In this post, I’m going to expand on an idea in my blues tonality treatise: that the distinctive scales and chords of the blues are an approximation of African-descended tuning systems based on the natural overtone series. Gerhard Kubik argues in his book Africa and the Blues that blues tonality comes from the overtone series …
Tag Archives: math
Circular chord charts
Being home with my kids all day is not very conducive to dissertation writing, but my fragmented attention is still up to the task of making infographics. I’ve been thinking about ways of visually representing grooves. Since circles work so well for rhythms, maybe they can work for harmonies too. Here’s a circular view of …
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 …
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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 …
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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 …