09 Feb

How Love for an 80’s Hip-Hop Drum Machine Is Leading to New Mathematical Theory


Introduced in the 1980’s, the TR-808 was the first programmable drum machine. You’re unwittingly familiar with sound of the TR-808; it’s featured in more hit songs than Pharell.  The 808 is literally THE sound of the 80’s including those synthed beats from Afrika Bambaataa and the Soul Sonic Force’s Planet Rock . The sounds of 808 are iconic; the deep bass, kick drum; the tinny handclaps; the ticky snare; the tishy high hat; that spacey cowbell.   Modern rap and hip-hop from the South, aka The Dirty South, continue to be influenced by the TR-808. Consider Outkast’s The Way You Move, it’s deep bass and addictive high hat are classic 808.

Speakerbox vibrate the tank, make it sound like aluminum cans in the back
But I know y’all wanted that 808 can you feel that B-A-S-S, bass

The machine’s affordability, a steal at $1195, and ease of use lead to its original popularity. However only 12,000 TR-808’s were ever made—the last in 1983. Securing a TR-808 today requires about $4,000 and hours entrenched in eBay bidding wars. Subsequently, most of those iconic 808 sounds in today’s music are recorded sounds, samples, not the actual drum machine itself. But the heroic efforts of one resolute Stanford University graduate student are giving this 80’s drum machine new life with an unlikely tool—mathematical theory.

The TR-808 was the last important analog drum machine ever made. The insides of the machine are a complicated mix of circuits with capacitors and resistors working to change the voltage, the signal that produces the sound. Some of these circuits are mundane, but others represent true innovations by Roland, the 808’s manufacturer. Other drum machines produce the sound of a kick drum with a band pass filter that cuts the high and low parts of the frequency leading to a very narrow and sharp wave oscillating at a signal frequency, with the oscillation eventually dying out. In the 808 the punch of that low kick drum is unique; produced by replicating the physical process of a real bass drum. Right after the start of the sound, the frequency of the oscillation is increased for a few milliseconds and then drops down again. The frequency is then allowed to drift and oscillate a minute producing a sighing sound. This sequence creates a very complicated trajectory during which the note evolves across a wide array of pitches. The complex kick drum sound of the TR-808 is accomplished with a complicated type of circuit, a Bridged-T, and therein lies the problem with mathematically modeling it’s sound.


At the top of a hill on the far south side of the Stanford campus sits The Knoll. Formerly home of the university’s president, the Knoll now houses the Center for Computer Research in Music and Acoustics (CCRMA, pronounced “karma”).   Here, a dozen faculty and a few dozen graduate students research everything from digital musical composition, to hardware and software, to psychoacoustics. The interior of the late 1800’s Spanish influenced mansion is a combination of recognizable instruments, computer workstations, and hacked-together Franken-equipment mashing the two together. On the second floor, Ph.D. student Kurt Werner is stretching a field of mathematics to reproduce the TR-808 sound. Werner, is the perfect person for the task—bachelors degrees in control systems engineering and music theory from the University of Illinois Urbana Champaign; a hobby of hacking the hardware or “circuit bending” of old musical machines; an interest in experimental electronic composition; and an unrivaled need to share the TR-808 love.

Werner’s research seeks to extend the mathematical field of Wave Digital Filter Theory. The TR-808 is simply a filter in which a voltage signal is passed through and altered to produce sound. A digital filter likewise takes one sequence of numbers and produces another sequence of numbers. Wave Digital Filter Theory, developed by Alfred Fettweis in the late 1960’s, simply tries to translate the filtering done by circuits composed of inductors, capacitors, resistors, diodes, transformers, and so on into filtering done by a set of equations. Through this mathematical transformation, the beloved sounds of analog devices, like the TR-808, can be replicated to modern digital machines. Wave Digital Filter Theory is not new to the music industry. , The theory was developed in the 1970’s to produce digital filters from analog filters already being designed, developed, and prototyped.

dcx6In the late 1990’s the music industry revived Wave Digital Filter Theory for an entirely different reason—people loved, and wanted to mimic, the sound of analog devices. However, the types of circuits in musical devices are often complex and while Wave Digital Filter Theory is an elegant theory, it remained incomplete. The theory can only handle certain circuit topologies. Think the physical way in which all those circuit components are wired together, namely the classic series or parallel circuit. In a series circuit all the current through one electrical element flows through another element. In a parallel circuit the voltage across one electrical element is also the voltage across another electrical element. These assumptions of voltage or currents being equal are vital for solving equations of how the wave changes at each step in the circuit.

fXWq9qHBut the insides of TR-808 is a cornucopia of much more complex circuits. Take the Bridged-T circuit in the 808’s kick drum, none of the elements of the circuit are in series or parallel and thus no two resistors have the same current or voltage across them. Werner’s research is making strides to actually allow Wave Digital Filter Theory to model the Bridged-T circuit and more generally an infinite number of complex circuits. To solve the Bridge-T problem, Werner borrowed from another field of mathematics called Modified Nodal Analysis. As Werner states, “Conveniently, writing out Modified Nodal Analysis equations is simple, even automatic.” But the kicker, pun intended, is that this allows for any circuit configuration to be solved because the equations are generalizable.

Untitled-3However, another issue with Wave Digital Filter Theory emerges­—the theory cannot handle multiple nonlinearities in the circuit. A linear relationship is where increases or decreases in variable A always cause increases or decreases in variable B. A nonlinear relationships might be where increases in variable A causes increases in variable B but only up to certain value of variable A, after which variable B decreases. The TR-808 cymbal circuit contains 21 such nonlinearities. Werner’s research solves this problem as well. Werner discovered the combination of those nonlinearities and the circuit configuration are simply a nonlinear state space system, which has its own theory of mathematics to solve.

Much like Dr. Dre’s 1992 hit Let Me Ride samples Funky Drummer by James Brown, Mothership Connection and Swing Down, Sweet Chariot by Parliament, and Kissing My Love by Bill Withers to create more than the sum of its parts, Kurt Werner is bringing together new mathematical theories to advance the field. Perhaps the advances of Wave Digital Filter Theory do not interest you, but you have to admit those theoretical advances have reproduced that beautiful 808 punch (make sure you have some good speakers or headphones). Because as the Beasties Boys rapped in Super Disco Breakin “nothing sounds quite like an 8-0-8”.

22 Nov

My Love of the TR-808


My twenty-four blades glistenin’, and my 808 kickin’ T.I. – Top Back

You do not have to read many of posts at Deep-Sea News or Science of the South to realize my love of hip-hop and rap.  Especially Southern hip-hop and rap.  If you haven’t already do check out Ben Westhoff’s book Dirty South.  A key to the southern sound is the TR-808.  Introduced in the 80’s the 808 was the first programmable drum machine.   The machine’s cheapness, $1195, and ease of use lead to its popularity.  As I begin to research Southern music, a common theme is the emphasis on sound produced by inexpensive or homemade instruments.  It seems this theme continues to Dirty South.  

TR-808_Groot1You know the sound of the TR-808.  It’s featured in more hit songs than any other drum machine.  It was literally the sound of the 80’s.   All those synthed beats in Afrika Bambaataa and the Soul Sonic Force’s Planet Rock are courtesy of the 808.


Many sounds of the 808 are just so iconic.   The deep bass, kick drum.  The tinny handclaps.  The ticky snare.  The tishy high hat.  That spacey cowbell.   The video below nicely highlights all of the 16 programmable sounds.  

One of my all-time favorite Southern hip-hop songs highlighting that deep 808 bass and addictive high hat is Outkast’s The Way You Move.

Speakerbox vibrate the tank, make it sound like aluminum cans in the back
But I know y’all wanted that 808 can you feel that B-A-S-S, bass

From Memphis, the Three 6 Mafia’s Stay Fly also greatly reflects the fast temp of the 808. So does their Poppin’ my Collar

The more recent trap hit, Higher Ground, by TNGHT also shows the TR-808 continues.

There is so many more like Shawty Lo’s Atlanta,GA, but I’ll stop.  In the next few weeks, I’ll be delving into the science inside of the TR-808.  How exactly are is that deep lingering base produced?  In the meantime, let’s celebrate Southern music and the 808. Below is a collaborative playlist on Spotify. Add your favorite songs to that list or in the comments below.

14 Apr

The difficulty of predicting tornadoes


Legendary blues singer, Alger “Texas” Alexander was born in Jewett, Texas, north of Houston in 1900. In 1934, Alger composed and sang with his big, deep voice the Frost Texas Tornado Blues. Just four years earlier a F4 tornado ripped through the town of Frost just south of Dallas. Sixty were killed and many more never found. The entire town was leveled and a mass funeral occurred on the porch of the only house left standing.

I was sitting looking: way out across the world

Said the wind had things switching: almost in a twirl

Says I been a good fellow: just good as I can be

Says it’s Lord have mercy: Lord have mercy on meOkeh_Record_Label

Mmm: mmm

Says I been a good fellow: just as good as a man could be

Some lost their baby: was blowing for two three miles around

When they come to their right mind: they come on back to town

Said rooster was crowing cows was lowing: never heard such a noise before

Does it seem like hell was broke out: in this place below 

frost_tornado_photo_12Although we still sing the blues about tornadoes, much has changed since the 1930’s with regard to tornadoes. We have better home construction and much, much better warnings now.  However, knowing exactly when and where  a tornado will occur…well that is a bit more challenging.

Let me clarify.

With ever-increasing precision we can predict, and warn, of conditions that are likely to produce a tornado. The ingredients—wind shear, instability, heat and moisture, and forcing mechanism—are mesoscale phenomena that can be modeled, quantified, and even predicted. Roger Edwards, lead forecaster at the Storm Prediction Center described the intricate process that it takes to predict a thunderstorm and tornado outbreak days to a week in advance. “It takes a combination of skill, luck, and a team of people. The key is trying to predict a phenomenon not just temperature and rain.” Data of different types—wind, temperature, moisture—at scales ranging from the globe to North America to a particular county in Oklahoma must all be integrated. The data itself comes from satellite, aircraft observations, weather balloons, weather stations, and radar. All of this data must be assimilated and ran through multiple modes that would fry your home computer and probably your neighbor’s on top of that. Then the computers spit out an answer. Of course that answer might be garbage. “Let’s not forget the human element to see that models are going awry. You need to conceptualize in three dimensions what is going on in atmosphere. We still analyze charts by hand which causes us to slow down and think with pencils and paper in hand. Our experience is vital. “

But these ingredients form a supercell, not a tornado itself, and not all supercells produce tornadoes.   “The atmosphere has a way of getting the four together in ways with minor differences to either create a large EF5 tornado or a just some rain. We don’t know when and where these ingredients form in just the right way,” states Edwards. Indeed, 70% of the time a tornado warning is issued no tornado actually forms. It’s important to understand this error would be much worse if it were reversed. In other words, if 70% of the time a tornado occurred no tornado warning was issued. That is the major advance I’m talking about. 

Scientists still have little idea what causes tornadogensis particularly those microscale phenomena, those minor winds, temperature, and pressure differences that occur in areas less than a mile to less than football field that trigger the whole shoot and caboodle. Measuring, analyzing, and modelling this is the cutting edge of tornado research.  In the last several weeks, I have been speaking with the biggest names in tornado researchers from Virginia to Oklahoma to Illinois. I asked everyone what is the biggest question in tornado science. Every one of them responded that the holy grail, my word not theirs, is the when, where, and how of which storm will make a tornado.

Charles Doswell is a meteorologist who although did not originate the concept of supercell, that’s thanks to a Brit named Keith Browning, did with Les Lemon improve Browning’s idea that gave us the modern conceptual model of supercells and how they form. That paper from 1979 is one of the most cited papers in meteorology and tornado science. I’ll leave with Charles’s words from our recent conversation. “We are still struggling with the area of tornadogenesis. Apparently you need every single one of the details…and very high confidence in them too.” Perhaps it’s fitting that Doswell and “Texas” Alexander share more in common that a fascination with tornadoes. Doswell is too a lover of the blues, perhaps fitting for a tornado scientist, and used to host a blues radio show.


18 Dec

A tomato for shiftless Arkansas squatters, robbers, cutthroats, and fiddle players

Photo by Corey Burger on Flickr (cc)

In the Ozark Mountains of Arkansas, where I hail from, an heirloom tomato originated before the 1900’s. The Arkansas Traveler is prized for very flavorful, medium-sized tomatoes that resist cracking and keep on coming, even in drought and hot weather. Indeed, the Arkansas Traveler for these reasons became a mainstay tomato for much of the South. Take these user reviews of the tomato from a popular plant company

Great tomatoes for the South! These were one of the first tomato plants to produce tomatoes last year. They kept on producing when it got hot last summer and taste great.

I live in Houston where the heat and humidity boil through September, but the tomatoes continue on, although with less yield beginning in August. The flavor is awesome.

best producing plant ever

Tomato_09_Arkansas_Traveler Despite these positive testimonies the Arkansas Traveler has had a shady past.

Perhaps no other State in the Union has been so misrepresented as Arkansas. She has had much bad advertising, and the ignorant beyond her borders have wrong ideas of her and her people. By such people she is supposed to be the home of shiftless squatters, robbers, and cutthroats, who make the bowie-knife and the pistol the law of the land . . . “The Arkansas Traveler” is largely responsible for the wrong impression of our State.

How could a tomato do this kind of damage? Well the history is complicated. 

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