Music, mathematics and horror

Written while I was still active in the Society for Creative Anachronism.

The True History of the Dumbek

The dumbek was never intended to be a musical instrument. It was invented during the Arabian Middle Ages (see Lafferty, R.A., Sindbad: The Thirteenth Voyage, for background on this period) by Scheherazade’s kid brother, Al, as a communications and computational device.


Ali Ali Aq Sinfri, to use his full name, was well-known in Baghdad as a mathematician, poet and socialite. His mathematical achievements include a system of notation for partial differential equations, an impressive feat considering that calculus had not yet been invented. He thought deeply about irrational numbers and speculated that they could be brought to their senses with shock therapy and counseling. He claimed to have discovered what is now known as the Factor of Finagle, but this is doubtful. It is likely, though, that he devised the refinement in which a mathematician divides both sides of a recalcitrant equation by zero and then discovers that the problem is meaningless.

His poetry, according to most sources, was not lost, but carefully collected after his death, and then equally carefully burned. His exploits as a professional guest were legendary; he boasted that he bought only one bottle of wine in his life, yet he woke up every afternoon with a hangover. He slept under a different roof each day, not because he had no place of his own (he did), but because it was so long since he had been there that he couldn’t remember where it was.

The invention of the dumbek (or doumbek, or doumbec, or doumbeck, etc.) was a result of Al’s perpetual impecuniety. He reasoned that if he could learn the result of each day’s Bassorah camel races before they were relayed by messenger to Baghdad, he could support himself in the style to which he had become accustomed, and also make timely payments to Akbar, Vercotti, Piranha and Jeff, Financial Services, by placing an occasional discreet wager with a Baghdad bookie. The problem was how to send and receive the message.

Previously he had studied the question of how the launch angle affected his air time when employees of an exasperated host forcefully showed him that he had overstayed his welcome, and he had devised a “minute-glass” to measure invervals of a few seconds. It was similar to the conventional hourglass but had a wider waist. Calibration and consistency presented insurmountable difficulties, but Al discovered that the pinched cylinder admirably amplified snide comments, maniacal laughter and barnyard noises.

Stretching a rawhide membrane across one end of the minute-glass, Al constructed a bi-modal tone generator. Taps near the edge of the skin produced a high-pitched, percussive sound, while those at the center yielded a deep, resonant tone with remarkable carrying power. The former he called “dek,” and the latter, “buum.” The original glass “buumdek” shattered during a test to determine its maximum lethal radius. (The “lethal radius” is the distance within which the number of survivors of an event equals the number of fatalities without, assuming uniform population density. The concept has applications in nuclear warfare and in musicology.) Subsequent buumdeks, or “dumbeks,” as a spooneristic associate of Al’s called them, were made of ceramic or brass.

Al assigned each camel scheduled to race a unique sequence of buums and deks and stationed dumbek operators along forest paths between Bassorah and Baghdad, each one just barely within listening distance of his two nearest neighbors. A confederate of Al in Bassorah observed the race and gave the first operator the sequence representing the winning camel. The second operator heard the sequence and repeated it on his dumbek, and then the third, and so on until the camel’s code reached Al in Baghdad, long before the official messenger arrived. Unfortunately, one of the operators fancied himself an improvisatory musician (the first of many such misguided induhviduals), and Al spent several months hiding in the Arabian rain forest.


Al’s friend Lefty (so-called because he had lost his right hand after being accused of theft) had only two fingers on his left hand (he lost one after being accused of pickpocketing, another after being accused of picking his nose in public, and the third after being accused of expressing by gesture what he thought of the justice of the Great Caliph). Consequently he couldn’t count to ten, but, being of a mathematical turn of mind, he spent hours counting, “One, two, one, two, one, …” and wondering how to enumerate larger quantities. As a one-legged beggar (he lost his right leg after being accused of scraping his sandal on the steps of the palace of the Great Caliph), he had ample time to ponder this problem.

Lefty lost yet another finger after being accused of digging the wax out of his remaining ear in the presence of the Great Caliph, and was reduced to counting to one. A lesser man would have despaired, but Lefty single-mindedly pursued his dream of enumeration to three and beyond. Speculating on what might happen were he to lose his last finger, he conceived the idea of counting “nothing.” Combining this notion with the Arabian fad of place-value notation, he invented what today is known as the binary system, which allows people and machines of limited intelligence to count as high as they wish.

Lefty, incidentally, was eventually cleared of all charges, but he was beheaded anyway to minimize papyrus-work. He was reconciled to his fate when the headsman pointed out that he would never again have to fill out a tax return.

10,000 Dumbeks

It occurred to Al that, using Lefty’s numeric scheme, one could assign to the buum the meaning of “one,” and to the dek, “nothing,” thus representing any number as a sequence of sounds. During his period of concealment he visualized vast arrays of dumbeks sounding numbers, adding numbers, subtracting numbers, multiplying and dividing numbers, and figuring the odds on camels. When he felt it was safe to be visible in Baghdad again he sought an audience with the Great Caliph. The Caliph, more out of amusement than intellectual excitement, agreed to subsidize Al’s experiments, and soon Al was able to assemble an array of dumbeks and operators 100 dumbeks square in a meadow in the woods near Baghdad.

Precisely how the array of dumbeks worked is not recorded; those with a background in computer science might find it interesting to reconstruct his techniques. All sources state that the “buumdek computator” did indeed work — so well, in fact, that no bookie would do business with Al after a few days.

Al also used his computator to explore philosophical questions. His results include “We stink, therefore we are,” “Semper ubi sub ubi,” “Machines never get anything right. I am a machine,” and “A whop boppa loobop, a lop Bam Boom.” (Al considered the last his greatest achivement; scholars disagree on its significance.) Other researches led him to formulate the metaphysical poser, “Why in general is there being rather than non-being, except in parts of Atlantia?”

Unfortunately, Al did not realize the risks involved in assembling so many dumbeks and operators in a small space. The grass in the meadow was scorched, and twigs smoldered when the computator was in operation, but Al ignored the signs of possible danger. Instead, he made plans to enlarge the computator.

To the Caliph he mentioned the possibility of extending it in the third dimension, building a scaffolding of 99 levels above the original array, each level with space for an array the size of the original. This would enable Al to employ techniques he had developed for “massively parallel reckoning and stuff.” The notion amused the Great Caliph, but he noted that there weren’t enough slaves and beggars in Baghdad to supply the necessary dumbek operators; maybe when there was an opening in his schedule he might arrange a war or two to procure sufficient numbers of prisoners. In the meantime, he said, Al could content himself with a second level.

Most authorities state that it was merely an incomparably fierce fire that permamently scorched the Middle East, transforming the lush Arabian forest into desert. Computer simulations, however, suggest that, combined with the enormous ambient sonorous energy and with the flapping of a dragonfly’s wings in what is now Kechi, Kansas, the concentration of dumbeks and operators reached critical mass at the arrival of the 10,293rd dumbek, triggering a massive fission disaster that in turn triggered an even more catastrophic fusion event. Researchers currently are boring into the polar ice caps seeking evidence of a Medieval nuclear winter. One recently-published paper speculates that a black hole was formed into which all the dumbeks and operators fell, but this is probably wishful thinking.

The Great Caliph, it is recorded, was vastly amused by the bright lights and loud noises.

The Horror

The buumdek computator was utterly destroyed, but some dumbeks remained in Baghdad. Unmathematical induhviduals discovered that the their tones were loud and annoying, appealing characteristics to a certain type of musician. In time the origin of the dumbek as a tool of communication and calculation was forgotten, and it took it place among such devices as the hurdy-gurdy, the bagpipes, the bowed psaltery and the long version of “Crimson and Clover” as an instrument of musical torment.

I will pass over its role as an tool for information retrieval and verification during the 30 Years’ War, the 100 Years’ War and the War of Jenkins’ Ear, as well as its unexpected appearance during the Spanish Inquisition. Neither will I discuss the allegations that the dumbek was in constant use in soundproofed Kremlin basements during the Cold War, nor that the core core curriculum at the School of the Americas includes a semester of “Dumbek: Theory and Applications.” I will not even consider the possibility that Richard Nixon was a closet dumbek player. Nor will I comment on the musicianship of dumbek executants in the Current Middle Ages, nor speculate about their intelligence, their morals or their heredity. These matters I leave for scholars who are prepared to sacrifice their peace of mind for knowledge. I just want to get a good night’s sleep at an event, just once. Please let me sleep. Please.

Effects of playing a dumbek

To study the effects of dumbek playing upon the executant, a volunteer was handed a dumbek and asked to play. The experiment was halted after five minutes for humanitarian reasons.

The subject before the experiment. Note bright, clear eyes, alert expression and general impression of intelligence and responsibility.
The subject before the experiment. Note bright, clear eyes, alert expression and general impression of intelligence and responsibility.
Photographs taken during the experiment. The deleterious effects of the dumbek are already apparent. Individuals who handle dumbeks for extended periods of time risk lowered intelligence, neurasthenia and depravity.
Photographs taken during the experiment. The deleterious effects of the dumbek are already apparent. Individuals who handle dumbeks for extended periods of time risk lowered intelligence, neurasthenia and depravity.

Frequently Asked Questions

Most of these have been floating around in various forms; I’ve gathered them here for the convenience of the student of musical pathology.

What is the difference between a dumbek and dripping faucet? The faucet has a sense of rhythm.

What is perfect pitch? Tossing a dumbek into a trash can without hitting the sides.

What do you get if you drop a dumbek off the Leaning Tower of Pisa? Applause.

What is the difference between an onion and a dumbek? Nobody cries if you chop up a dumbek.

What has eight legs and flies? Four dumbek players.

What is the ultimate sincere compliment you can pay a dumbek player? “Nice tooth.”

You are holding a morningstar and you see before you a set of bagpipes and a dumbek. Which do you crush first? The bagpipes; business before pleasure.

What do you call 500 dumbeks at the bottom of the Mediterranean Ocean? A good start.

What is the difference between a dumbek and a lawnmower engine? The lawnmower can be tuned.

What has 24 legs and three teeth? The front row at a dumbek workshop.

How can you tell if the ground is level? The dumbek player drools out of both sides of his mouth.

What do you call a hundred dumbeks up to their rims in sand? Not enough sand.

What is the difference between a dead skunk in the road and a dead dumbek player? There are skid marks in front of the skunk.

What is the difference between a dumbek and a chainsaw? The chainsaw has dynamics.

What did the dumbek player get on his IQ test? Drool.

Why is the dumbek more popular than the bowed psaltery? There’s more room for drugs.

You are lost in the woods and you see a musical dumbek player, a dumbek player with no sense of rhythm, Santa Claus and the Easter Bunny. Whom do you ask for directions? The dysrhythmic dumbek player; the others are hallucinations.

How do you get a dumbek player off your front porch? Pay for the pizza.

What do you call a dumbek player with half a brain? Gifted.

Why is a dead armadillo in the road more tragic than a dead dumbek player? The armadillo was on its way to a gig.

Why was the dumbek player buried 20 feet deep? Because deep down he was a nice guy.

Which is larger — a dumbek or conga drum? They’re both the same size; dumbeks just look smaller because a dumbek player’s head is bigger.

What do you call those people who hang around musicians? Dumbek players.

What’s the difference between a dumbek and a jack-hammer? A jack-hammer only repeats itself 10 times a second.

You are in a room with Saddam Hussein, Osama bin Laden and a dumbek player, and your gun has only 2 bullets left. What do you do? Shoot the dumbek player twice just to make sure.

When should a dumbek player tune his dumbek? Whenever a difficult section come up in the music.

What do you call a beautiful woman on a dumbek player’s arm? A tattoo.

What do you say to a dumbek player in a three-piece suite? Will the defendant please rise and face the jury.

What’s the similarity between a dumbek player and a philosopher? They both perceive time as an abstract concept.

What’s the difference between a dumbek player and a large pizza? A large pizza can feed a family of four.

Copyright © 1999 by Don McClane. All rights reserved.