Building even more keys in the diatonic scale

Click here for the general overview

In the previous blog, we discovered the Circle Of Fifths, and how use it to build other keys in the diatonic scale, by adding sharp notes, starting with F# :

• F# : key of G
• F# + C# : key of D
• F# + C# + G# : key of A
• F# + C# + G# + D# : key of E

Another way to look at the Circle of Fifths is that you add tetrachords (the miniscales of which the diatonic scale is made) to the “right” of the 2 original tetrachords of the key of C :

So, the 2nd mini-scale in the key of C acted as the 1st mini-scale in the key of G, etc..

But what if we reversed the direction ? What if we took the 1st mini-scale in the key of C and let it act as the 2nd key of another key ? In other words, what if we build the tetrachords to the “left” of the original key of C ?

Well, let’s try that. Below you’ll find the diatonic pattern we’re looking for, and the 1st tetrachord in the key of C acting as the 2nd tetrachord in the other key :

First question : in what key are we here ? Well, as we know from the definition “a scale is a pattern to go from the root note to the octave”, and the octave is F in this case, then the root note is also F, so we are in the key of F !

Ok, now we know that, let’s fill in the notes, and see if they fit !

OMG, they don’t fit at all ! At first sight, it seems impossible to build the diatonic scale this way. Well, don’t despair just yet, let’s have a closer look. The 2nd mini-scale is ok, and that’s because it’s the 1st tetrachord of the original key of C.

But then, the 1st mini-scale has 3 whole steps in stead of 1+1+1/2, and the connecting interval between notes 4 and 5 is only half a step in stead of a whole step.

But isn’t the connecting interval the real problem here ? If we lower the B half a step, making it B-flat or Bb, then not only the correct interval is restored, but we got a correct 1st mini-scale as well ! So, here’s the corrected diagram :

So, we come to the conclusion that in the diatonic scale, the key of F has 1 flat note : Bb. Put even more strongly : there is only 1 key which has 1 flat note. That key will be F, and the flat note will be Bb.

Ok, now that we have the diatonic scale back, how about repeating the same process to the left, and using the 1st mini-scale as the second mini-scale in search of the next key.

Again the first question is : in what key are we in. And looking at the octave the answer is : Bb.(BTW this is the 4th note in the key of F, as was F in the key of C).

Ok, let’s fill in the missing notes :

Just as with building mini-scales to the right (Circle Of Fifths), this method of building to the left also reveals an ever recurring problem. It’s situated in the connecting interval. Indeed, between E and F there is only half a step difference, but the scale requires a whole step. And again, the solution is simple : we only have to lower the E by half a step, resulting in Eb, to have the problem fixed :

So, now we have 2 flat notes : Bb (from the key of F), an Eb in the key of Bb. Or put more strongly : there is only 1 key with 2 flat notes, and that is the key of Bb. Those flat notes are : Bb and Eb.

I think, with all the practice that you have building keys in the previous blog, and with the above examples, you should be able to answer the following questions :

• What would be the next key that you build ?
• Where do you expect to run into a problem ?
• How do you think you would solve that problem ?
• And last question : how many flat notes do you expect that key to have ?

Think about those questions for a while before reading the answers below.

Well, the next key I would build is the key of Eb. Why ? Because it’s the 4th note of the current key, which is Bb. I would expect to have a problem in the connecting interval (between the 4th and the 5th note). Indeed between A and Bb, there is only half a step difference, but it should be a whole step. The solution is to lower the 4th note from A to Ab. My conclusion would be : there is only 1 key with 3 flat notes. That key is Eb, and the 3 flat notes are : Bb, Eb, and Ab.

And again, you could continue building other keys “to the left”, that comes down to using the 4th note as the root. That’s why this process is called the “Circle Of Fourths”.

You may be wondering what is the use of building keys in Bb or Eb or Ab. Aren’t the keys of C, G, D, A and E enough ?

Well, like I said in the previous blog, when you are playing folk or bluegrass music, they probably are. But the “flat” keys are the realm of jazz !

Why ? Very simple : brass wind instruments are for the most part tuned in those flat keys ! And since these instruments are used a lot in jazz, it’s obvious that songs would be written in those keys.

Conclusions

I think it’s time for some conclusions.

A. Getting the key

• If there no sharp or flat notes, then you’re in the key of C.
• Sharp notes always start with F#, and you continue adding 5ths to it :
  • F# : key of G
  • F# + C# : key of D
  • F# + C# + G# : key of A
  • etc.
• Flat notes always start with Bb, and you continue adding 4ths to it :
  • Bb : key of F
  • Bb + Eb : key of Bb
  • Bb + Eb + Ab : key of Eb
  • etc.

Try to find a mnemonic that helps you remembering those rules quickly. I have such a mnemonic, but I won’t tell you, because it’s better that you find your own !

B. A flat note is not a sharp note !

Like I mentioned in the previous blog, a sharp note and a flat note can sound the same, but by no means they are the same !

Take for instance Db. It sounds the same as C#, but the two notes have a whole different function. The first time you encounter a C#, it acts as the 7th note in the key of D. The first time you encounter Db, it acts as the 4th note in the key of Ab. You will quite agree with me that those are totally different keys !

Another thing to notice : a key has either sharp notes, or flat notes. Not both !

C. Key signature

When you look at a music sheet, in many cases you will see the “key signature”. A bunch of sharp or flats at the beginning of each line of the sheet.

The key signature serves 2 purposes. First, it tells you what key to use. So, if there isn’t one, you know you’re in the key of C. Otherwise, look at the sharps or flats, and you know it what key the song is written. In the example above, the piece is in the key of …. well, I’ll let you figure it out !

The second purpose of the key signature is to make life easier for musicians, more particularly composers. In stead of decorating every sharp or flat note in the key with the appropriate symbol, they just say : “Hey, look at the key signature, I wrote it once there, and it goes for the entire line !”. So, in a musical sheet with the key signature “F# – C#”, every F and every C is to be played as F# and C# (unless otherwise noted).

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So far, we have gained a lot of knowledge about scales and keys. But we’re not there yet ! However, for the moment we’ll leave the notes for a while and we’ll direct our attention to another very important phenomenon in Music : Time !

We’ll talk about that a bit more in the next Pomodoro. Hope to find you there !