The notes in the major scale are spaced in a funny way. Look at the white keys on the piano: some have black keys between them, other don't. But you can understand the major scale using the circle of fifths. Start with C. Go up a fifth and you get G. Go up another fifth and you get D. Go up another and you get A. Go up another and you get E. Go up another and you get B. Go up another and you get F. And these are the notes in the C major scale!
That sounds like satisfying explanation. But it's a lie!
I lied only at the end. When you go up a fifth from B, you don't get F. You get F#. So you don't get the notes in the major scale. You get the notes in another scale, called Lydian!
This is why George Russell argued that Lydian is more fundamental than the major scale.
Russell is the theorist who helped Miles Davis switch to a new style of jazz in Kind of Blue - the best-selling jazz album of all time. In his book The Lydian Chromatic Concept of Tonal Organization, Russell tried to redo harmony theory from the ground up. For a great explanation of Russell's ideas, watch the video.
But here's something else. In the modern system of modes, if you start the major scale at different points you get different scales or 'modes' called Ionian (major), Dorian, Phrygian, Lydian, Mixolydian, Aeolian (minor) and Locrian.
But in the old system of modes used in Gregorian chants, Ionian and Aeolian were missing!
That's right: the major and minor scales, which we consider the most important, were not on the list! They were only added in 1547 by a theorist named Heinrich Glarean.
So maybe major wasn't considered as important as Lydian???
(1/n)
I'm having trouble understanding the Gregorian system of modes. It's probably worth understanding, because it was used for EIGHT CENTURIES - much longer than everything we call Renaissance, Baroque and Classical music. But I don't think you can understand it without understanding how Gregorian chants work.
The Gregorian system had 4 "authentic" modes - Dorian, Phrygian, Lydian and Mixolydian - but also 4 "plagal" modes called Hypodorian, Hypophrygian, Hypolydian and Hypomixolydian. The authentic modes seem to correspond to the modern modes with the same names, but I don't understand the plagal modes.
Anyway, here's the thing: in the Lydian mode you were allowed to sing the fourth a half-tone lower. That's exactly what would turn the F# that I mentioned into an F, turning Lydian into the major scale! So you *could* sing a Gregorian chant in the major scale - but it considered an optional variant of Lydian!
I don't know how important this is. It may be more evidence for the idea that Lydian is in some ways more fundamental than major. Or maybe not. Only an expert on Gregorian chants could say.
But please don't think I've gone off the deep end. Lydian is *not* more important than major in modern Western music. It's used less often, and there's a damn good reason. That F I keep talking about is a fourth above C. The major scale has it, Lydian doesn't. And that fourth is really important in modern Western harmony!
You could say the 1, 4 and 5 are the "backbone" of modern Western harmony. They provide the simplest vibrational frequencies: the 5 vibrates 3/2 times as fast as the 1, and the 4 vibrates 4/3 times as fast.
(2/n)
Oh yeah - one last piece of evidence for this crazy theory that Lydian is secretly more major than major, like the power behind the throne. If you take the 7 modern modes and order them by "brightness", the Lydian mode is the brightest of all, while Ionian - that is, major - comes in second.
What's "brightness"? Basically it's a measure of how high the notes are in a scale that starts with a fixed note, like C. To get from Lydian to Ionian you lower the fourth a half-step, turning F♯ to F in this chart. To get from Ionian to Mixolydian you lower the seventh a half-step, turning B to B♭. And it keeps going like that: you keep flatting more notes, going to "darker" modes.
In bright modes the notes are "pushed up". In dark modes the notes are "pushed down". Once you listen enough you get the idea. Bright modes aren't always "happier", but they are higher, more "celestial". Dark modes aren't always "sadder", but they are further down.
Another fun thing about Lydian is that the two half-steps occur right before the 5 and the 1. The half-step before the 1 is important in classical music: it's called the "leading-tone" because there's an intense pressure to go up a half step from that note to the 1, which brings a sense of rest: this has been the real motor of Western music ever since the Renaissance. The 5 is the second most important note after the 1, since 3/2 is the simplest fraction bigger than 1. So, having a half-step right before the 5 is almost like having another leading tone, given the importance of the 5.
Anyway, these patterns are fun to think about.
(3/n, n = 3)
@johncarlosbaez something about Lydian I only realised recently is made very clear by that diagram above.
Suppose, in the top row, you treat F# as a “natural” and colour it white instead of orange. Then under F# there would be a blue column of F starting in the second row and going all the way down, giving two blue staircases of flatted notes as you move through the modes. Much more pleasing (even more so if you renamed F# to F and F to Fb).
@johncarlosbaez Furthermore, which note is flatted cycles through the circle of fifths. If you continue the pattern past the bottom row the next note to be flattened would be the C down to a B, creating a B Lydian scale. So the whole pattern through the modes repeats a half step down.
@mdreid - EXCELLENT observations! I will probably turn my posts here into a blog article, and I'll try to make a chart like you're suggesting. The pattern of blue columns becomes much more systematic and pleasing that way!
I'd heard that the patterns of notes that get flatted circles though the cycle of fifths but it was quite a while ago, when I was too inexperienced to absorb it. I still don't see why this automatically follows from other facts (though in some sense it must).
It's great how flatting the C of Locrian takes you around to Lydian. It reminds me of an endlessly falling sandpile, where one grain slips down after another. (I'm having trouble expressing this....)
@johncarlosbaez Yet another nice feature of Lydian appears if you think of it as a chord instead of a scale.
Take C Lydian and note Cmaj7 is the usual major + minor + major pattern. The upper extensions to Cmaj7 in Lydian form a D chord: F# A (9, #11, 13). This continues the alternating major/minor pattern after the Cmaj7. Continuing that pattern further creates a Dmaj7 with its upper Lydian extensions (E = 9th, G# = #11th, B = 13th) – an E chord.
@johncarlosbaez So you get a series of overlapping maj13 (#11) Lydian chords: C, then D, E, F#, G#, and through all 12 keys.
@johncarlosbaez I was thinking about modes again recently and found what may be an even nicer way of organising them via the circle of fifths:
- Start at C, take it and the next 6 notes going clockwise: C G D A E B F# = Lydian
- Start at C, take it, one note CCW, and 5 notes CW: F C G D A E B = Ionian
- C + 2 notes CCW + 4 notes CW: Bb F C G D A E = Mixolydian
So each mode is a contiguous piece of the circle containing the root. More CCW = “darker”, more CW = “brighter”.
@johncarlosbaez I’m sure this must be common knowledge to those who know more music theory than me but I haven’t seen it described this way before.
It makes much more sense to me in terms of certain modes being brighter and darken too since “more fifths” = “brighter” and “more fourths” = “darker”.
@johncarlosbaez I also realised you can think about pentatonic scales like this too.
Taking C and 4 more notes clockwise gives C major pentatonic.
Taking C, 3 notes CCW, and 1 note CW gives the C minor pentatonic.
This suggests C plus 4 notes CCW would be a “darker” pentatonic mode than the minor pentatonic (in fact it’s F minor pentatonic starting on the 4th degree = Ab major pentatonic from the 3rd degree).