Music Theory for the 21st-Century Classroom

> why does piano have 88 keys?

I'm only ok at music theory, so I might get bits somewhat wrong, but the gist is right.

Notes with wavelengths that are integer multiples/fractions of each other sound the same. 440 Hz sounds similar to 220 Hz and 880 Hz (and this makes sense if you just look at the waveform), so we give them the same name. Western music slices the range between ω and 2ω into 12 points evenly divided along a log scale (we call this an octave). The log scale means the relationship of nearby notes is always the same; it takes an exponentially growing scale (frequency) and makes it linear.

You said 7 have names, but there are 12 notes in an octave. You'll learn more about that difference with scales, but the short answer most western music won't use all 12 notes because, for a given key; a specific subset of 7 sound a lot better together than the others.

88 keys is somewhat arbitrary, and there are pianos with more or less. What's important is how many and which octaves the piano covers.

Why is it called an octave when it has 7 named notes? I guess so we can repeat the first one and drive home the 2ω relationship.

It's like understanding syntax or grammar for a language. Making explicit names, categories, and systems to take apart what you're doing/saying. 99% of the time though people don't think about that, they go by "feel."

But if you can understand the underlying framework, you can also work to intentionally use those to your advantage such as by reinforcing expectations or subverting them in clever ways. Obviously you can also do this by "feel," but an understanding of the underlying mechanics and systems gives you a better framework to spot the points where you can get away with things. When you want to get deeper and push the boundaries of a craft it also helps to understand what "best practices" are in place and why, and then look to exploit them.

I have a friend who was self-taught guitar and a variety of other instruments and only recently started on piano and proper theory. It's been fun watching him recognize and get a framework for why things he's intuitively known, such as how a cadence works or key transitions through a circle of fifths, be brought to the surface explicitly.

Using music theory they can understand why certain composition works and then use the listeners intuition against them to subvert those expectations while still providing something coherent.

An example is something like Bleed by Meshuggah. Most people assume it uses some complex time signature but I am pretty sure its just 4/4. Periphery will have pieces that sound 4/4 but are actually 6/8s. Basically most time signatures (if not all, idk) are effectively extended 4/4, so they can create a riff that eventually hits the 4/4 your internal clock expects to hear but in between you can't necessarily find the pattern.

But like you said, music theory tells you all the rules so you can break them. It's sort of like any other set of rules. You need to understand why they are there so you can understand the right why to subvert them.

> Conversely, there appears to often be many ways to "explain" a certain composition in terms of music theory.

Remember that music theory is descriptive, not prescriptive. It's a description of existing musical practice, not a set of rules that say what is right and wrong.