What does the Well-Tempered Clavier sound like in actual well temperament?

First, some niche Twitter comedy: Twelve-tone equal temperament is socialism, Make Intonation Just Again — ethanhein.bsky.social (@ethanhein) June 26, 2020 The Well-Tempered Clavier is a book of JS Bach compositions for keyboard instruments in each of the twelve major and twelve minor keys. The name refers to Bach’s preferred tuning system, which made it possible …

Teaching note values

Western music notation is a graph of pitch (on the vertical axis) and time (on the horizontal axis.) It’s mostly self-explanatory on the pitch axis, but it’s harder to understand on the time axis. It helps if you visualize your rhythms on a circle, like the Groove Pizza does. Everything I talk about in this …

Scales, keys and modes on the circle of fifths

If you want to understand Western music theory, the circle of fifths is an invaluable tool. For one thing, it can help you understand how key signatures work. But it also helps explain how the major scale and diatonic modes relate to each other, and gives a possible explanation for why they sound good. Here’s …

RIP Godfried Toussaint

I was sad to learn about the recent death of Godfried Toussaint, whose work on the geometry of musical rhythm has been a major inspiration for me. I never met Godfried, but I have read and re-read his work. His rhythm necklace diagrams were the direct inspiration for the Groove Pizza – I saw them …

The Groove Pizzeria

For his NYU music technology masters thesis, Tyler Bisson created a web app called Groove Pizzeria, a polyrhythmic/polymetric extension of the Groove Pizza. Click the image to try it for yourself.  Note that the Groove Pizzeria is still a prototype, and it doesn’t yet have the full feature set that the Groove Pizza does. …

Why can’t you tune your guitar?

Short answer: because math. Longer answer: because prime numbers don’t divide into each other evenly. To understand what follows, you need to know some facts about the physics of vibrating strings: When you pluck a guitar string, it vibrates to and fro. You can tell how fast the string is vibrating by listening to the …

Kumbaya

When you look up “Kumbaya” on Urban Dictionary, you get an adjective meaning “blandly pious and naively optimistic.” This is the sense in which Fox News often uses the word to make fun of bleeding heart liberals like me. I learned the song from numerous earnest white folk singers, many of whom learned it from …

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 …

Four bars of Mozart explains everything humans like in music

I’m not arguing here that everyone loves Mozart, or that I’m about to explain what all humans enjoy all the time. But I can say with confidence that this little bit of Mozart goes a long way toward explaining what most humans enjoy most of the time. The four bars I’m talking about are these, …

The vocoder and Auto-Tune

The vocoder is one of those mysterious technologies that’s far more widely used than understood. Here I explain what it is, how it works, and why you should care. Casual music listeners know the vocoder best as a way to make the robot voice effect that Daft Punk uses all the time. Here’s Huston Singletary …