Mozart on the Lattice

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 an E, he wrote (spelled) the notes as D# and E, probably to make the music easier to read. In just intonation, D# is an entirely different note, and makes less harmonic sense than Eb.

I got curious as to how the two spellings would sound and look on the lattice. I also made one in equal temperament. They are quite different, and I think it’s fun to compare them. These are on YouTube with the following descriptions:


A passage from Sonata in F, K. 332. This is the spelling suggested by W.A. Mathieu, Harmonic Experience, p. 105. The melody moves between the major and minor third. Listen to the major/minor interplay in just intonation.


A passage from Sonata in F, K. 332. This is how Mozart spelled it, with a #2 instead of a b3. He likely did this to make it easier to read. This video shows how that spelling would look, and sound, in just intonation, if taken literally. The melody moves by a diatonic semitone (112 cents) rather than by a chromatic semitone (70 cents), and the effect is quite different.


A passage from Sonata in F, K. 332, in equal temperament. In ET, the b3 and #2 are both tuned to a compromise pitch, in between the two. I think the ear turns it into a b3 here, but the effect is off, the note is quite flat. The whole passage feels different than it does in either of the JI versions.

How beautiful Mozart’s music is! I have watched the first video, in JI with the major/minor pair, many times. Try following just the orange one a couple of times, then just the yellow one.

Next: Melodic Space, Harmonic Space

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