Abandoned

Since infogami has been abandoned by its creators, I’m out too. Back to web.fisher.cx for me. Everything that was here is there.

Robert Fisher

Just thinking out loud

The justly intonated major third

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A little something I learned from the Wikipedia article on Eddie Van Halen.

Electric guitar players often rely on intentionally driving their amplifiers to distortion to create certain timbres. With distortion, we typically avoid certain intervals—such as major or minor thirds—because the distortion makes them unmusically dissonant. We tend to play bare perfect fourths & fifths (the so-called “power chords”) leaving the thirds out of the chords. Or stack fourths & fifths to create quartal or quintal triads.

Western musical instruments are almost universally tuned by a system called equal temperment. (Or, more specifically, twelve-tone equal temperment.) This mistunes each note slightly in order to make the instrument sound roughly the same in every key. With just intonation an instrument would sound different in each key. e.g. On an instrument justly intonated to the key of C major, the third of D minor would be out-of-tune.

It turns out that a justly intonated major third sounds just fine with distortion. Which makes sense, but I’d have never thought of it.

The justly intonated major third is sometimes called a “perfect third” in parallel to perfect fourths & perfect fifths. The “perfect” (pedantically) only applies to fourths, fifths, & unisons. It’s still a major third, it’s just a justly intonated rather than a well tempered one.

Of course, a guitar’s frets are placed according to equal temperment. So, you can’t just retune the strings to just intonation. (Even if you moved the frets, I think just intonation would either require all strings to be tuned to the same note or require different fret placement for each string.)

You can, however, retune a single string so that you can produce some justly intonated major thirds. The second (B) string is a good candidate since it is already tuned a major third above the third (G) string. Then you can play some distorted-but-consonant major triads. Of course, there’s a price to be paid. This throws off some other intervals between that string & the others. Plus you still have plenty of well tempered major thirds around the fretboard. So, you have to be careful.