Tiled With Pentagons

(Epistemic status: Philosophy of observation and memories of physics. The math is real and the metaphysics are probably reasonably solid too. As usual, morally correct, skipping over some of the finer details. Dedicated with bittersweet fondness for the Integrated Sciences Curriculum program. Even still, everything is a spring.)   Plucked guitar strings and the quantized modes of trumpet blasts. Carbon dioxide's vibrational modes. Cyclical stock market trends, despite the efficient market hypothesis. The length of a day over the course of a year. These and many other phenomensta should make you ask one simple question: why do so many physical systems like to vibrate? Why are so many such systems well-modelled by reducing them to simple or damped harmonic oscillators? That is: Why is everything a spring? After years of chewing it over in quiet moments, I've eventually come to a conclusion, and I'm not sure whether it's profound, trivial, both, or some secret fourth thing...

Here are two extra bits to talk about that were out of scope for my previous post about microtonal music, but which I still think are valuable to read. First, some music I recommend, if you want to try listening to microtonal/xenharmonic/untwelvish music. If you like guitar-driven rock, Brendan Byrnes is a surprisingly prolific musician who’s done a lot with sharp-fifth tunings like 22edo and 27edo; I recommend starting with the albums “Realism” and “Holocene Dream”. (“Neutral Paradise” is one of my favorites, and “Micropangaea” is his older and most varied album.) For a better-known option, King Gizzard and the Lizard Wizard has done plenty of music in 24edo, mostly emulating Anatolian, traditional Arabic, and Jewish scales; “Flying Microtonal Banana” is the starring example among albums, and the two-part album “K. G.”/”L. W.” presents another excellent example. For jazz, go looking for the sweetened thirds and flat fifths of 31edo; Hear Between the Lines has published some excellent ...

So you’ve heard about this “microtonal” thing, and you’ve become curious about it. Maybe you even listened to some music, and it sounded weird and kind of… out of key but maybe also simultaneously “locked-in” in the way that a cappella choirs and barbershop quartets are. Or maybe you’re wondering why we would ever want more than 12 notes in an octave at all, or you’re familiar with musical traditions - Arabic, Anatolian, Indian classical, klezmer, and gamelan among many others - that make use of scales and harmonies beyond or totally separate from the modern Western canon. Even the sweetness of old church organs - you know, the ones that sometimes have weird split black keys? - are an example of microtonal music! But why would we ever want to make use of such dissonant intervals as we find crunched beneath the semitone distance of a minor second? Before we can talk about that, we need to think a little more closely about the nature of musical pitches. While pure sine wave tones are com...