The Dorian Brightness Quotient

Dorian Brightness Quotient

This is an article inspired by a great musician and YouTuber named Adam NeelyIn the linked video, the discussion turns to the idea of brightness and darkness in chords and scales and introduces the idea of the Dorian Brightness Quotient.

Simply put, the Dorian Brightness Quotient describes a scale’s brightness (or darkness) compared to the Dorian mode. Of course, there’s more to it than that, and more to discuss, so let’s get into it!


A Brief Intro to Brightness

The concept of brightness and darkness in music theory is applied to chords, scales, and harmony in general. Brightness is always relative!

Let’s look at some quick points:

Keys are bright or dark compared to other keys
  • Modulating keys clockwise around the circle of fifths brightens the sound.
  • Modulating keys counter-clockwise around the circle of fifths darkens the sound.
Modes are bright or dark compared to other modes
  • Raising scale degrees in a mode brightens the mode.
  • Lowering scale degrees in a mode darkens the mode.
Chords are bright or dark compared to other chords
  • Making the chord tone intervals larger brightens a chord.
  • Making the chord tone intervals smaller darkens a chord.

This is a brief intro to brightness but gets the point across, I hope 🙂

The Dorian Brightness Quotient is a way of determining the brightness or darkness of a heptatonic scale or mode


Back to Dorian

The Dorian Mode is best known as the second mode of the Major Scale and has the following scale degrees:

1        2      ♭3         4         5         6     ♭7

In terms of brightness and darkness, Dorian is considered neutral.

Yes, even though it contains both a minor triad and minor seventh chord. Remember that minor is darker than major, but brightness as a quality is relative, whereas minor and major are absolute qualities.

More on this later! First, let’s talk about the main focus of this article:

What is the Dorian Brightness Quotient?

The Dorian Brightness Quotient is a number we assign to a heptatonic scale (a scale containing 7 notes) which tells us how bright or dark the scale is relative to Dorian.

The Dorian Brightness Quotient (DBQ) is always an integer value. And it is either negative, positive, or zero.

The DBQ of a scale is determined by the number of scale degrees that are raised or lowered (sharp or flat) when compared to Dorian (having two flats and no sharps).

The lower the number, the darker the scale. The higher the number, the brighter the scale.

For example, the Aeolian Mode (Natural Minor) is made up of the following scale degrees:

1        2      ♭3         4         5     ♭6     ♭7

Aeolian has 1 more flat than Dorian and therefore has a DBQ of -1. It is one scale degree darker than Dorian!

Let’s look at another example in the Lydian Mode:

1        2         3     ♯4        5        6        7

Lydian has a DBQ of +3. The 3rd, 4th, and 6th degrees have been raised compared to Dorian. So Lydian is 3 scale degrees brighter than Dorian!

But Why is Dorian our reference point?

Since we write our scales as alterations to the Major Scale, why wouldn’t we keep with the same system and make the Major Scale our reference point? Thus making it the Ionian Brightness Quotient rather than the Dorian Brightness Quotient.

The answer comes in the “neutrality” of the Dorian Mode and in its palindromic nature (oh yeah there are palindromes in music theory!)

Jeff Brent explains this in his book Modalogy. The book is a bit theory intensive, as is this article. But I’ll try to break it down simply for you 🙂

By neutral, I mean the Dorian mode is not too dark, and not too bright.

The reason for this can be found in the Circle of Fifths:

Dorian Brightness Quotient

There are two directions we may take around the circle of fifths:

  1. Clockwise – The bright direction
  2. Counter-clockwise: The dark direction

Moving from C Major to G Major, we get brighter by one note (F becomes F♯). Notice in the circle of fifths that we moved one position clockwise (the brighter direction).


By the same token, let’s look at C Ionian in the circle of fifths. The root, C, is in orange and the other 6 notes of the C Ionian mode are in blue.

Dorian Brightness QuotientIn C Ionian, we have 1 “dark note” (counter-clockwise) and 5 “bright notes” (clockwise) from the root.

F Lydian is the 4th mode of C Major. Let’s restate our circle of fifths with F as our starting point:

Dorian Brightness Quotient

In F Lydian, we have no “dark notes” (counter-clockwise) and 6 “bright notes” (clockwise) from the root.

Lydian is one scale degree brighter than Ionian.

Notice how the brighter mode has more notes clockwise of its root?

In fact, Lydian is the brightest mode of the Major Scale (it only has notes clockwise of its root).

The Neutrality of Dorian

By looking now at D Dorian (again from C Major) on the Circle of Fifths, we can see that it has three notes in either direction of its root. Three “dark” notes and three “bright” notes. This is what gives Dorian its neutrality!

Dorian Brightness Quotient

It’s interesting to note which notes are on the bright and dark side of our root. Let’s take a look at the intervals on the bright and dark sides of our root, D:

On the “dark side” of D Dorian we have:
  • G (the perfect fourth of D)
  • C (the minor seventh of D)
  • F (the minor third of D)
And on the “bright side” of D Dorian we have:
  • A (the perfect fifth of D)
  • E (the major second of D)
  • B (the major sixth of D)

Since minor is darker than major, these intervals seem to check out!

We can even argue that the minor third is a darker interval than a minor seventh and that a major sixth is a brighter interval than a major second.

Back to the Dorian Brightness Quotient

So now that we’ve got a good primer on what the Dorian Brightness Quotient is, let’s look at how it applies to some of the heptatonic scales. We’ll take the scale degrees of a given scale/mode and assign a DBW.

Let’s reiterate the scale degrees of Dorian since it’s our reference:

1        2      ♭3         4         5         6     ♭7

Let’s start with the modes of the Major Scale:

Ionian: 1        2         3         4         5         6          7

Ionian has a raised 3rd and 7th degree compared to Dorian, so Ionian has a DBQ of +2.

Dorian: 1        2      ♭3         4         5         6     ♭7

Dorian is Dorian. There’s no difference in the scale degrees, so it has a DBQ of 0.

Phrygian: 1     ♭2     ♭3         4         5     ♭6     ♭7

Phrygian has a lowered 2nd and 6th degree compared to Dorian, so Phrygian has a DBQ of -2.

Lydian: 1        2         3     ♯4         5         6          7

Lydian has a raised 3rd, 4th and 7th degree compared to Dorian, so Lydian has a DBQ of +3.

Mixolydian: 1        2         3         4         5         6     ♭7

Mixolydian has a raised 3rd degree compared to Dorian, so Mixolydian has a DBQ of +1.

Aeolian: 1         2     ♭3         4         5     ♭6     ♭7

Aeolian has a lowered 6th degree compared to Dorian, so Aeolian has a DBQ of -1.

Locrian: 1     ♭2     ♭3         4     ♭5     ♭6     ♭7

Locrian has a lowered 2nd, 5th and 6th degree compared to Dorian, so Locrian has a DBQ of -3.

Let’s put these modes into a chart

Dorian Brightness Quotient

Now let’s rearrange the modes from brightest to darkest (the highest DBQ to the lowest DBQ):

Dorian Brightness Quotient

So we can see above that Lydian is the brightest mode and Locrian is the darkest mode of the Major Scale.

Up to here has pretty well been covered in my article on Brightness and Darkness.

But to add more value with the Dorian Brightness Quotient, let’s dive into some other heptatonic scales!

What About the other Heptatonic Scales?

Well, it’s sometimes difficult to determine the difference in brightness between two different parent scales. However, the Dorian Brightness Quotient can help us to determine the brightness of modes within a single scale. Let’s check out some favourite heptatonic scales of mine:

The Melodic Minor Scale

Here are the modes of the Melodic Minor Scale arranged from brightest to darkest:

Dorian Brightness Quotient

The Harmonic Minor Scale

Here are the modes of the Double Harmonic Major Scale arranged from brightest to darkest:

Dorian Brightness Quotient

The Harmonic Major Scale

Here are the modes of the Harmonic Major Scale arranged from brightest to darkest:

Dorian Brightness Quotient

The Double Harmonic Major Scale

Here are the modes of the Double Harmonic Major Scale arranged from brightest to darkest:

Dorian Brightness Quotient

Like I had mentioned, things can get a bit ambiguous between parent scales. For example, the Double Harmonic Major and Dorian both have a DBQ of 0, but it could be argued that the Double Harmonic Major is brighter since a major seventh chord is built on its scale degrees, whereas a minor seventh chord is built on Dorian’s scale degrees.

All ambiguity aside, there’s another reason we’ve chosen Dorian as a reference for determining brightness:

The Dorian Palindrome

We know by looking at the circle of fifths that stacking three fifths in both directions from the root gives us the Dorian mode. In D, stacking lower gives G C and F, while stacking higher gives A E, and B. Put these all together in one octave, and we have D Dorian:

D         E         F         G         A         B         C         D

Now, looking at the resulting intervals in this order, we have:

w-h-w-w-w-h-w
*w=whole step // h=half step*

Reverse or mirror those intervals and we have the same thing:

w-h-w-w-w-h-w

Dorian is a palindrome!

Which is another reason to consider Dorian “neutral.” When speaking in terms of intervals, Dorian is the same forwards as it is backwards.

This may seem pseudo-intellectual, but something really cool happens when we start assigning DBQs to modes within parent scales. Reversing a “bright” mode will yield an equally “dark” mode and vice versa.

Instead of calling this “reversing scales,” let’s refer to the process of reversing the order of intervals of a scale “mirroring”.

Mirroring Modes of the Major Scale

If we look at the other modes in the Major Scale and assign them a DBQ, we see something else that’s pretty neat.

Let’s again look at the modes of the Major Scale complete with their Dorian Brightness Quotients from brightest to darkest:

Dorian Brightness Quotient

 

So we know that Dorian mirrors Dorian (0 to 0). But +1 mirrors -1, as does +2 <-> -2 and +3 <-> -3.

Let’s quickly go through some proofs:

Mixolydian (+1) <-> Aeolian (-1)

Dorian Brightness Quotient

Ionian (+2) <-> Phrygian (-2)

Dorian Brightness Quotient

Lydian (+3) <-> Locrian (-3)

Dorian Brightness Quotient

It’s pretty neat that these modes mirror themselves perfectly to other modes within the same parent scale. And that the brighter the mode, the darker its mirror image.

I get into this in greater detail the article “Palindromic Scales and Mirror Modes.”

Recap

Dorian as a scale is a neutral reference for the brightness and darkness of other scales. The Dorian Brightness Quotient is a concrete number to show a scale’s brightness compared to Dorian.

We assign a Dorian Brightness Quotient to a scale by determining its scale degrees compared to Dorian (2 flats):

  • For every raised scale degree, +1 to the DBQ
  • For every lowered scale degree, -1 to the DBQ

In Closing,

The Dorian Brightness Quotient is a simple tool we can implement to rank a scale’s brightness.

How do you think about and use brightness and darkness in your music? And what do you think of the idea of the Dorian Brightness Quotient? It may seem a bit much, but it can be an interesting tool nonetheless.

As always, thanks for reading and for your support,

-Art

[kkstarratings]