in unison, couldn’t the waves be out of phase (so one peaking when the other is in a trough)? Or if not why not? And does this have any effect on the sound?
Yes they could, and if they were out of phase totally it would make the sound totally silent.
In practice, they’re extraordinarily unlikely to be completely out of phase, as the notes would have to be played precisely at the right times, about three milliseconds apart.
Other than that extreme difference, what really matters isn’t that the two waveforms be in phase, but that they don’t shift in and out of phase irregularly (or seemingly-irregularly).
Hmm, nothing to disagree with this time :-)
I might have introduced the octave+fifth interval as three times the base frequency, then noted that it follows that half of that — 3/2 of the base frequency — gives you the fifth without the additional octave.
This is weirdly super-helpful with me learning my new piano keyboard. I have ten new ideas now, that I didn’t have before.
Glad to hear it! Hope the rest of the series is equally helpful when I get round to them.
If I’m being quiet it’s because I’m learning.
So a chord is like getting two Judy Garlands and getting them to sing “some” and “WHERE” at the same time as each other?
That would be one example. A chord is technically just any two or more notes played at the same time. (There are more specific types of chords, which Andrew might talk about more later.)
That would be a chord, but not a very interesting one, because they’re singing the same note an octave apart. The power chords I’m talking about at the end have the notes a fifth apart, which is like singing the “twin” and “kle” of “twinkle twinkle little star” at the same time.
But the “twin” and “kle” are on the same note! Do you mean the interval between the two “twinkle”s?
Yes I did. I was very tired when I wrote that, and messed up.