What is a Mode?

In a recent post I mentioned some myths about modes, and promised I'd try to give my own account of this often-confusing idea. If you've read the first chapter of Scale and Arpeggio Resources then you'll know exactly what a mode is, but I thought I'd try a brief and slightly different explanation here in case either you found that chapter difficult or you don't have the book. Although it's a bit more abstract than most, I hope those of you who are confused about modes will find it enlightening.

A Scale is an Interval Map

I'm going to start by asking what a "scale" is. Many people, without thinking too hard, would say that a scale is a collection of notes, but this can't be right. Consider these two "scales":

C  D  E  F  G  A  B  C
D  E  F# G  A  B  C# D

Certainly they don't contain the same notes, so if a scale is just a collection of notes then these are two different scales. Yet in fact they're both examples of "the Major scale" in different keys. So in a sense these are both the same scale. What's "the same" about these two collections of notes that makes them both "the same scale"?

Let's look at the intervals -- that is the distances between the notes -- that the two scales contain. I'm only going to look at intervals between adjacent notes, and I'm just going to write the number of frets between them, so 1 is a semitone, 2 is a tone and so on. Here are the intervals in the first of the two Major scales given above:

C  D  E  F  G  A  B  C
  2  2  1  2  2  2  1

and here they are for the second Major scale, the one in the key of D:

D  E  F# G  A  B  C# D
  2  2  1  2  2  2  1

I hope you can see that these intervals are exactly the same: 2212221. It's this, not the pitches like C or C#, that makes a set of notes a Major scale. I call this list of intervals (like 2212221) the "interval map" of the scale. A moveable guitar fingering, if you think about it, is really just an interval map laid out on the fretboard for you.

A Mode is a "Rotation" of the Interval Map

Let's assume know know that there's something called the "Dorian scale" that in the key of D does like this:

D  E  F  G  A  B  C  D

This is not a Major scale. Why not? Look at the interval map:

D  E  F  G  A  B  C  D
  2  1  2  2  2  1  2

This is 2122212, which is quite different from 2212221. If 2212221 means "Major scale" then 2122212 means "Dorian scale", and the two are definitely not the same.

Yet anyone can see that the Dorian scale in D and the Major scale in C must have some kind of relationship -- after all, they contain the same notes! This relationship can be hard to see at first. I have a neat way to visualise it, but you'll have to trust me for a minute because at first it might look slightly weird.

Think of the 12 notes in the octave laid out in a circle, like this:

Each white bar represents a note, and from one bar to the next one around the circle is a semitone -- that is, one fret. We call the bar that's pointing straight up (at 12 o'clock, as it were) the "root note" of the scale, which by convention we put first when we're working out the notes it contains. [Note this has nothing at all to do with the order in which we play the notes in real life!]

If we start with that root note then we can make a Major scale by colouring in black the bars that the scale contains. We know the interval map is 2212221 so we colour the first bar, then skip one and colour the next one to create the first two-semitone interval, and so on around the clock-face, colouring intervals as we go:

If the 12 o'clock bar is C; skip C# and the next coloured bar is D. If the 12 o'clock bar is E instead, we skip F and find the next note in the Major scale is F#, then G#, then A and so on. The interval map gives us a recipe for colouring in the bars, and if we assign a pitch to the bar representing the root note then we can find all the other pitches automatically.

OK, let's do the same for the Dorian. Again we colour the 12 o'clock bar and then use the interval map to tell us which ones to colour as we work our way clockwise around it:

Look closely at these last two diagrams. Can you see that the second one is just the first one rotated around a little bit? Imagine turning the first one anticlockwise 2 steps and you'll see what I mean. This is the relationship called "modality": a scale is a mode of another scale if (and only if) you can rotate the interval map of the first to become the interval map of the second.

A less visual way to look at it is to think of "rotation" as "taking the first interval and moving it to the end", like this:

2212221          Major scale
 2122212         Dorian scale
  1222122        Phrygian scale
   2221221       Mixolydian scale
    2212212      Lydian scale
     2122122     Aeolian (Natural Minor) scale
      1221222    Locrian scale

If you think about it, this is just exactly what rotating the clockface representation does, as long as you always have a black bar pointing at 12 o'clock. [If you don't, you end up with a bunch of notes that don't have a root, which for now we don't allow].

A Scale Group is the Set Generated by Rotation

In the terminology of Scale and Arpeggio Resources, the group to which a scale belongs is the set of all scales that can be obtained by rotating some other member of the group in the way just described. In common parlance, scales that are in the same group are all modes of each other.

I mentioned before that a fingering for a scale is the interval map laid out on the fretboard. Well, you know that all the scales in a given group have the same interval map, but rotated in different ways. Unsurprisingly it turns out that they also all have the same fingerings only with some variations caused by the rotation. These variations aren't to do with where you put your fingers but how you find the mode in relation to the root of the underlying harmony. That's a topic for another day, although it isn't particularly complicated.

The point is that learning a fingering for a scale is pretty hard work, and you may as well get the most out of it. Once you know a fingering for one scale you also nearly know the fingerings for all the other scales in its group (i.e., all its modes); you just need to learn how to position them. This is an amazing timesaving device that will really help you if you embrace it. Beware, though: if you try to take the wrong kind of shortcut with modes you may find yourself regretting it later and having to do a lot of extra work to undo it.

I know all this seems a bit abstract and nerdy. I know it doesn't look like a quick way to get ripping up and down the fretboard and impressing your friends. Many, many good guitarists go through their entire lives without ever thinking about modes in this way. Yet ten minutes spent coming to terms with what it really means for two scales to be modes of each other will give you a rock-solid foundation for working will all kinds of advanced resources and for developing beyond just learning other people's licks.