Chord pizzas

The Groove Pizza uses geometry to help visualize rhythms. The MusEDLab is planning to create a similar tool for visualizing music theory by merging the aQWERTYon with the Scale Wheel. When you put the twelve pitch classes in a circle, you can connect the dots between different notes in a chord or scale to form shapes. My hypothesis is that seeing these shapes along with hearing the notes will help people learn music theory more easily. In this post, I’ll talk through some concept images.

First, let’s look at two different ways to represent the pitch classes on a circle. On the left is the chromatic circle, showing the notes in the order of pitch height (the way they are on a piano keyboard.) On the right is the circle of fifths. These two circles have an interesting relationship: the circle of fifths is the involute of the chromatic circle. Notice that C, D, E, G-flat, A-flat and B-flat are in the same places on both circles, while the other six notes trade places across the circle. Pretty cool!

The chromatic circle and the circle of fifths

The colors represent the harmonic function of each note relative to the root C. Purple notes are perfect (neither major nor minor.) Green notes are major or natural. Blue notes are minor or flatted. You could technically think of, say, B-flat as being the sharp sixth rather than the flat seventh, but that usage is rare in real life. G-flat is a special case–it’s equally likely to be the sharp fourth or flat fifth. I represented this ambiguity by making it blue-green. (We could make it blue if we knew it was flat fifth from Locrian mode, or green if it was the sharp fourth from Lydian mode.)

Once the Scale Wheel and aQWERTYon get combined, then whenever you play more than one note at a time, they will be connected on the circle. Here are some common chord progressions, and what their shapes can tell us about how they function. First, let’s look at the I-vi-ii-V jazz turnaround in C major.

Major scale chords

Seeing things on the circle really helps you understand the voice leading. You can see how the notes move very little from one chord to the next. To get from Cmaj7 to Am7, you just move the B to A while keeping the other three notes the same. To get from Am7 to Dm7, you move the G to F and the E to D while keeping the other two notes the same. To get from Dm7 to G7, you move the A to G and the C to B while keeping the other two notes the same. Finally, to get from G7 back to Cmaj7, you move the D to C and the F to E while keeping the other two notes the same. In general, any chord you can produce by moving the notes as little as possible from the current chord is likely to sound smooth and logical.

The pitch circle doesn’t represent musical “real life” perfectly–while pitch classes are circular, actual notes belong to specific octaves. That makes the voice leading harder to figure out, because you will need to introduce some jumps or additional chord voices to make it work. That said, thinking in terms of pitch class rather than pitch makes it easier to learn the concept; then you can work out the logistics of voice leading actual pitches from a place of understanding.

Next, let’s look at the Mixolydian mode I-bVII-IV-I turnaround that’s ubiquitous in rock, e.g. the “na na na” section in the Beatles’ “Hey Jude.”

Mixoydian mode chords

The circle of fifths view is more clear here. Getting from the Bb to the F is just a matter of rotating the little triangle clockwise by one slot. If you voice the C7 chord like a jazz musician and leave out the G, then the voice leading in this progression becomes exquisitely clear and simple.

Finally, here’s a more exotic-sounding progression from Phrygian dominant, the I-bvii you hear in Middle Eastern and Jewish music like “Hava Nagilah.”

Phrygian dominant mode chords

Seeing these chords on the circle of fifths is not very enlightening–while Western functional harmony keeps things close together on the circle of fifths, non-Western harmony jumps around a lot more. But on the chromatic circle, you can see exactly what’s happening: To get from C7 to Bb-7, B-flat stays the same, but all the other notes move one scale degree clockwise. To get from Bb-7 back to C7, B-flat stays the same while the other notes move one scale degree counterclockwise. This is very close to the way I conceptualize this progression in my head. It’s like the notes in Bb-7 are lifting or pulling away from their homes in C7, and when you release them, they snap back into place. You could also think of this progression as being iv-V7 in the key of F minor, in which case the Bb-7 is acting more like C7sus(b9 #5). Here the suspension metaphor makes even more sense.

Beyond the fact that it looks cool, seeing geometric representations of music gives you insight into why it works the way it does. The main insight you get from the circles is that perfect symmetry is boring. On the Groove Pizza, squares and equilateral triangles produce steady isochronous rhythms, like the four on the floor kick drum pattern. These rhythms are musical, but they’re boring, because they’re perfectly predictable. The more exciting rhythms come from shapes that don’t evenly fit the metrical grid. On a sixteen-step grid, pentagons produce clave patterns, while hexagons make habanera and tresillo.

The same concept applies to the pitch wheel. A square on the pitch wheel is a diminished seventh chord; an equilateral triangle is an augmented triad; and a hexagon is a whole tone scale. (Interestingly, this is true both on the chromatic circle and the circle of fifths.) These sounds are fine for occasional use or special effects, but they get tedious very quickly if you repeat them too much. By contrast, the harmonic devices we use most commonly, like major and minor triads and seventh chords, are uneven and asymmetrical. The same uneven seven-sided figure produces the major scale and its modes on the pitch wheel, and the “standard bell pattern” on the Groove Pizza. Food (ha) for thought.

The aQWERTYon pitch wheels and the future of music theory visualization

The MusEDLab will soon be launching a revamped version of the aQWERTYon with some enhancements to its visual design, including a new scale picker. Beyond our desire to make our stuff look cooler, the scale picker represents a challenge that we’ve struggled with since the earliest days of aQW development. On the one hand, we want to offer users a wide variety of intriguing and exotic scales to play with. On the other hand, our audience of beginner and intermediate musicians is likely to be horrified by a list of terms like “Lydian dominant mode.” I recently had the idea to represent all the scales as colorful icons, like so:

Read more about the rationale and process behind this change here. In this post, I’ll explain what the icons mean, and how they can someday become the basis for a set of new interactive music theory visualizations.

Musical pitches rise and fall linearly, but pitch class is circular. When you go up or down the chromatic scale, the note names “wrap around” every twelve notes. This naming convention reflects the fact that we hear notes an octave apart as being “the same”, probably because they share so many overtones. (Non-human primates hear octaves as being equivalent too.)

chromatic circle

The note names and numbers are all based on the C major scale, which is Western music’s “default setting.” The scale notes C, D, E, F, G, A and B (the white keys on the piano) are the “normal” notes. (Why do they start on C and not A? I have no idea.) You get D-flat, E-flat, G-flat, A-flat and B-flat (the black keys on the piano) by lowering (flatting) their corresponding white key notes. Alternately, you can get the black key notes by raising or sharping the white key notes, in which case they’ll be called C-sharp, D-sharp, F-sharp, G-sharp, and A-sharp. (Let’s just briefly acknowledge that the imagery of the “normal” white and “deviant” black keys is just one of many ways that Western musical culture is super racist, and move on.)

You can represent any scale on the chromatic circle just by “switching” notes on and off. For example, if you activate the notes C, D, E-flat, F, G, A-flat and B, you get C harmonic minor. (Alternatively, you could just deactivate D-flat, E, G-flat, A, and B-flat.) Here’s how the scale looks when you write it this way:

C harmonic minor - monochrome

This is how I conceive scales in my head, as a pattern of activated and deactivated chromatic scale notes. As a guitarist, it’s the most intuitive way to think about them, because each box on the circular grid corresponds to a fret, so you can read the fingering pattern right off the circle. When I think “harmonic minor,” I don’t think of note names, I think “pattern of notes and gaps with one unusually wide gap.”

Another beauty of the circle view is that you can get the other eleven harmonic minor scales just by rotating the note names while keeping the pattern of activated/deactivated notes the same. If I want E-flat harmonic minor, I just have to grab the outer ring and rotate it counterclockwise a few notches:

E-flat harmonic minor

My next thought was to color-code the scale tones to give an indication of their sound and function:

C harmonic minor scale necklace

Here’s how the color scheme works:

  • Green – major, natural, sharp, augmented
  • Blue – minor, flat, diminished
  • Purple – perfect (neither major nor minor)
  • Grey – not in the scale

Scales with more green in them sound “happier” or brighter. Scales with more blue sound “sadder” or darker. Scales with a mixture of blue and green (like harmonic minor) will have a more complex and ambiguous feeling.

My ambition with the pitch wheels is not just to make the aQWERTYon’s scale menu more visually appealing. I’d eventually like to have it be an interactive way to visualize chords too. Followers of this blog will notice a strong similarity between the circular scale and the rhythm necklaces that inspired the Groove Pizza. Just like symmetries and patterns on the rhythm necklace can tell you a lot about how beats work, so too can symmetries and patterns on the scale necklace can tell you how harmony works. So here’s my dream for the aQWERTYon’s future theory visualization interface. If you load the app and set it to C harmonic minor, here’s how it would look. To the right is a staff notation view with the appropriate key signature.

When you play a note, it would change color on the keyboard and the wheel, and appear on the staff. The app would also tell you which scale degree it is (in this case, seven.)

If you play two notes simultaneously, in this case the third and seventh notes in C Mixolydian mode, the app would draw a line between the two notes on the circle:

If you play three notes at a time, like the first, fourth and fifth notes in C Lydian, you’d get a triangle.

If your three notes spell out a chord, like the second, fourth and sixth notes in C Phrygian mode, the app would recognize it and shows the chord symbol on the staff.

The pattern continues if you play four notes at a time:

Or five notes at a time:

By rotating the outer ring of the pitch wheel, you could change the root of the scale, like I showed above with C harmonic minor. And if you rotated the inner ring, showing the scale degrees, you could get different modes of the scale. Modes are one of the most difficult concepts in music theory. That is, they’re difficult until you learn to imagine them as rotations of the scale necklace, at which point they become nothing harder than a memorization exercise.

I’m designing this system to be used with the aQWERTYon, but there’s no reason it couldn’t take ordinary MIDI input as well. Wouldn’t it be nice to have this in a window in your DAW or notation program?

Music theory is hard. There’s a whole Twitter account devoted to retweeting students’ complaints about it. Some of this difficulty is due to the intrinsic complexity of modern harmony. But a lot of it is due to terminology and notation. Our naming system for notes and chords is a set of historically contingent kludges. No rational person would design it this way from the ground up. Thanks to path dependency, we’re stuck with it, much like we’re stuck with English grammar and the QWERTY keyboard layout. Fortunately, technology gives us a lot of new ways to make all the arcana more accessible, by showing multiple representations simultaneously and by making those representations discoverable through playful tinkering.

Do you find this idea exciting? Would you like it to be functioning software, and not just a bunch of flat images I laboriously made by hand? Help the MusEDLab find a partner to fund the developer and designer time. A grant or gift would work, and we’d also be open to exploring a commercial partnership. The aQW has been a labor of volunteer love for the lab so far, and it’s already one of the best music theory pedagogy tools on the internet. But development would go a lot faster if we could fund it properly. If you have ideas, please be in touch!

Update: Will Kuhn’s response to this post.

Deconstructing the bassline in Herbie Hancock’s “Chameleon”

If you have even a passing interest in funk, you will want to familiarize yourself with Herbie Hancock’s “Chameleon.” And if you are preoccupied and dedicated to the preservation of the movement of the hips, then the bassline needs to be a cornerstone of your practice.

Chameleon - circular bass

Here’s a transcription I did in Noteflight – huge props to them for recently introducing sixteenth note swing.

And here’s how it looks in the MIDI piano roll:

The “Chameleon” bassline packs an incredible amount of music into just two bars. To understand how it’s put together, it’s helpful to take a look at the scale that Herbie built the tune around, the B-flat Dorian mode. Click the image below to play it on the aQWERTYon. I recommend doing some jamming with it over the song before you move on.

B-flat Dorian

Fun fact: this scale contains the same pitches as A-flat major. If you find that fact confusing, then feel free to ignore it. You can learn more about scales and modes in my Soundfly course.

The chord progression

The opening section of “Chameleon” is an endless loop of two chords, B♭-7 and E♭7. You build both of them using the notes in B-flat Dorian. To make B♭-7, start on the root of the scale, B-flat. Skip over the second scale degree to land on the third, D-flat. Skip over the fourth scale degree to land on the fifth, F. Then skip over the sixth to land on the seventh, A-flat. If you want to add extensions to the chord, just keep skipping scale degrees, like so:

B-flat Dorian mode chords

To make E♭7, you’re going to use the same seven pitches in the same order, but you’re going to treat E-flat as home base rather than B-flat. You could think of this new scale as being E-flat Mixolydian, or B-flat Dorian starting on E-flat; they’re perfectly interchangeable. Click to play E-flat Mixolydian on the aQWERTYon. You build your E♭7 chord like so:

B-flat Dorian mode chords on E-flat

Once you’ve got the sound of B♭-7 and E♭7 in your head, let’s try an extremely simplified version of the bassline.

Chord roots only

At the most basic level, the “Chameleon” bassline exists to spell out the chord progression in a rhythmically interesting way. (This is what all basslines do.) Here’s a version of the bassline that removes all of the notes except the ones on the first beat of each bar. They play the roots of the chords, B-flat and E-flat.

That’s boring, but effective. You can never go wrong playing chord roots on the downbeat.

Simple arpeggios

Next, we’ll hear a bassline that plays all of the notes in B♭-7 and E♭7 one at a time. When you play chords in this way, they’re called arpeggios.

The actual arpeggios

The real “Chameleon” bassline plays partial arpeggios–they don’t have all of the notes from each chord. Also, the rhythm is a complicated and interesting one.

Below, you can explore the rhythm in the Groove Pizza. The orange triangle shows the rhythm of the arpeggio notes, played on the snare. The yellow quadrilateral shows the rhythm of the walkups, played on the kick–we’ll get to those below.

The snare rhythm has a hit every three sixteenth notes. It’s a figure known in Afro-Latin music as tresillo, which you hear absolutely everywhere in all styles of American popular and vernacular music. Tresillo also forms the front half of the equally ubiquitous son clave. (By the way, you can also use the Groove Pizza to experiment with the “Chameleon” drum pattern.)

As for the pitches: Instead of going root-third-fifth-seventh, the bassline plays partial arpeggios. The figure over B♭-7 is just the root, seventh and root again, while the one over E♭7 is the root, fifth and seventh.

Adding the walkups

Now let’s forget about the arpeggios for a minute and go back to just playing the chord roots on the downbeats. The bassline walks up to each of these notes via the chromatic scale, that is, every pitch on the piano keyboard.

Chromatic walkups are a great way to introduce some hip dissonance into your basslines, because they can include notes that aren’t in the underlying scale. In “Chameleon” the walkups include A natural and D natural. Both of these notes sound really weird if you sustain them over B-flat Dorian, but in the context of the walkup they sound perfectly fine.

Putting it all together

The full bassline consists of the broken arpeggios anticipated by the walkups.

If you’re a guitarist or bassist, you can play this without even shifting position. Use your index on the third fret, your middle on the fourth fret, your ring on the fifth fret, and your pinkie on the sixth fret.

              .          . .
G|----------.-3----------3-6--|
D|----------6-----------------|
A|---------------3-4-5-6------|
E|--3-4-5-6-------------------|

If you’ve got this under your fingers, maybe you’d like to figure out the various keyboard and horn parts. They aren’t difficult, but you’ll need one more scale, the B-flat blues scale. Click the image to jam with it over the song and experience how great it sounds.

B-flat blues

There you have it, one of the cornerstones of funk. Good luck getting it out of your head!

Freedom ’90

Since George Michael died, I’ve been enjoying all of his hits, but none of them more than this one. Listening to it now, it’s painfully obvious how much it’s about George Michael’s struggles with his sexual orientation. I wonder whether he was being deliberately coy in the lyrics, or if he just wasn’t yet fully in touch with his identity. Being gay in the eighties must have been a nightmare.

This is the funkiest song that George Michael ever wrote, which is saying something. Was he the funkiest white British guy in history? Quite possibly. 

The beat

There are five layers to the drum pattern: a simple closed hi-hat from a drum machine, some programmed bongos and congas, a sampled tambourine playing lightly swung sixteenth notes, and finally, once the full groove kicks in, the good old Funky Drummer break. I include a Noteflight transcription of all that stuff below, but don’t listen to it, it sounds comically awful.

George Michael uses the Funky Drummer break on at least two of the songs on Listen Without Prejudice Vol 1. Hear him discuss the break and how it informed his writing process in this must-watch 1990 documentary.

The intro and choruses

Harmonically, this is a boilerplate C Mixolydian progression: the chords built on the first, seventh and fourth degrees of the scale. You can hear the same progression in uncountably many classic rock songs.

C Mixolydian chords

For a more detailed explanation of this scale and others like it, check out Theory For Producers.

The rhythm is what makes this groove so fresh. It’s an Afro-Cuban pattern full of syncopation and hemiola. Here’s an abstraction of it on the Groove Pizza. If you know the correct name of this rhythm, please tell me in the comments!

The verses

There’s a switch to plain vanilla C major, the chords built on the fifth, fourth and root of the scale.

C major chords

Like the chorus, this is standard issue pop/rock harmonically speaking, but it also gets its life from a funky Latin rhythm. It’s a kind of clave pattern, five hits spread more or less evenly across the sixteen sixteenth notes in the bar. Here it is on the Groove Pizza.

The prechorus and bridge

This section unexpectedly jumps over to C minor, and now things get harmonically interesting. The chords are built around a descending chromatic bassline: C, B, B-flat, A. It’s a simple idea but with complicated implications, because it implies four chords built on three different scales between them. First, we have the tonic triad in C natural minor, no big deal there. Next comes the V chord in C harmonic minor. Then we’re back to C natural minor, but with the seventh in the bass. Finally, we go to the IV chord in C Dorian mode. Really, all that we’re doing is stretching C natural minor to accommodate a couple of new notes, B natural in the second chord, and A natural in the fourth one.

C minor - descending chromatic bassline

The rhythm here is similar but not identical to the clave-like pattern in the verse–the final chord stab is a sixteenth note earlier. See and hear it on the Groove Pizza.

I don’t have the time to transcribe the whole bassline, but it’s absurdly tight and soulful. The album credits list bass played both by Deon Estus and by George Michael himself. Whichever one of them laid this down, they nailed it.

Song structure

“Freedom ’90” has an exceedingly peculiar structure for a mainstream pop song. The first chorus doesn’t hit until almost two minutes in, which is an eternity–most pop songs are practically over that that point. The graphic below shows the song segments as I marked them in Ableton.

Freedom '90 structure

The song begins with a four bar instrumental intro, nothing remarkable about that. But then it immediately moves into an eight bar section that I have trouble classifying. It’s the spot that would normally be occupied by verse one, but this part uses the chorus harmony and is different from the other verses. I labeled it “intro verse” for lack of a better term. (Update: upon listening again, I realized that this section is the backing vocals from the back half of the chorus. Clever, George Michael!) Then there’s an eight bar instrumental break, before the song has really even started. George Michael brings you on board with this unconventional sequence because it’s all so catchy, but it’s definitely strange.

Finally, twenty bars in, the song settles into a more traditional verse-prechorus-chorus loop. The verses are long, sixteen bars. The prechorus is eight bars, and the chorus is sixteen. You could think of the chorus as being two eight bar sections, the part that goes “All we have to do…” and the part that goes “Freedom…” but I hear it as all one big section.

After two verse-prechorus-chorus units, there’s a four bar breakdown on the prechorus chord progression. This leads into sixteen bar bridge, still following the prechorus form. Finally, the song ends with a climactic third chorus, which repeats and fades out as an outtro. All told, the song is over six minutes. That’s enough time (and musical information) for two songs by a lesser artist.

A word about dynamics: just from looking at the audio waveform, you can see that “Freedom ’90” has very little contrast in loudness and fullness over its duration. It starts sparse, but once the Funky Drummer loop kicks in at measure 13, the sound stays constantly big and full until the breakdown and bridge. These sections are a little emptier without the busy piano part. The final chorus is a little bigger than the rest of the song because there are more vocals layered in, but that still isn’t a lot of contrast. I guess George Michael decided that the groove was so hot, why mess with it by introducing contrast for the sake of contrast? He was right to feel that way.