I have a theory that what people find most interesting in music is self-reference, recursion and fractal-like scale-invariance. Rhythms based on powers of two are a great way to get this kind of recursion because they can be compounded or subdivided so easily. A bar of four can be treated as two bars of two, …
Category Archives: Math
Tuning system geekery
If you’re a guitarist, you may have noticed that it’s hard to get your instrument perfectly in tune. This is not your imagination. If you tune each string perfectly to the one next to it, the low E string will end up out of tune with the high E string. If you use an electronic …
The mystical tritone
I’ve picked up some new guitar students lately, so I’m once again doing a lot of explaining what a tritone is and why people should care. Whenever I find myself explaining something a lot, I like to encapsulate it as a blog post. So here we go. A tritone is the interval between the notes …
Repetition, repetition, repetition, repetition
I’ve had a lot of music teachers, formal and informal. The best one has been the computer. It mindlessly plays anything I tell it to, over and over. Hearing an idea played back on a continuous loop tells me quickly if it’s good or not. If the idea is bad, I immediately get annoyed, and …
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A synthesizer is like an axe
I found this picture of Herbie Hancock on a stranger’s blog. There was no caption or any other context. So I posted it on my Flickr with a note asking if anyone could identify the computer Herbie is sitting in front of. A couple of days later my friend Mike responded with this video of …
Jimi Hendrix, electronic musician
People had been playing electric guitar for decades before Jimi Hendrix. Mostly they used it as a louder, less effortful version of the acoustic guitar. Jimi was one of the first musicians to think of the guitar amp as a musical instrument unto itself, an early analog synth, with the guitar as a very sophisticated …
Songwriting and computer programming
Writing a song is a lot like writing a computer program. They both require clever management of loops and control flow. The simplest sheet music reads as a straightforward top-to-bottom list of instructions. You start on measure one and read through to the end sequentially. That’s fine unless the music is very repetitive, which most …
So what is the big deal with Einstein?
I’m a humanities guy, but I’ve never lost my childhood love of math and science. I’m looking forward to the Large Hadron Collider being fired up next year the way normal male Americans look forward to the NBA playoffs. I like to be an informed fan, and since Einstein is the Michael Jordan of scientists, …
Be brave, go ahead and divide by zero
When you learned division in school, the teacher probably brushed off the issue of dividing by zero in one sentence: you can’t do it, moving on. You might feel like you got shortchanged by that explanation. Why not? What happens when you divide by zero?
Learning music theory with Auto-Tune
Auto-Tune makes producing music easier. It can also make understanding music theory easier. The way you dial up different keys and scales doesn’t just guide your ear, it also guides your eye. Your voice can produce a smooth continuum of pitches. To sing, you eliminate most of those possibilities, vibrating your mouth and throat only …