Sep 27

Rootless Scales & Phantom Modes

by Anton Schwartz

The root of a scale, also called the tonic, is the most important note of the scale—the note after which the scale is named, and relative to which the whole scale is understood.

In conventional music theory, the root is always one of the notes of the scale: namely, the first note when the scale is written ascending or descending. So every E scale begins with E.

In this post I’m going to challenge that convention. I’ll propose that we allow scales not to contain their root. Why? Because it makes our terminology more consistent and, above all, because it’s so USEFUL. First some background…

Background: Scales

Before we meddle with such an important concept, let’s take a step back and remind ourselves: what is a scale, and what use does it serve?

(If you’re impatient to cut to the chase I’ll make it easy for you to skip the details here.)

What is a scale?

A scale is a set of notes relative to one special note we call the root.

The Details (click to read)

There are two parts to the above definition:

  1. A scale specifies a set of notes. A set means that we include each note only once. And we use octave equivalence in the notion of a note: notes that differ exactly by one or more octave are only counted once.
  2. A scale specifies a root. One note is designated as the reference point of the scale, after which the scale is named. For example: the white notes on a piano, ignoring octave, form a set of seven notes: A, B, C, D, E, F, G. To speak of these notes as a scale, we must select a root, which we always write as the first note of the scale. For instance, if we choose C as the root, then we have the C major scale (C, D, E, F, G, A, B). If we designate E to be the root, then the scale is E Phrygian (E, F, G, A, B, C, D). Without a designated root, the white notes of the piano are neither major nor minor. Without a root, they are not a scale.

Note that nowhere in the definition above do we stipulate that the root must be chosen from the notes of the scale. It must because of this third convention:

  1. A scale is written by listing its notes in chromatically ascending order, starting with the root. This implies, of course, that the root is one of the notes in the scale.

What use is a scale?

A scale is more than something your teacher tells you to practice. 🙂

The Details (click to read)

A scale designates a particular sound. It tells us which notes we can play to evoke that sound, and which note is the reference note that gives harmonic meaning to what we play. We can compose melodies with a scale or improvise using a scale.

In either case, we needn’t restrict ourselves exclusively to those notes; but other notes reflect just momentary departures from the scale—quick deviations like chromatic approach notes, or laonger deviations reflecting passing harmonies. But the scale remains the primary palette.

Going Rootless

The crux of the argument is simple: Scales are a way of specifying which notes are to be used, and sometimes we don’t want to use the root.

DEFINITION:
A ROOTLESS SCALE is a set of notes (“the notes in the scale“), along with a designated root that is not in the scale.

So every scale still has a root. But what sets “rootless” scales apart is that the root is not a member of the scale. Let’s look at an example.

Pentatonic Examples

The major pentatonic scale is one of the world’s most widely used scales—for both melodies and improvisations. It is a 5-note scale representing the major scale with its brightest and darkest notes removed. (See here for a discussion of bright & dark.) In the key of C, the darkest note of the major scale is F (the fourth) and the brightest note is B (the seventh). So the C major pentatonic is the C major scale without F or B—namely C, D, E, G, A.

For a slightly brighter sound in the key of C, one might want to include the major seventh, B… by using the 5 brightest notes of the C major scale. Those notes are D, E, G, A, B. And in fact that is a common choice of scale over a C or Cmaj7 chord. The catch? It doesn’t contain a C. That’s because C is the second darkest note of the C major scale. In order for the scale to include the five brightest notes, it must omit the root, C. What do we call this scale? The simplest conventional name is: “G major pentatonic over C.”

While that name makes sense, I put forth that it’s needlessly long, and also misleads the student to thinking that there’s something unusual going on—some sort of superimposition or polytonality. By contrast, look at “Eb major pentatonic over C.” That has a special name: C minor pentatonic. Likewise with all the modes of the major scale and melodic minor scale. Instead of referring to “F major over C” we say “C Mixolydian.” “G melodic minor over C” we call “C Lydian dominant.” So why are we forced to say “G major pentatonic over C” instead of, say, “C major 7 pentatonic.” Simply because it does not contain a C?

Phantom Modes

Background: Conventional Modes

Many, many scales that we use can be described as a common scale over an alternate root. And in most cases, we call those modes of the common scale, because the alternate root belongs to the common scale in question. Because convention has that scales start on their root, we often describe a mode as “Scale X starting on note Y.” Or we may specifically call them “the nth mode of X scale” (that is, the 1st mode or 2nd mode or 3rd mode, etc.) to mean “Scale X starting on its nth note.” Very often these modes have special names, such as Aeolian and Altered and Phrygian Dominant.

Leveraging the Modes

The concept of a mode is very useful. Each mode of a scale tells us a distinct way we can use the scale’s notes so as to convey a unique sound. Looking at the scale’s notes on the circle of fifths, with the bright notes clockwise of the root and the dark notes counterclockwise of the root, it’s easy to see how changing the root can make the scale sound brighter or darker. (See Harmonic Brightness & Darkness.)

To revisit our pentatonic example above: take C, D, E, G, A—the notes of a C major pentatonic.

  • Relative to a bright root such as A (bright in that it is toward the clockwise end of the group), most of the other the notes are dark (counterclockwise), so they form a dark scale: the minor pentatonic.
  • D is in the middle of the notes on the circle of fifths, so choosing it as the root gives us a scale that is neither bright nor dark, containing neither a major nor minor third. This is called the sus pentatonic and is perfect for sus chords.
  • C is the darkest of the notes, so with a root of C the notes become a bright scale—the major pentatonic.

Leveraging them Further

When we want a sound that is still brighter still, we can pick a root that is darker than C, such as F or Bb. These give us very useful scales, ideal for major 7 chords and major 7(♯11) chords, respectively. Unfortunately, obeying convention, we can’t call them modes of the original scale because their roots aren’t contained in the scale. Think about it: what would it mean to have a scale that starts on a note that isn’t even in the scale! 🤣

I propose the following…

DEFINITION:
A PHANTOM MODE of a scale is a scale with the same notes, taken relative to a root that is not in the scale.

The scales above are examples of two phantom modes:

Phantom Mode Definition
“C Major 7 Pentatonic”G Major Pentatonic over C
“C Lydian Pentatonic”D Major Pentatonic over C

Key-Independent Names

It’s nice to be able to say the “Major Scale” which doesn’t specify a key, but still tells us the relationship of each note in the scale to the root. Similarly, we can say “the 3rd mode of the major scale” to refer to a particular scale, without committing to what key it’s in.

In the case of the major pentatonic scales, some of the modes have common names, while others do not, but each can be referred to as the nth mode of the major pentatonic:

Scale Which mode
of major pentatonic
The New Root*
relative to original root
Scale Degrees*
relative to new root
bright / dark
Major Pentatonic1st(unchanged)root, 2, 3, p5, 6brightest
Sus Pentatonic2nd2root, 2, p4, p5, m7middle
(3rd mode)
uncommon
3rd3root, m3, p4, m6, m7darkest
(4th mode)
uncommon
4thp5root, 2, p4, p5, 62nd brightest
Minor Pentatonic5th6root, m3, p4, p5, m72nd darkest
*p=perfect, m=minor, unlettered=major.

About the Audio

Throughout this post, the audio samples are brief, random melodies using the respective scales, generated by the ScaleMate app for iOS. Feel free to use them to hear the scales… and to try out ScaleMate, which fully supports rootless scales and phantom modes.

Let’s add the two phantom modes to our table:

Rootless Scale Which mode
of major pentatonic
The New Root*
relative to old root
Scale Degrees*
relative to new root
bright / dark
“Major 7 Pentatonic”(phantom)p42, 3, p5, 6, 7even brighter than major pentatonic
“Lydian Pentatonic”(phantom)m72, 3, ♯4, 6, 7brightest of all
* p=perfect, m=minor, unlettered=major.
not contained in major pentatonic scale

For these phantom modes, the “nth mode” description isn’t an option. This makes it all the more appealing to give them their own names as full-fledged scales. Otherwise, the only key-independent options available are awkward descriptions like “major pentatonic built on the fourth.”

I’ve argued separately elsewhere that the nth mode notation is a poor way of organizing the modes. For example, the third mode of the major scale is Phrygian, a very dark mode, but the third mode of the melodic minor scale is Lydian Augmented, an extremely bright scale… so to say a scale is the 3rd mode (or, more generally, the nth mode) of another scale tells us nothing about what it will sound like.

By contrast, the third column is very informative. Note that the darker a degree in column 3, the brighter its corresponding ranking in column 5, and vice versa. (That’s because relative to a dark root, all the other notes look bright.) So ranking the modes by the brightness/darkness of their new root relative to the original root makes a lot of sense.

A Few Rootless Scales

Phantom Major Pentatonic Modes

We’ve already seen the following two bright phantom modes of the major pentatonic scale, to which we add a very dark one:

Rootless Scale The New Root*
relative to original root
Scale Degrees*
relative to new root
Uses
“Major 7 Pentatonic”p42, 3, p5, 6, 7 Cmaj7, Cmaj9
“Lydian Pentatonic”m72, 3, ♯4, 6, 7 Cmaj7, Cmaj9, Cmaj7(11)
“Locrian Pentatonic”5m2, m3, 5, m6, m7 Cm75, C7alt
* p=perfect, m=minor, unlettered=major.
not contained in major pentatonic scale

The Insen Pentatonic

Let’s also take a look at Insen, a Japanese pentatonic scale that serves as a valuable source scale for modes, both conventional and rootless. It is the same as the sus pentatonic scale, above, except that its second degree is lowered a half step, making it a perfect choice for sus(b9) chords.

Here we see the Insen scale itself, followed by two useful phantom modes of Insen:

Rootless Scale The New Root*
relative to root of Insen
Scale Degrees*
relative to new root
Uses
Insen(unchanged)root, m2, p4, p5, m7 C7susb9
“Insen Altered”6 m2, m3, 3, m6, m7
(b9, #9, 3, b13, m7)
C7alt
“Dominant 13 Pentatonic”m32, 3, p5, 6, m7 C7, C9, C13,
* p=perfect, m=minor, unlettered=major.
not contained in Insen scale

(Incidentally, if you’re wondering why Insen works well for melodic minor modes like Altered & Lydian Dominant—and others too—check out the 5th mode Insen, starting on its m7. 🙂)

Not Just Pentatonics

So far our rootless scales have all been pentatonics. One can see why rootless seven-note scales might be less common. For starters, pentatonic scales have only five notes with which to convey harmony, so it stands to reason that one might not want to “waste” one of them on the root, especially in settings such as jazz where the root is likely to be played by the bass.

Here’s an additional reason why seven-note scales are likely to contain the root. Unlike pentatonics, most seven-note scales are built from half-steps and whole-steps. If a scale consists of no interval larger than a whole step, then for it not to contain the root, it must contain the two notes chromatically adjacent to the root: the major seventh and the minor second. But it would be hard to see the rationale of including both a note so bright as the major seventh AND a note so incredibly dark as the minor second in the same scale.

Super Lydian

One exception to this is when the minor second is used as an extremely bright note. In this case we refer to it as the ♯15 because it is the major seventh of the upper structure chord built on the 9, which contains the ♯11 and 13. Also because it is a fifth above the ♯11, making it the next in the series of notes that start at the root and grow progressively brighter around the circle of fifths.

When we take the Lydian scale and replace the root with the ♯15 a half-step higher, the result is a rootless scale one “notch” brighter than the brightest mode of the major scale, Lydian. We can call this scale “Super Lydian”. It is the phantom mode of the major scale relative to the minor 7th—which is to say that when you take a D major scale and play it over a C root, the result is a Super Lydian scale. Listen:

The Super Lydian Scale (example)

Why doesn’t convention allow rootless scales?

You might wonder: if rootless scales are so useful, why doesn’t standard terminology allow for them?

It’s impossible to know, but here are a few ideas.

  1. Scales are what we practice. Rootless scales are complicated to practice.
    When we practice a scale we not only practice playing it but hearing it too. Mostly when musicians practice scales they are playing them alone… which means that if the scale does not include the root, the musician practicing a scale without accompaniment never gets to hear the root at all. Imagine never getting to hear the one sound that gives meaning to the whole scale! By contrast, when a scale does include the scale it is always the first note, so that when a scale is practiced the context-setting root is played first. And first is exactly how it needs to be played in order to set the context.
  2. Avoiding difficult questions.
    What exactly is the root?
    Perhaps it’s: the primary, prevailing sound in the ears of the listener?
    Or maybe: the note that serves as a reference in relation to which all the other notes have their meaning?
    For such an essential concept, the root sure is hard to define!!
    BUT, if we decide that scales all start with the root, then we can define the root as the first note of the scale. Or the lowest note in the scale. Either way, we avoid the deep question altogether of the root’s meaning, replacing it with essentially this: the root of a scale is the first note I play when I practice the scale. Pretty sneaky, huh? An invaluable dodge for music educators everywhere.
  3. The issue never came up.
    Maybe the best reason is the simplest: it’s never been an issue. In all the popular idioms of Western music, the root has been an essential part of melody making, never something one would want have a way to systematically avoid.

OK, what now?

Rootless scales may be odd to look at (when you write them out, what note should they start on?) but they’re pretty easy to use and to talk about. So I suggest you try one on for size and see if you like it. How about the “major 7 pentatonic”. Sure, you can think of it as a G pentatonic that you play over a Cmaj7 chord, but instead try thinking of the notes relative to C major. That gives you the advantage of hearing a 9th and being able to think “the 9th of C” rather than having to think of it as a 5th (of G). Try it out as a C scale for a while and see if you start to like it. If you do, there are plenty others waiting for you.

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