{"id":418,"date":"2018-04-14T15:15:52","date_gmt":"2018-04-14T15:15:52","guid":{"rendered":"http:\/\/andrew-may.com\/blog\/?p=418"},"modified":"2018-04-14T15:15:52","modified_gmt":"2018-04-14T15:15:52","slug":"symmetry-in-music","status":"publish","type":"post","link":"https:\/\/andrew-may.com\/blog\/2018\/04\/symmetry-in-music\/","title":{"rendered":"Symmetry in Music"},"content":{"rendered":"

\"Symmetric<\/a>I recently came across the idea of applying set theory to musical analysis<\/a> (which apparently has been around for some time, although I\u2019d never heard of it before). For most people, who have a stronger intuitive grasp of music than mathematics, this must seem a pointless exercise, but for anyone like me who\u2019s the other way around it\u2019s really very illuminating.<\/p>\n

Take symmetry, for example. In most areas of the arts and sciences, symmetry is seen as a good thing \u2013 but in music, that\u2019s not the case. All the most popular chords are asymmetric in terms of interval content. You can see that in the left-hand image above, which shows the three notes of the C major chord on the chromatic circle. They\u2019re separated by intervals of 3, 4, and 5 semitones.<\/p>\n

In contrast, an augmented C chord, shown on the right, is perfectly symmetric, with all three intervals equal to 4 semitones. The problem (as far as musicians are concerned) is that it\u2019s not very firmly tied to C major. It could equally well be A flat or E major. In the same way, the four-note symmetric chord C \u2013 E\u266d \u2013 F\u266f \u2013 A can be interpreted in four different ways: as Cdim7, E\u266ddim7, F\u266fdim7 or Adim7.<\/p>\n

There\u2019s even a completely symmetric two-note interval, in the form of the tritone, consisting of two notes 6 semitones apart (or 3 whole tones, which is how it gets its name). That\u2019s exactly half an octave, for example from C to F sharp. But it\u2019s also the distance from F sharp to C, so you really don\u2019t know which key you\u2019re in. That\u2019s why composers spent centuries trying to avoid it. They called it diabolus in musica<\/em>, or \u201cthe devil in music\u201d.<\/p>\n

Being a symmetry-loving scientist rather than a musician, I decided to try writing something that consisted only of symmetric chords. It\u2019s a sort of canon, in the key of everything.<\/p>\n

Here\u2019s a link to a YouTube video, with added graphics depicting the various chords on the chromatic circle. Hopefully you\u2019ll enjoy the graphics even if you don\u2019t like the music!<\/p>\n