Theoretically Speaking: S1 : E3

Music Theory For Non-Musicians

This occasional series is about how music is made, and it’s for people who don’t already make music. It’s part music appreciation and part music theory.
I hope to cover rhythm, melody, intervals, chords, inversions, and more. Maybe we’ll get into extended chords and modes. Let’s see!

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S1E3: Every Little Step

In the last episode, we looked at string instruments. Specifically, we talked about their physics and how the tension and length of a string determines its pitch. I pointed out that if a string is tuned to A and you hold it down at the exact middle point, you’ll get another A – but an octave higher.

It stands to reason that if you hold your finger in 11 certain places between the full length of the string and its middle point, you’ll get the various notes from A to A. On a fretted instrument, there are 12 frets between the nut and the middle point. The notes they would produce on an A string are, from low to high:
B flat, B, C, D flat, D, E flat, E, F, G flat, G, A flat, and A an octave above the open string.

We’ll get into sharps and flats as we go along, but if you were to continue up the string, the 13th fret would produce an B flat an octave above the B flat at the 1st fret, the 14th fret would produce a B an octave above the 2nd fret, and so on.

From here on out, I’ll use a lower case b to mean flat, like Bb for B flat, and # for sharp, like F#. It’s just easier that way, and you’ll see it everywhere when reading about music. Notes that are neither sharp or flat – e.g., the white keys – are called natural, like C natural or just plain old C.

Anyway, those are the notes on a fretted instrument. On a fretless instrument, there are theoretically an infinite number of points where you can place your finger, so there are an infinite number of pitches you can play.

This is a good place to say that I’ll only cover western music theory here.

Many of us came here from The Number Ones. Anything that made the Top 40 in the US is extremely likely to use western scales and meters. The notes, scales, and beats used in Middle Eastern, Indian, African, and other cultures can be quite different from the European ones that we Westerners think of as standard. They’re only standard here in the west. 

Bassist and music educator Adam Neely has a video about this, and I recommend it. He got some political backlash for it, because it’s the 2020s and everything is political, but Neely does a good job remaining factual. It’s definitely worth your time.

So, where you put your finger on a string determines the length of the part that vibrates, which determines the frequency of its wave, which determines the pitch you hear. That’s how you play different notes.

With brass instruments, like trumpet or tuba, it’s a combination of holding down valves and adjusting the tension of your lips when you’re blowing. The valves send your breath through different tubes. The longer the tube, the lower the pitch. 

If you were to unravel a trumpet into a straight tube, and do the same with a tuba, the trumpet’s tube would be a lot shorter than the tuba’s. That’s why it plays higher notes.

There are three valves, which means there are eight possible notes to play: holding down the first valve, the second valve, the third valve, the first and second at the same time, the first and third, the second and third, all three, and none. Tighten the tension of your lips, and you’ve got eight more notes. Tighten again and you’ve got another eight, and so on. 

The tighter your lips, the higher the note. Put your lips together and blow air through them. I don’t care if you’re reading this in your dentist’s waiting room, just try it.

If your lips are really loose, you’ll make a low, farty sound. Tighten your lips and you’ll get a higher pitch. That’s what brass players are doing inside their instruments’ mouthpieces. Some brass instruments, like the bugle, have no valves, so all its notes are controlled with the lips.

Think about the kind of practice it takes to produce a pitch, then tighten your lips to get a higher one, and go back to exactly the first note. That’s hours and hours of practice to get the tension of your lips just so.

On a woodwind instrument, like saxophone or flute, you press buttons that open and close holes on the instrument’s body. That changes the vibration of the air you’re blowing through it, and that’s how you play different notes. Woodwinds are complicated instruments, and we may have to cover them separately.

Ever look inside a piano? When you press a key, a little hammer hits a string, or a group of strings, tuned to a certain pitch. So it uses strings but isn’t considered a string instrument because you don’t adjust the length of the string with your fingers. You hit entirely different strings for each note you play. That’s also why pianos are so expensive.

So now that we know how musicians play individual notes, how do they know which notes to play? Again, it comes down to waves.

Take a look at these two sound waves. In the same length of time, there’s one red wave and two blue ones. The blue wave has twice the frequency as the red wave. These two notes will probably sound good together. (To the true music theorists who might happen to read this, yes, it’s an oversimplification and sure doesn’t take the 12 tone equal temperament vs. just intonation argument into account. Baby steps.)

Now, does this mean musicians think about waves when they’re choosing notes? Absolutely not. This is just a glimpse at the science behind why two notes sound good together. Their frequencies are mathematically related. Their waves cross each other at regular intervals. The same is true for notes where one has a frequency, say, one and a half times more than the other. Notes sounding good together came first, and then we found the science to explain why, and a theory of music so we can discuss what sounds good to us.

What musicians do think about is the notes in the key they’re playing in. The key is a group of notes that we’ve already agreed sound good together in the same song. Or don’t sound good together, depending on the kind of atmosphere you want to give your song.

For the sake of simplicity, let’s talk about the key of C Major. This is all the white keys on the piano. In other words, there are no sharps or flats. The notes in C Major are C, D, E, F, G, A, B, and again C. You know this scale as do re mi fa so la ti do.

And if you don’t know it as do re mi fa so la ti do, it’s time to go watch The Sound Of Music again.

Remember that each key on the keyboard, white or black, is equal to one fret on the guitar. The difference in pitch between one note and the next, like C and Db, is called a half step, or a semitone. That’s going from one key on the keyboard to the key next to it. On a fretted instrument, it’s the going from one fret to the next one.

Q: Why is it called a half step and not just a step?

A: No idea.

Someone in western music history decided that it was a half step and the distance from C to D is a whole step, and not two steps. Weird, but there you go. I could Google it, but it’s no more important than knowing the wavelength frequencies of all the notes. The only important thing is that we all know what to call the move from one note to the next so we can describe it to each other.

Like I said before, C Major is all the white keys, C, D, E, F, G, A, B, and C. That means C is the first note of the C Major scale. The first note is  called the tonic. To play the C Major scale, start at the tonic, C, and then go up a whole step up to D. And then up another whole step up to E, but then only a half step to F.

Then it’s a whole step to G, a whole step to A, another whole step to B, and then a half step to the octave, C.

The entire pattern is whole step, whole step, half step, whole step, whole step, whole step, half step.

Here’s the cool part. Now that we know the pattern of half steps and whole steps to create the major scale in C, we can use the same pattern starting on a different note to create the major scale in another key. 

So look at the keyboard diagram above and let’s start on Db. Remember the pattern. A whole step from Db gives us Eb. Another whole step gives us  F, and a half step gives us Gb. Then three whole steps in a row gives us Ab, Bb and C, and then a final half step back to Db.

There! You now know the Db Major scale. What’s more, you can go to any keyboard, start on any note, and play its major scale. Whole step, whole step, half step, whole step, whole step, whole step, half step. Start on F, do the whole steps and half steps, and you have the F Major scale. do re mi fa so la ti do.

Want to make it a minor scale? There are various minor scales so let’s do the simplest one, which is the harmonic minor scale. All you have to do is flatten the third and the sixth notes. C harmonic minor would be C, D, Eb, F, G, Ab, B, and C. Or Whole step, half step, whole step, whole step, half step, whole step, half step.

Simple, right? Here’s the big secret: Every scale in western music is just various patterns of half steps, whole steps, and the occasional step and a half. That’s it.

Figure out what scale your song is in and use those notes. You’ll sound like a musical genius.

There are, of course, many, many, many exceptions to these rules…

but let’s not get ahead of ourselves…

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