Sixth notes

Sticky Notes is an excellent podcast about classical music, by the conductor Joshua Weilerstein. A recent episode was on Bruckner’s fourth symphony, a piece I wasn’t familiar with. In Bruckner’s work, there appears the “Bruckner rhythm”, which is two quarter notes followed by three quarter note triplets. And in musical terminology, that’s entirely correct!

But if the terminology made mathematical sense, that would be a “sixth note”, which somehow I had never realized. A few people have pointed this out (here, here, here). It seems like this is most natural to programmers creating software that has to deal with music. For example – and I can’t believe I remember this – QBasic had a PLAY command that played music through the computer speaker, specified note by note. For the main theme of the first movement of Bruckner’s fourth symphony, something like

PLAY "O3 E-4 < B-4 A-6 G6 F6 E-4"

would have played the example

Main theme of first movement of Bruckner’s fourth symphony

(That’s a tenor clef, the fourth line from the bottom is middle C.). The - represents flat, the O3 represents the starting octave, and the < represents an octave change. (I cannot guarantee this code actually works, because it’s 2020.)

The PLAY command mishandles the other tricky bit of notation, which is “dotted” notes. For example C4 is a quarter-note C. C4. is a dotted-quarter-note C, that is, one and a half times as long as a quarter-note. But C4.” is one and a half times as long as that, or 2.25x the original quarter-note. But a double-dotted note in ordinary musical notation is 1.75x as long. If I remember correctly I thought it was 2.25 because I found the PLAY command before I ran across double dots in any actual music.

Also, in music, the ordinary fact “2 + 2 = 4” becomes “3 + 3 = 5” – that is, two thirds make a fifth. Every so often on Music Stack Exchange one sees people saying musical notation and nomenclature don’t make sense, which is true if you’re coming at things fresh, but is also an example of how Stack Exchange sites get weird as you go conceptually further away from StackOverflow.

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