It would be natural to read these posts and wonder why I’m so passionate about intonation, and why I’m going to so much trouble to explore it in this blog and in real life. After all, we’re talking about tiny differences in tuning here, why be so picky when it’s the heart that counts? It’s…
Even though I love just intonation, I have a couple of problems with the term itself. One is grammatical. It’s a noun, and sometimes I want an adjective, as in “the just intonation version compared with the equal tempered version.” Kind of awkward. How else would you say this? “Justly intonated”? “The version in just…
In one of my favorite passages in Harmonic Experience (p. 104-105), W.A. Mathieu points out that by the time Mozart came around, equal temperament was well enough established that a D# and an Eb could be thought of as the same note. So when Mozart wanted his melody to go back and forth between an Eb and…
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…
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…
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 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…
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…
The notes 1, 2, 3, 4, 5, 6 and 7, clustered at the center of the lattice, constitute a major scale. This tuning uses the smallest ratios (the ones with the lowest numbers) available for each position in the scale. It goes back at least to Ptolemy in the 100’s AD. I find it visually…
Musical nomenclature has been cobbled together over the centuries like a medieval city. Different systems leave their imprint in convention, later developments try to be compatible with accepted names, and the whole thing ends up confusing and contradictory. Take enharmonic equivalents, for example. G# and Ab are the same note on the piano, the black…