What's weirder is that if you're using just intonation in, say, the key of C major, there's two different D's. One is 9/8, and the other is 10/9. The note we

What's weirder is that if you're using just intonation in, say, the key of C major, there's two different D's. One is 9/8, and the other is 10/9. The note we call D in equal temperament is about half-way between the two. If you want to play these chords in C major: Cmaj, Fmaj, Gmaj, Dmin, Emin, and Amin, you'll need to use both of those D's: 9/8 for the 5th of Gmaj, and 10/9 for the root of Dmin. If you try to play Dmin with the 9/8 instead, it sounds absolutely awful. In other words, if you want to play those six chords that are regarded as belonging to C major, you'll need two different D's. Which means the C major scale should really have 8 notes instead of seven. But we don't have a symbol to distinguish between 9/8 and 10/9 in standard notation, they're both just plain D. Some 12-EDO music makes use of the ambiguity between these two notes (or any two notes with the same relation to each other) to string together chord progressions that don't actually make sense mathematically. If you used those progressions in just intonation, you'd find you don't return to the chord you started on, you actually shifted up or down by a small interval of 81/80. It's sort of the musical equivalent of some formula that only works if you assume that pi is equal to exactly three.