Organizing notes : scales and keys

Click here for the general overview

In the previous blog, we saw 2 important conventions :

1. A note with a frequency that you divide by or multiply with 2, remains the same note. For example, A = 440 Hz, but also 220 Hz, 110 Hz, 880 Hz, and so on.
2. Between 2 adjacent notes there is an “auditive” distance which can be a tone or a semi-tone (half-tone). On an instrument with frets, that interval is easy to find : a semi-tone is 1 fret, a whole tone 2 frets.

Now, let’s do the following experiment on your guitar : from any string, play the open string, then all the semi-tones until you have the same note as the open string again.

I’ll wait a minute here until you’ve finished.

If you did the experiment right, you played 13 different pitches : first the open string, then you put your finger on the 1st fret, then the 2nd, then the 3rd, and so on, until you arrive at the 12th fret. As we’ve seen in the previous blog, the 12th fret is half the string, so there’s the same note as the open string.

Congratulations ! You played your first scale ! The chromatic scale to be more precise. So, what is a scale ? Before I can answer that, I need to introduce yet 2 other terms. Don’t worry, they’re both very simple.

The first term is : the “root note” – or “root” in short. The root is the note with which you start a scale. It’s also called the “key”. So, if you started the scale with the 1st open string, your root or key was “E”. If it was the 2nd open string, the root was B, if it was the 3rd then the root was G, the 4th was G, the 5th was A and the 6th was again E.

Now, the second word I want to introduce is the “octave”. We’ll see more about that later, but for now, let’s say that an octave is the same note as the root note, but with twice (or half) its frequency. In other words : it’s the note you play on the 12th fret.

With those 2 terms, we have all the information to define what a scale is : a scale is a pattern of tones (whole tones and semi-tones) to go from a root note to its octave.

That’s it. Simple, isn’t it ?

In the chromatic scale, the pattern is really really really easy : it’s all semi-tones from the root to the octave. You demonstrated that when you played every fret from the open string to the 12th fret.

You can play a scale in ascending or descending order : from the root to it’s upper octave (from the open string to the 12th fret), or from the root to it’s lower octave (from the 12th fret to the open string). That’s why I like the Dutch word for scale : “toonladder” : it shows nicely that you can go up or down. I’m sure it doesn’t need an English translation. By the way, in English, in stead of talking of a whole tone and semi- or half tone, you can also say : a whole step or half a step. In a way, this also refers to a ladder.

But the chromatic scale is by no means the only scale, or pattern, to organize notes ! You have many of them, amongst which is for example the very important “minor pentatonic scale”, that is used abundantly in blues-music.

But there is one that is overly dominant in western music, and that is really “home” for music theory. It is the diatonic scale.

The pattern of the diatonic scale seems a bit complex at first sight, but we’ll see later how we can break it down into simpler fractions. Ok, here’s the pattern :

whole tone – whole tone – half-tone – whole tone – whole tone – whole tone – half-tone

(remember, in stead of “tone”, you can also use the word “step”)

If you like numbers, I guess you can write it down like this :

1 – 1 – 1/2 – 1 – 1 – 1 – 1/2

Or, if you – like me – prefer a more visual way :

Now, let’s apply this pattern on the guitar, and we choose the first fret of the 2nd string as our root note, which happens to be C.

Before we start playing the scale, let’s think a moment where we want to end up. If we start on the 1st fret of the string, which fret on that string will be the octave ? We know from the previous blog that from the 12th fret onwards, the notes repeat themselves. So, the note of the open string and the 12th fret are the same, and so are the notes on the 1st fret and the 13th fret. In other words, the 13th fret is the octave of the 1st fret, so that’s where we’re want to land on.

Here we go : we play the 1st fret, then leave a whole tone (we move 2 frets), that means the 3rd fret. Then leave again a whole tone (move 2 frets) and play the 5th fret. Then only a half step (move 1 fret), play the 6th fret, then a whole tone (2 frets), so play the 8th fret, again a whole tone, play the 10th fret, and again a whole step, play the 12th fret, and then finally a half step, which brings us indeed to the 13th fret, the octave.

Congratulations again ! You just played the diatonic scale in the key of C ! (C being the root).

You can do that again if you like, and you can also play it in ascending order : 13th – 12th – 10th – 8th – 6th – 5th – 3rd – 1st. I’ll just wait here until you’ve finished…

Now, let me ask you the following question : how many different pitches did you play ? And the next question : how many different notes ? Maybe, get back to your guitar and count the number of pitches and notes you play in the diatonic scale ! (Again, I’ll wait a bit….)

The answer is that you played 8 different pitches, but you only played 7 different notes ! The different notes were : 1st fret – 3rd fret – 5th fret – 6th fret – 8th fret – 10th fret – 12th fret, which are of course also different pitches. But then you played also the 13th fret, which is indeed a different pitch, but not a different note (I refer to the 1st convention : the octave is the same note as the root !).

So, now everything falls into place : in the specific pattern of tones that is called the diatonic scale, there are only 7 notes. In the key of C which we played, these notes are : C – D – E – F – G – A – B. The high C was the 8th pitch that you played, and that’s why it’s called the “octave” (the Latin word “octo” means 8, e.g. the “octopus” has 8 arms).

Wow ! We’ve come a long way ! From the thousands of frequencies that a human ear can hear, we organized them all in only 7 notes ! That’s quite a trick !

Some things to remember :

• from the E to the F, and from the B to the octave C, there’s a half step interval. Or in other words : from the 3rd note to the 4th, and from the 7th to the 8th, only half a step. Between all other notes, there’s a whole step difference.
• A scale is a pattern of whole and half tones, the root or the key is the note on which you start the scale !
  Having said that, because the diatonic scale is so overdominantly used in western music, and because the key of C is the “mother of all keys”, the terms “scale” and “key” (in particular the key of C) are often intermixed. So, if you read somewhere “the G-scale”, that means the diatonic scale in the key of G. (There’s no such thing as a “G-scale”).

I guess this is enough stuff to think about for this Pomodoro. At least (and at last) we know the notes in the key of C. But what about other keys ? We’ll see about them in another Pomodoro. But my next Pomodoro will first show how you can play the diatonic scale in the key of C on different strings on your guitar. And I’ll talk about a bit more too ! See you there !