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.

              .          . .

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!

Inside the aQWERTYon

The MusEDLab and Soundfly just launched Theory For Producers, an interactive music theory course. The centerpiece of the interactive component is a MusEDLab tool called the aQWERTYon. You can try it by clicking the image below.

aQWERTYon screencap

In this post, I’ll talk about why and how we developed the aQWERTYon.

One of our core design principles is to work within our users’ real-world technological limitations. We build tools in the browser so they’ll be platform-independent and accessible anywhere there’s internet access (and where there isn’t internet access, we’ve developed the “MusEDLab in a box.”) We want to find out what musical possibilities there are in a typical computer with no additional software or hardware. That question led us to investigate ways of turning the standard QWERTY keyboard into a beginner-friendly instrument. We were inspired in part by GarageBand’s Musical Typing feature.

GarageBand musical typing

If you don’t have a MIDI controller, Apple thoughtfully made it possible for you to use your computer keyboard to play GarageBand’s many software instruments. You get an octave and a half of piano, plus other useful controls: pitch bend, modulation, sustain, octave shifting and simple velocity control. Many DAWs offer something similar, but Apple’s system is the most sophisticated I’ve seen.

Handy though it is, Musical Typing has some problems as a user interface. The biggest one is the poor fit between the piano keyboard layout and the grid of computer keys. Typing the letter A plays the note C. The rest of that row is the white keys, and the one above it is the black keys. You can play the chromatic scale by alternating A row, Q row, A row, Q row. That basic pattern is easy enough to figure out. However, you quickly get into trouble, because there’s no black key between E and F. The QWERTY keyboard gives no visual reminder of that fact, so you just have to remember it. Unfortunately, the “missing” black key happens to be the letter R, which is GarageBand’s keyboard shortcut for recording. So what inevitably happens is that you’re hunting for E-flat or F-sharp and you accidentally start recording over whatever you were doing. I’ve been using the program for years and still do this routinely.

Rather than recreating the piano keyboard on the computer, we drew on a different metaphor: the accordion.

The accordion: the user interface metaphor of the future!

We wanted to have chords and scales arranged in an easily discoverable way, like the way you can easily figure out the chord buttons on the accordion’s left hand. The QWERTY keyboard is really a staggered grid four keys tall and between ten and thirteen keys wide, plus assorted modifier and function keys. We decided to use the columns for chords and the rows for scales.

For the diatonic scales and modes, the layout is simple. The bottom row gives the notes in the scale starting on 1^. The second row has the same scale shifted over to start on 3^. The third row starts the scale on 5^, and the top row starts on 1^ an octave up. If this sounds confusing when you read it, try playing it, your ears will immediately pick up the pattern. Notes in the same column form the diatonic chords, with their roman numerals conveniently matching the number keys. There are no wrong notes, so even just mashing keys at random will sound at least okay. Typing your name usually sounds pretty cool, and picking out melodies is a piece of cake. Playing diagonal columns, like Z-S-E-4, gives you chords voiced in fourths. The same layout approach works great for any seven-note scale: all of the diatonic modes, plus the modes of harmonic and melodic minor.

Pentatonics work pretty much the same way as seven-note scales, except that the columns stack in fourths rather than fifths. The octatonic and diminished scales lay out easily as well. The real layout challenge lay in one strange but crucial exception: the blues scale. Unlike other scales, you can’t just stagger the blues scale pitches in thirds to get meaningful chords. The melodic and harmonic components of blues are more or less unrelated to each other. Our original idea was to put the blues scale on the bottom row of keys, and then use the others to spell out satisfying chords on top. That made it extremely awkward to play melodies, however, since the keys don’t form an intelligible pattern of intervals. Our compromise was to create two different blues modes: one with the chords, for harmony exploration, and one just repeating the blues scale in octaves for melodic purposes. Maybe a better solution exists, but we haven’t figured it out yet.

When you select a different root, all the pitches in the chords and scales are automatically changed as well. Even if the aQWERTYon had no other features or interactivity, this would still make it an invaluable music theory tool. But root selection raises a bigger question: what do you do about all the real-world music that uses more than one scale or mode? Totally uniform modality is unusual, even in simple pop songs. You can access notes outside the currently selected scale by pressing the shift keys, which transposes the entire keyboard up or down a half step. But what would be really great is if we could get the scale settings to change dynamically. Wouldn’t it be great if you were listening to a jazz tune, and the scale was always set to match whatever chord was going by at that moment? You could blow over complex changes effortlessly. We’ve discussed manually placing markers in YouTube videos that tell the aQWERTYon when to change its settings, but that would be labor-intensive. We’re hoping to discover an algorithmic method for placing markers automatically.

The other big design challenge we face is how to present all the different scale choices in a way that doesn’t overwhelm our core audience of non-expert users. One solution would just be to limit the scale choices. We already do that in the Soundfly course, in effect; when you land on a lesson, the embedded aQWERTYon is preset to the appropriate scale and key, and the user doesn’t even see the menus. But we’d like people to be able to explore the rich sonic diversity of the various scales without confronting them with technical Greek terms like “Lydian dominant”. Right now, the scales are categorized as Major, Minor and Other, but those terms aren’t meaningful to beginners. We’ve been discussing how we could organize the scales by mood or feeling, maybe from “brightest” to “darkest.” But how do you assign a mood to a scale? Do we just do it arbitrarily ourselves? Crowdsource mood tags? Find some objective sorting method that maps onto most listeners’ subjective associations? Some combination of the above? It’s an active area of research for us.

This issue of categorizing scales by mood has relevance for the original use case we imagined for the aQWERTYon: teaching film scoring. The idea behind the integrated video window was that you would load a video clip, set a mode, and then improvise some music that fit the emotional vibe of that clip. The idea of playing along with YouTube videos of songs came later. One could teach more general open-ended composition with the aQWERTYon, and in fact our friend Matt McLean is doing exactly that. But we’re attracted to film scoring as a gateway because it’s a more narrowly defined problem. Instead of just “write some music”, the challenge is “write some music with a particular feeling to it that fits into a scene of a particular length.

Would you like to help us test and improve the aQWERTYon, or to design curricula around it? Would you like to help fund our programmers and designers? Please get in touch.