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Modes | Azimuth

I’ve been away from my piano since September. I really miss playing it. So, I’ve been sublimating my desire to improvise on this instrument by finally learning a bunch of basic harmony theory, which I practice just by singing or whistling.

For example, I’m getting into modes. The following 7 modes are all obtained by taking the major scale and starting it at different points. But I find that’s not the good way for me to understand the individual flavor of each one.

Much better for me is to think of each mode as the major scale (= Ionian mode) with some notes raised or lowered a half-step — since I already have an intuitive sense of what that will do to the sound:

For example, anything with the third lowered a half-step (♭3) will have a minor feel. And Aeolian, which also has the 6th and 7th lowered (♭6 and ♭7), is nothing but my old friend the natural minor scale!

A more interesting mode is Dorian, which has just the 3rd and 7th notes lowered a half-step (3♭ and 7♭). Since this 6th is not lowered this is not as sad as minor. You can play happy tunes in minor, but it’s easier to play really lugubrious tear-jerkers, which I find annoying. The major 6th of Dorian changes the sound to something more emotionally subtle. Listen to a bunch of examples here:

Some argue that the Dorian mode gets a peculiarly ‘neutral’ quality by being palindromic: the pattern of whole and half steps when you go up this mode is the same as when you go down:

w h w w w h w

This may seem crazily mathematical, but Leibniz said “Music is the pleasure the human mind experiences from counting without being aware that it is counting.”

Indeed, there is a marvelous theory of how modes sound ‘bright’ or ‘dark’ depending on how many notes are sharped—that is, raised a half-tone—or flatted—that is, lowered a half-tone. I learned about it from Rob van Hal, here:

The more notes are flatted compared to the major scale, the ‘darker’ a mode sounds! The fewer are flatted, the ‘brighter’ it sounds. And one, Lydian, is even brighter than major (= Ionian), because it has no flats and one sharp!

So, let’s list them from bright to dark. Here’s a chart from Rob van Hal’s video:

You can see lots of nice patterns here, like how the flats come in ‘from top down’ as the modes get darker: that is, starting at the 7th, then the 6th and then the 5th… but also, interspersed with these, the 3rd and then the 2nd.

But here’s something even cooler, which I also learned from Rob van Hal (though he was surely not the first to discover it).

If we invert each mode—literally turn it upside down, by playing the pattern of whole and half steps from the top of the scale down instead of from bottom to top—the brighter modes become the darker modes, and vice versa!

Let’s see it! Inverting the brightest, Lydian:

w w w h w w h

we get the darkest, Locrian:

h w w h w w w

Inverting the 2nd brightest, the happy Ionian (our familiar friend the major scale):

w w h w w w h

we get the 2nd darkest, Phrygian:

h w w w h w w

Inverting the third brightest, Mixolydian:

w w h w w h w

we get the third darkest, the sad Aeolian (our friend the natural minor):

w h w w h w w

And right in the middle is the palindromic Dorian:

w h w w w h w

What a beautiful pattern!

By the way, it’s also cool how both the ultra-bright Lydian and the ultra-dark Locrian, and only these modes, have a note that’s exactly half an octave above the 1. This is a very dissonant thing for a mode to have! In music jargon we say it like this: these modes have a note that’s a tritone above the tonic.

In Lydian this note is the sharped 4th, which is a ‘brighter than usual 4th’. In Locrian it’s the flatted 5th, which is a ‘darker than usual 5th’. But these are secretly the same note, or more technically ‘enharmonic equivalents’. They differ just in the role they play—but that makes a big difference.

Why do both Lydian and Locrian have a note that’s a tritone above the tonic? It’s not a coincidence: the tritone is mapped to itself by inversion of the octave, and inversion interchanges Lydian and Locrian!

This stuff is great, especially when I combine it with actually singing in different modes and listening to how they sound. Why am I learning it all just now? Because normally when I want to think about music I go to the piano and start playing!

More on individual modes

For music, more important than the mathematical patterns relating different modes is learning the ‘personality’ of individual modes and how to compose or improvise well in each mode.

Here are some introductions to that! Since I’m in awe of Rob van Hal I will favor his when possible. But there are many introductions to each mode on YouTube, and it’s worth watching a lot, for different points of view.

Locrian is so unloved that I can’t find a good video on how to compose in Locrian. Instead, there’s a good one on how Björk created a top 20 hit that uses Locrian:

and also a good one about Adam Neely and friends trying to compose in Locrian:


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