Just intonation harmonicas

A commenter on the last post informed me of a remarkable fact: for most of the twentieth century, Hohner harmonicas were tuned in just intonation, not twelve-tone equal temperament. This is surprising! Just about every fixed-pitch instrument in the Western world is tuned in 12-TET unless it’s highly specialized or esoteric. The most detailed information …

Tuning is hard

I am committed to teaching my students something about the history of tuning in Western European music. I don’t expect them to retain any details or do any math, I just want them to know that the history exists. In preparation, I continue to refine my explanation of this history to myself. Before the year …

Why are D-sharp and E-flat considered to be two different notes

Why do the black keys on the piano each have two different names? If the posts on r/musictheory are any indication, this is a persistent point of confusion, especially when music theory teachers get all persnickety about using the correct name. This confusion applies to all of the black keys, but in this post, I’ll be …

Led Zeppelin and the folkloric integrity of the blues

There is a fascinating moment in “When The Levee Breaks” by Led Zeppelin where Robert Plant plays a very flat ninth on the harmonica. I love this note, because there is so much music theory and history encoded within it. Listen at 0:41. Before we can get into the details of this note and what …

The harmonic family tree

My blog stats have made it crystal clear that very few of you want to read about tuning systems. However, a vocal minority of you do love reading about them, and I definitely enjoy writing about them. So, let’s dig in and see how much Western harmony we can derive from the natural overtone series!

Seventh chords in just intonation vs 12-TET

I enjoy listening to Jacob Collier explain his music more than I enjoy the music itself. His arrangement of “Moon River” is mostly exhausting. However, Miles Comiskey pointed me to an interesting moment in this explainer video at the 1:04:22 mark where Jacob talks about how Kontakt enables you to change your instrument tuning on …

The blues and the harmonic series – a visual guide

Does the harmony of the blues come from the natural overtone series? Is it a just intonation system that later got shoehorned into Western twelve-tone equal temperament? Whether the blues comes from just intonation, or just intonation happens to sound like the blues, this is a rich and promising avenue of inquiry, both for understanding …

The problem with just intonation – a visual guide

Tuning is the final frontier of my musical understanding. I start reading about it, and then I hit a big table of fractions or logarithms and my eyes immediately glaze over. However, tuning is important and interesting! So I continue to struggle on. Fortunately, as with so many music theory concepts, the right computer software …

The Well-Tempered (and not-so-well-tempered) Clavier

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 …

Just intonation and key changes

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 …