Bach wrote The Well-Tempered Clavier as a showcase for a new tuning system that could play in all twelve major and all twelve minor keys. Up until that point, the various European tuning systems only worked for some keys, not all of them. If you were in or near the key of C, you were …
Continue reading “The Well-Tempered (and not-so-well-tempered) Clavier”
Western people like two things in harmony: intervals derived from the natural overtone series, and the ability to play in multiple keys. Unfortunately, it’s not possible to do both of these things within the same tuning system. If you want to use just intonation intervals derived from harmonics, then they will not work in every …
We all love This Is Spin̈al Tap, but you’re not supposed to take it literally. Nevertheless, this very silly Rolling Stone article tries to prove Nigel right. The author is a doctoral student in quantitative methods. She should probably have asked a music theorist about this before publishing it, or really any musical person. I …
Continue reading “No, Rolling Stone, D minor is not the saddest of all keys”
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 …
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 …
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 …
Continue reading “What does the Well-Tempered Clavier sound like in actual well temperament?”
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 …
Toni Blackman was a guest on the Clinical BOPulations podcast to talk about her song, “Why Worry,” and to discuss her freestyle rap practice in the context of music therapy. I did a remix of the song interspersed with Toni and her hosts’ discussion of it, enjoy: https://soundcloud.com/ethanhein/toni-blackman-why-worry-clinical-bopulations-mix The track represents Toni’s first foray into …
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. …
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 …
