HN Theater @HNTheaterMonth

I can help with a couple of these. 12 notes is a kludge, because powers of 2^(1/12) well approximate simple ratios. These simple ratios (such as 3:2) sound good. I like this video for explanation: https://www.youtube.com/watch?v=1Hqm0dYKUx4

Also, the reason that the letters are in the wrong order is that we're playing the wrong scale. The monks who invented the scale usually sang in A-minor (so we use the first letter for that scale). Nowadays, we use the major scale, which has the same spacing between notes, but in a different order. It just so happens that C-major has the same notes as A-minor, so that's why we count from C. A great channel for this is Michael New, he explains everything very clearly: https://www.youtube.com/watch?v=UcviIQg_BlU

Music, much like language, has a lot of technical debt.

⬐ exporectomy

Thanks. Those are very enlightening. The fraction names are really nothing like what you'd expect them to mean! Now I realize why when someone was trying to explain a circle of fifths to me and how it was like a clock, it wasn't a 5-numbered clock!

⬐ madcaptenor

The other thing to keep in mind is that in musical intervals, X and Y add up to X + Y - 1. For example, two thirds (say, C-E and E-G) make a fifth (C-G). That's because both endpoints get counted in the interval.

Equal temperament just means equally out of tune.

Minute physics does a great video on it: https://youtu.be/1Hqm0dYKUx4

⬐ kazinator

Equal temperament is certainly not "equally out of tune". It has terrific octaves and very good fourths and fifths, compared to some other intervals.

It really does mean equal geometric steps between successive tones.

Each key is equally "out of tune" under equal temperament; e.g. C# minor and D minor are basically the same, modulo pitch.

minutephysics had a nice video about the mathematics that go behind piano tuning too.

"Why It's Impossible to Tune a Piano" https://www.youtube.com/watch?v=1Hqm0dYKUx4

⬐ kzrdude

If you really want to dive deep into historical tuning systems, check out early music sources, https://m.youtube.com/channel/UCJOiqToQ7kiakqTLE7Hdd5g/video...

Related, why you can't tuna fish, or tune a piano: [Minute Physics] https://www.youtube.com/watch?v=1Hqm0dYKUx4

⬐ ashmud

Thanks for this. I was unfamiliar with Henry Reich's videos.

A related video on the numbers behind piano music, on why it is mathematically impossible to perfectly tune a piano :

https://www.youtube.com/watch?v=1Hqm0dYKUx4

⬐ ta0o0o0

Interesting video, I just have a few nitpicks.

The problem is not that the piano has too many strings, it's that the notes are fixed. The same is true for any string instrument with frets, like a guitar, or wind instruments with fixed holes, like a flute.

The video also refers to the fact that equal temperament allows playing in any key, but doesn't really explain why that's important or what the tuning has to do with it. (Short answer, before equal temperament, different compromises were made in which notes were out of tune with respect to which others, and the schemes commonly chosen only allowed some of the keys (as in "c major" not the physical key) to be sufficiently in tune to be usable.)

⬐ analog31

As I understand it, people were aware of the problems of the temperaments, but a temperament is a technology. Each of the old temperaments came with an algorithm, that your regular Joe musician could use to keep their own instrument in tune. This in turn was needed because instruments didn't stay in tune for very long.

Equal temperament requires an expert, which in turn requires an instrument with stable tuning -- the modern piano.

Wind instruments actually have no straightforward temperament, but are just as close as possible, and the musician is expected to bend notes as needed. For all practical purposes, an orchestra is an un-tempered instrument.

⬐ ta0o0o0

OK. I guess I shouldn't have talked about instruments I don't know well.

⬐ None

None

⬐ themattbook

I will forever take this into account the next time I tune my guitar using harmonics by ear. Very interesting!