Modes and Fretboard Geometry

This post came about because of a reader's request by email, referring to an unfulfilled promise at the end of this venerable post. There I said I wanted to get round to writing about how the abstract picture of modes can translate into something concrete on the fretboard.

At the risk of being self-indulgent, I suggest looking through the original post so I don't have to rehearse all that here. The relevant paragraph is:

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.

So, my claim is that thinking about modes as "rotations of the interval map" is not just intellectually satisfying but useful in practice. That's what I'll try to spell out here.

Look at this pattern of notes on the fingerboard:

If you recognise it, pretend you don't for now. Just see it as a visual pattern of notes you could play. Feel free to position the pattern at any fret you like, it won't matter for this exercise. Forget about key, harmony, chords etc -- none of that matters either.

What does the pattern represent? Not the notes, because you can play it at any fret and get a variety of different notes. The structure of the pattern isn't the notes but the distances between them -- the intervals. Look at the steps you take when you play from the lowest note to the highest:

Here red indicates a whole step (two semitones) and green a half step (one semitone). The sequence from top to bottom goes whole-whole-half-whole-whole-whole-half. If you play it in a mindless, noodling kind of way you'll conjure up a certain sound-world that's defined purely by that particular sequence of intervals.

You probably know that the major scale is defined by the sequence whole-whole-half-whole-whole-whole-half. So is that fretboard pattern a "major scale pattern"? No it isn't! Why not? Because the major scale is neither of these things:

  • A sequence of notes that must be played in a specified order
  • An interval structure that starts from the lowest-pitched note in a collection

It is perfectly possible to play a major scale with the notes all mixed up (this is almost a basic prerequisite for making music with it at all), and to play a melody in which the root note is not the lowest-pitched.

What turns this pattern into a major scale is the declaration that the first and last notes are the root:

If you make the red note an F#, the pattern contains all and only the notes of the F# major scale. But there is nothing magical about making the root the first and last notes of the pattern. For example, suppose we were to fill out this pattern to cover all the major scale notes we can reach in this position (there's more than one way to do this):

A way to do this in this case is to follow the interval pattern going downwards from the root on the high E string, and copy those same intervals going down from the root on the G string.

The resulting pattern starts and ends on different notes, so we can't say the lowest and highest pitches are the root. We have to just pick one and stick with it.

Let's pick a different note in the pattern and make it the root instead:

We have to pick all the others that are the same pitch class -- i.e. all the notes that are "the same note up or down an octave" -- in this case there's only one more:

Now we already know that the interval map of this scale will be the same as the one we started with, except the first interval has been moved to the end:

these arrows are exactly the same as the previous ones -- tone tone semitone tone tone tone semitone. Conventionally we usually write them down starting with the first interval after the root, in which case we would have tone semitone tone tone tone semitone and then another tone at the end to take us back to the root. This is the interval structure of the Dorian scale.

Now, what's changed? What is the actual difference between the major and Dorian scales? As long as we're only looking at patterns of notes on the fingerboard, the answer is "nothing". And if we're playing music that gives no significance to a "root note" -- such as some strictly atonal music -- the answer is still "nothing". They're the same thing. There's only a difference if the red or blue note in the patterns above is in some sense functioning as a "root note", which can mean different things in different contexts but is a "musical context thing", not an isolated "scale structure thing".

(Note that functioning as a root note is not the same as functioning as a tonic. Even in a tonal context like G7-C, the G in G7 is the root note but C is the tonic throughout. And it's quite possible to have chords with root notes but no overall tonal centre.)

If root notes do mean something to you, simply take this pattern of notes (or any other) and pick one to act as the root note. This is what I call a scale. If you pick another root note, you get a different scale that's a mode of the first one. That's what's explained in the old post.

Finally, what if you choose a root note that isn't in the pattern, such as this green one?

Here we get what I call a "hypermode" -- a perfectly good scale, in a way, it's just that the pattern doesn't contain the root note. This is actually really common practice in jazz with things like extended applications of arpeggios or the common pentatonic scale.

From a practical perspective there's very little difference between "normal" modes and hypermodes; you have a pattern, and you have a root note, and you put them together to get something you can play. And of course you can play anything you like; the important thing is that the pattern has a certain sound (because of its interval structure) and so as you "suspend" it over different root notes you get a family of sounds that all have a kind of common resemblance.