If you are a musician or audio engineer, it is very important to know what decibels are. Unfortunately, decibels are extremely confusing. For one thing, there are so many different kinds of decibels! You only care about two of them: the decibels you see on a noise meter, and the decibels you see on a …
Tag Archives: math
The whole tone scale
Like diminished chords, the whole tone scale is not very widely used, but when you need that specific vibe, nothing else will do. Whole tone scales are easy to understand, because there are only two of them total. Whichever key you are in, there is a whole tone scale that includes the tonic, and another …
The chromatic circle and the circle of fifths
The heart of Western tonal theory is this diagram: It’s called the chromatic circle, and it shows all of the notes you can play with a piano keyboard or guitar fretboard. It is closely related to another extremely important diagram called the circle of fifths: In this post, I explain where these diagrams come from …
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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 …
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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 …
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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 …
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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 …
The blues and the harmonic series
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 …
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 …