Summary (So Far)

I messed around with electronics quite a bit as a kid. I’d put things together according to diagrams, and if they didn’t work, I’d change something and see what happened, and get a feeling for what was happening inside the black box. When I started doing audio electronics in earnest, I found the oscilloscope. Here’s…

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Seven

My favorite contemporary band is the Black Keys. I think Dan Auerbach is a harmonic genius. The video is funny. Dinosaur? What dinosaur? This song lives in the universe of 7. I just spent a half day taking apart the main riff and seeing how it works out on the lattice. It strictly uses a…

The Augmented Fourth

I’ve described eleven notes now, and each one has a piano key to go with it, an equal tempered equivalent. The one remaining black key has a lot of names. It’s the note between the 4 and 5, right in the middle of the octave — the tritone, devil’s interval, flatted fifth, augmented fourth. In…

The Minor Second

The last three notes (b6, b3 and b7) are related to each other. They all contain a reciprocal third. There is a family resemblance of sound and function. (They also all happen to be a little flat in equal temperament. On a guitar it’s a nice trick to bend them a little to sweeten them.)…

Untempered Vs. Tempered

I’ve been listening to yesterday’s chord progression showing off the b7. I think it offers an excellent opportunity to hear the difference between equal temperament and just intonation. Equal temperament works by implying or evoking a note rather than playing it exactly. There are dozens of singable notes per octave; ET represents them all with just…

The Minor Seventh

The farther we get from the center, the less consonant the notes are, when played against the tonic. Consonance is a whole subject. It’s generally spoken of as though it could be plotted on a scale, from consonance to dissonance. I think this is a big mistake. Consonance has more than one dimension. Trying to…

The Minor Third

Here’s an interesting and perhaps misunderstood note. It’s a compound move on the lattice: down a third and up a fifth. Or up a fifth and down a third, it doesn’t matter what order. So the ratio is 3/5, or 6/5, octave reduced. The note is the minor third. I call it b3. It lives a…

Reciprocal Thirds

There are four basic moves available on the lattice of fifths and thirds. They are: Up a fifth (x3) Down a fifth (÷3) Up a major third (x5) Down a major third (÷5) Each of these moves has its own harmonic flavor, and they can be combined to create new flavors. The major scale only…