## 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 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.

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.”

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.”

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.

## Groove challenges with the Groove Pizza

One of our key design principles at the NYU MusEDLab is not to confront beginners with a blank canvas. We want to introduce people to our tools by giving them specific, real-world music to play around with. That was the motivation behind creating presets for the aQWERTYon, and a similar impulse informs Ableton’s approach to their online music tutorials. The Groove Pizza comes with some preset patterns (specials), but there aren’t direct prompts for creative beatmaking. This post introduces some prototype prompts.

## The Funky Drummer boom-bap challenge

The pattern below is the first quarter note of the kick and snare pattern in Clyde Stubblefield’s classic drum break. Fill in the missing kick and snare hits to make your own golden age breakbeat. Try removing some hi-hats as well.

Musical inspiration:

## The Levee break asymmetrical kick challenge

The groove below uses the kick and snare pattern from “When The Levee Breaks” by Led Zeppelin. Add hi-hats and customize the kick and snare to best convey the Awesome Majesty of Rock.

Musical inspiration:

## Four-on-the-floor squares challenge

These two squares make a classic dance beat, kicks on the quarter notes with hi-hats in between. Add snares and break up the symmetry to make a dance floor filler.

Musical inspiration:

## So Fresh So Clean challenge

The pattern below is the basis for a sixteenth note hip-hop groove. Place more kicks and snares to make a crunk Dirty South beat in the spirit of OutKast.

Musical inspiration:

## It’s A Trap challenge

The pattern below is the basis for a thirty-second note groove. Add kicks and snares and remove hi-hats to make a radio-friendly trap beat.

Musical inspiration: I would include a link to a Future song but can’t find one that whose lyrics aren’t extremely objectionable. Just turn on the radio.

## Seeing classic beats with the Groove Pizza

We created the Groove Pizza to make it easier to both see and hear rhythms. The next step is to create learning experiences around it. In this post, I’ll use the Pizza to explain the structure of some quintessential funk and hip-hop beats. You can click each one in the Groove Pizza, where you can customize or alter it as you see fit. I’ve also included Noteflight transcriptions of the beats.

## The Backbeat Cross

View in Noteflight

This simple pattern is the basis of just about all rock and roll: kicks on beats one and three (north and south), and snares on beats two and four (east and west.) It’s boring, but it’s a solid foundation that you can build more musical-sounding grooves on top of.

## The Big Beat

View in Noteflight

This Billy Squier classic is Number nine on WhoSampled’s list of Top Ten Most Sampled Breakbeats. There are only two embellishments to the backbeat cross: the snare drum hit to the east is anticipated by a kick a sixteenth note (one slice) earlier, and the kick drum to the south is anticipated by a kick an eighth note (two slices) earlier. It isn’t much, but together with some light swing, it’s enough to make for a compelling rhythm. The groove is interestingly close to being symmetrical on the right side of the circle, and there’s an antisymmetry with the kick-free left side. That balance between symmetry and asymmetry is what makes for satisfying music.

## Planet Funk (eighth notes)

View in Noteflight

This pattern reminds me of Saturn viewed edge-on. The hi-hats are the planet itself, the snares are the rings, and the lone kick drum at the top is a moon. To make the simplest funk beats, all you need to do is add more moons into the kick drum orbit.

## It’s A New Day

View in Noteflight

The Skull Snaps song isn’t too well known, but the break that kicks it off is number five on the WhoSampled list. The Planet Funk template has some extra kick drums embellishing particular beats. The kick on the downbeat (the topmost slice) has a kick anticipating it a sixteenth note (one slice) earlier, and another following it an eighth note (two slices) later. The snare drum hit to the west is anticipated by two more kicks. All that activity is balanced by the southeast half of the pizza, which is totally kick-free. Like “The Big Beat,” “It’s A New Day” is close to being symmetrical, with just enough variation to keep it interesting.

## When The Levee Breaks

View in Noteflight

This Led Zeppelin classic embodies the awesome majesty of rock. Rhythmically, though, it has more in common with funk. The crucial difference is beat three, the southernmost point on the pizza. In rock, you usually have a kick there. In funk, you usually don’t. The Levee break has a kick a sixteenth note before beat three, which is quite a surprise. Try moving that kick a slice later, and you’ll hear the groove lose its tension and interest. Like “It’s A New Day,” the Levee break sets up the second snare hit with two kicks. There’s another interesting wrinkle, too, a kick that immediately follows the first one. The result is another symmetrically asymmetrical drum pattern.

## Planet Funk (sixteenth notes)

View in Noteflight

If you put a hi-hat on every slice of the pizza, you get a busier version of the basic funk groove. With twice as many hi-hats, you can slow the tempo down and still have an energetic feel.

## So Fresh, So Clean

View in Noteflight

This OutKast banger has a fascinating drum machine pattern. The snare and hi-hat stick to the Planet Funk pattern above, but against all this predictable symmetry, the kick drum is all over the place. To understand what’s going on here, you need to know something about the concept of strong and weak beats. Strong beats are where you expect drum hits to fall, and weak beats are where you don’t expect them. The more times you have to divide the circle in half to get to a given beat, the weaker it is. The weakest beats are the even-numbered pizza slices. In the first bar, pictured above, every single even-numbered slice has a kick on it. This is, to put it mildly, not typical. Usually the base of your beat is stable and predictable, and the higher-pitched ornaments are more unpredictable. That’s what makes “So Fresh, So Clean” so cool.

## Nas Is Like

View in Noteflight

While this track is best known for its samples, and deservedly so, the underlying drum machine rhythm is pretty remarkable too. Like the OutKast song above, the snares and hi-hats are mostly stable, with most of the variation in the kick. I won’t verbally analyze all four bars of the pattern, but if you play with it, you’ll see the idea of balanced symmetry and asymmetry at work.

## Amen Break

View in Noteflight

The Amen break is the most complex rhythm here, and it’s a post unto itself to really explain the whole thing. The important thing is to compare the simplicity of the hi-hatsadditional sound, an open hi-hat in the last bar. Displacement!

## Space Oddity: from song to track

If you’ve ever wondered what it is that a music producer does exactly, David Bowie’s “Space Oddity” is a crystal clear example. To put it in a nutshell, a producer turns this:

Into this:

It’s also interesting to listen to the first version of the commercial recording, which is better than the demo, but still nowhere near as majestic as the final version. The Austin Powers flute solo is especially silly.

Should we even consider these three recordings to be the same piece of music? On the one hand, they’re all the same melody and chords and lyrics. On the other hand, if the song only existed in its demo form, or in the awkward Austin Powers version, it would never have made the impact that it did. Some of the impact of the final version lies in better recording techniques and equipment, but it’s more than that. The music takes on a different meaning in the final version. It’s bigger, trippier, punchier, tighter, more cinematic, more transporting, and in general about a thousand times more effective.

The producer’s job is to marshall the efforts of songwriters, arrangers, performers and engineers to create a good-sounding recording. (The producer might also be a songwriter, arranger, performer, and/or engineer.) Producers are to songs what directors are to movies, or showrunners are to television.

When you’re thinking about a piece of recorded music, you’re really talking about three different things:

1. The underlying composition, the part that can be represented on paper. Albin Zak calls this “the song.”
2. The performance of the song.
3. The finished recording, after overdubbing, mixing, editing, effects, and all the rest. Albin Zak calls this “the track.”

I had always assumed that Tony Visconti produced “Space Oddity,” since he produced a ton of other Bowie classics. As it turns out, though, Visconti was underwhelmed by the song, so he delegated it to his assistant, Gus Dudgeon. So what is it that Gus Dudgeon did precisely? First let’s separate out what he didn’t do.

You can hear from the demo that the chords, melody and lyrics were all in place before Bowie walked into the studio. They’re the parts reproduced by the subway busker I heard singing “Space Oddity” this morning. The demo includes a vocal arrangement that’s similar to the final one, aside from some minor phrasing changes. The acoustic guitar and Stylophone are in place as well. (I had always thought it was an oboe, but no, that droning sound is a low-tech synth.)

Gus Dudgeon took a song and a partial arrangement, and turned it into a track. He oversaw the addition of electric guitar, bass, drums, strings, woodwinds, and keyboards. He coached Bowie and the various studio musicians through their performances, selected the takes, and decided on effects like echoes and reverb. He supervised the mixing, which not only sets the relative loudness of the various sounds, but also affects their perceived location and significance. In short, he designed the actual sounds that you hear.

If you want to dive deep into the track, you’re in luck, because Bowie officially released the multitrack stems. Some particular points of interest:

• The bassist, Herbie Flowers, was a rookie. The “Space Oddity” session was his first. He later went on to create the staggeringly great dual bass part in Lou Reed’s “Walk On The Wild Side.”
• The strings were arranged and conducted by the multifaceted Paul Buckmaster, who a few years later would work with Miles Davis on the conception of On The Corner. Buckmaster’s cello harmonics contribute significantly to the psychedelic atmosphere–listen to the end of the stem labeled “Extras 1.”
• The live strings are supplemented by Mellotron, played by future Yes keyboardist Rick Wakeman, he of the flamboyant gold cape.
• Tony Visconti plays some flute and unspecified woodwinds, including the distinctive saxophone run that leads into the instrumental sections.

You can read a detailed analysis of the recording on the excellent Bowiesongs blog.

The big difference between the sixties and the present is that the track has assumed ever-greater importance relative to the song and the performance. In the age of MIDI and digital audio editing, live performance has become a totally optional component of music. The song is increasingly inseparable from the sounds used to realize it, especially in synth-heavy music like hip-hop and EDM. This shift gives the producer ever-greater importance in the creative process. There is really no such thing as a “demo” anymore, since anyone with a computer can produce finished-sounding tracks in their bedroom. If David Bowie were a kid now, he’d put together “Space Oddity” in GarageBand or FL Studio, with a lavish soundscape part of the conception from the beginning.

I want my students to understand that the words “producer” and “musician” are becoming synonymous. I want them to know that they can no longer focus solely on composition or performance and wait for someone else to craft a track around them. The techniques used to make “Space Oddity” were esoteric and expensive to realize at the time. Now, they’re easily within reach. But while the technology is more accessible, you still have to have the ideas. This is why it’s so valuable to study great producers like Tony Visconti and Gus Dudgeon: they’re a goldmine of sonic inspiration.