{"id":574,"date":"2019-07-18T18:27:47","date_gmt":"2019-07-18T18:27:47","guid":{"rendered":"http:\/\/andrew-may.com\/blog\/?p=574"},"modified":"2019-07-18T18:27:47","modified_gmt":"2019-07-18T18:27:47","slug":"musical-symmetry-revisited","status":"publish","type":"post","link":"https:\/\/andrew-may.com\/blog\/2019\/07\/musical-symmetry-revisited\/","title":{"rendered":"Musical Symmetry Revisited"},"content":{"rendered":"\n
\"Symmetric<\/figure>\n\n\n\n

In a blog post last year<\/a> I talked about symmetric musical sets \u2013 such as the tritone, the augmented triad, the diminished 7th, the whole-tone scale and the chromatic scale \u2013 which divide the octave into 2, 3, 4, 6 and 12 equal parts respectively. For various reasons musicians dislike these groupings, so they\u2019re used very sparingly in classical music and virtually never in pop music. But as someone who\u2019s always been more into maths than music, I\u2019m fascinated by any kind of symmetry. <\/p>\n\n\n\n

Traditionally the octave is divided into 12 semitones, so the symmetric sets I just mentioned are the only possible ones. But what if you wanted to divide the octave into 8 equal parts? That seems an obvious choice, because it\u2019s what the word octave implies. But to do it we need to invoke quarter tones. There are 24 of these in an octave, and 24 divided by 8 is 3, so we\u2019re looking for notes 3 quarter tones (or one and a half semitones) apart.<\/p>\n\n\n\n

Writing music in quarter tones isn\u2019t easy, because the MIDI format defines pitch as an integer number of semitones. But it does allow something called \u201cpitch bending\u201d (presumably to simulate bending the string of a guitar), and with a bit of patience you can use that feature to raise the necessary notes by a quarter tone.<\/p>\n\n\n\n

Here\u2019s a short (1 minute) piece I wrote to see what it would sound like. It\u2019s basically a random composition using the 8 equally spaced notes shown in the diagram above.<\/p>\n\n\n