Xenharmonic music theory part 3: Tuning theory

This is the final part of a series introducing xenharmonic music theory. In the first part, I talked about musical perception, especially the perception of microtones. In the second part, I explained roughness theory, which is an empirical theory of dissonance independent of musical tradition. The first two parts overlap with conventional music theory, but in this third part, I finally reach the music theory that is more particular to the xenharmonic tradition.

I’m just going to scratch the surface here, with an eye towards how you would actually use it in practice, if you were a composer. Most readers, I imagine, are not composers. It’s okay if it’s just a hypothetical for you, as long as you learn something.

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Xenharmonic music theory part 2: Dissonance Theory

See part 1

Dissonance in music is analogous to conflict in a story. Dissonance sounds “unpleasant” in the same way that conflict is unpleasant to the characters within the story, but then it would be an odd to have a story without any conflict. The opposite of dissonance is called consonance. Music commonly alternates between dissonance and consonance–creating tension, and then resolving it.

Conventional musical theory comes with a bunch of ideas about what’s consonant or dissonant. 400 cents, the major third, is considered consonant; 300 cents, the minor third, is considered dissonant. There’s some physical basis for these ideas, but arguably a lot of it has to do with tradition. 300 cents is more dissonant than 400 cents because that’s the meaning we’ve absorbed from our musical culture.

When you go outside the usual tuning system, musical tradition offers less guidance on what’s more or less dissonant. So this is the part of my intro to xenharmonic theory where I discuss a theory of dissonance that is independent of musical tradition.

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Xenharmonic music theory part 1: Perception of microtones

Microtonal music is music that goes outside of the standard western 12-tone tuning system. There are many microtonal traditions throughout history and the world, but xenharmonic music refers to a specific modern musical tradition that makes a point of being microtonal.  If you’d like to listen to examples, I have a list of popular xenharmonic artists. Xenharmonic music is associated with music theories that might be considered heterodox. Heterodoxy is good though because conventional music theory is too narrowly focused on a certain European classical music tradition, and we could use an alternate perspective.

This is part of a short series introducing xenharmonic theory. Part 1 is about the perception of sound, with a particular focus on small differences in pitch. Part 2 is about dissonance theory. Part 3 is about tuning theory. The first two parts overlap with conventional music theory, but focus on aspects that are independent of tuning. Part 3 is where we get into theory that’s more specific to the xenharmonic tradition.

I freely admit that I don’t know everything, I just know enough to point in some interesting directions. The idea here is not to write an authoritative intro to xenharmonic music theory (which might be better found in the Xenharmonic Wiki), but to write an accessible intro with a bit of a slant towards what I personally think is most important.

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Answering physics FAQs without preparation

Experts don’t know everything. Often, they only know how to look things up, and how to understand what they find. If you’ve ever seen physicists answering a physics FAQ, those answers took a lot of effort to get right. Some common questions are in fact really complicated, or hard, or maybe they just aren’t about the things that physicists normally think about.

With humorous intent, I’m going to answer a bunch of frequently asked questions, sampled from this physics FAQ by John Baez. And I’m doing it without preparation, so the answers will be bad.

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Sexual identity and topology

One of the consequences of having a great deal of math and physics education, is that whenever I learn about something, I internally encode it as math, even if nobody else is thinking of it that way. Today I’m going to share one of the more ridiculous examples, the analogy between identity labels and topology.

I’m mainly thinking about sexual identity labels, and especially arguments over boundaries of those labels. I’m thinking of how people claim “everyone is a little bisexual”; or they argue about the validity of bisexual lesbians; or they ask “isn’t demisexuality just normal?”; or they draw sharp distinctions between asexual, gray-asexual, and allosexual.

In all these arguments, there is the essentialist viewpoint, which says that everyone has an underlying sexuality, and each word covers (or should cover) a specific space of sexualities. If your underlying sexuality falls within the domain of the identity label you use, then your label is “correct”, and if it doesn’t, then your label is “incorrect”.

I disagree with the essentialist viewpoint, and I frequently point to prototype theory, family resemblance theory, and Wittgenstein as alternatives. But I also feel that if you’re going to take the essentialist viewpoint, obviously you should take it all the way, and learn about the math that you’re implicitly using. I am not going to “prove” that essentialism is wrong, and if you summarize my essay as “Mathematics disproves essentialism” then so help me, you did not read the fourth paragraph. The goal is to explore the implicit mathematical framework of essentialism, and point out its unaesthetic aspects.

Of course, I don’t recommend actually using this in an argument, since it relies on teaching people math.

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Unbiased estimators in a Monty Hall problem

In my previous post, I talked about the German Tank Problem. And while discussing the frequentist approach, I defined the “unbiased” estimator. But seriously, unbiased estimators are really weird. Let me show you an example, in the form of a Monty-Hall-like problem.

Suppose that I’ve set up three closed doors A, B, and C, each with a prize behind it. Two of them have $1000, and one has $2000. Doors A and B don’t really matter, your prize is behind door C. How much is this prize worth to you? But before you answer, please, look behind one of the other doors, A or B.

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The German Tank Problem

The German Tank Problem supposes that there are N tanks with ID numbers from 1 to N. We don’t know what N is, but have looked at a single tank’s ID number, which we’ll denote m. How would you estimate N?

This is a well-known problem in statistics, and you’re welcome to go over to Wikipedia and decide that Wikipedia is a better resource than I am and, you know, fair. But, the particular angle I would like to take, is using this problem to understand the difference between Bayesian and frequentist approaches to statistics.

I’m aware of the popular framing of Bayesian and frequentist approaches as being in an adversarial relationship. I’ve heard some people say they believe that one approach is the correct one and the other doesn’t make any sense. I’m not going to go there. My stance is that even if you’re on Team Bayes or whatever, it’s probably good to understand both approaches at least on a technical level, and that’s what I seek to explain.

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