by Tyler Boyd

Through the common language of mathematics, music and religion have always been intertwined. Today the connection is easily overlooked, but back in Europe's dark ages, before Bach and Beethoven made their way on the scene, it wasn't so subtle. One chord in particular was believed to invoke Lucifer himself, and was labeled diabolus in musica (see Slayer, 1998). This chord, now known as the tritone, which lies roughly three whole notes above the root note, is considered the most dissonant chord in the modern scale. Unlike the major and minor thirds and sixths which began as dissonances but were later considered harmonious, the tritone still remains dissonant to most ears.

But why are some chords dissonant while others are harmonious, or consonant? It all comes down to mathematics. It was Pythagorus who recognized that if one plucked a string, pinched it right in the middle (halving its length), and plucked it again, you would have an octave. The octave has a ratio of two to one, making it the most harmonious chord possible other than perfect unison (one to one). More complex interactions of numbers give rise to the broad spectrum of chords we’re accustomed to today: 3/2 gives you the perfect fifth, 4/3 the perfect fourth, 5/3 the major sixth, and so on.

Before the 1600s, music was formed mostly out of these basic ratios, in a tuning system called “just intonation.” Already you can see the moral connotations inherent in harmony emerging for us. This is different from our modern system of tuning because the ratios were not symmetrical, and the space between E and D was not the same as the space between D and C. Since Western composers in this era were working with only the friendliest of ratios, hideous deformities like the tritone simply were not part of the musical inventory of the time.

Just intonation was mathematically pure, but constricted the music of that time to operating in only one key. However, on the tail end of the 16th century, a solution to this dilemma was brought over from China. It was Chu Tsai-Yu in the Ming dynasty who first codified the system of twelve-tone equal temperament which we in the West take so much for granted today. The adoption of this tuning signified a grand shift in the priorities of the Western composer – mathematical simplicity was sacrificed in favor of symmetry. This is why, when you tune a guitar by ear, all six strings will never match up precisely. Equal temperament is a compromise. Now, all melodies could be played in every key, but the ratios were no longer pure. What’s more, some of the chords made possible in this system were dissonant and made their listeners uncomfortable.

Composers soon found that as their scores leapt (“progressed,” if you must) from chord to chord, they were being forced to confront more and more weird combinations of tones, and the flowerbed of harmony to which their innocent melodies had been accustomed was now a briar patch of dissonance. This gave rise to the grand tradition of dissonance and resolution, which saturates European classical music from the Baroque period until the contemporary movement in the 1900s.

But it doesn’t end there. From the standpoint of composition, it might be said that the pop music of today has more in common with classical music in the Baroque period than modern classical. While contemporary music has moved on to explore the realms of the minimalist, the random and the microtonal, most popular music hangs precariously back, telling this tried-and-true tale of dissonance and resolution.

It’s a very old fable that no one ever seems to get tired of, even though it’s been told to us for hundreds of years. First, a familiar setting for the story is established (the key). Then, an element of conflict is introduced, in the form of a rogue dissonant tone. After an exciting journey in which the tone travels through many diverse climates, the tone is resolved. Story ends. How inspirational! But we need to come back to the original question: what exactly is it that makes certain select chords dissonant in the first place?

The numbers that make up a harmonious ratio are small. Three to two. Five to four. These are numbers which can be digested without difficulty. Dissonant chords are what happen when you put together larger numbers, such as nine and eight, or sixteen and nine. The mind recoils in horror! The tritone, granddaddy of them all, is commonly located at one over the square root of two, which is not even a rational number. I think I’m going to be sick.

The logic behind this classification system is clear: simplicity fosters harmony, and complexity fosters dissonance. When understood this way, the story we just observed changes significantly. No longer is it about happy music notes who run into trouble on the way to the ice cream parlor only to reunite later, unscathed. This is really about the flow of information. Familiar simplicity explodes gloriously into a bewildering, frightening chaos of complex ratios that must immediately be “resolved.” Or does it? If dissonance is nothing but unrestrained complexity, then just what is this relief, this satisfaction that comes along with a properly resolved chord?

The line between consonance and dissonance has been erased and redrawn several times in European musical tradition. There’s nothing stopping any of us from continuing this trend in our own minds. Religious fundamentalists may condemn rock music for all its distorted swaggery, but the truth behind the rhetoric is that listening to music that makes you uncomfortable (for whatever reason) just might make you comfortable with being uncomfortable. And (if you’re in the mood for philosophizin’) it just might force you to confront an age-old dilemma: will I avoid what I don’t understand, or will I dance in the rain?

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