There's also a huge amount of math behind music that is fascinating.

The first-approximation engineer realization about music (which I suspect the GP is going off of) is "okay, there are 12 notes in the chromatic scale, each octave doubles frequency, therefore the frequency ratio between two adjacent notes is the 12th root of 2 and we should just have 12 names for the notes". This is what's called an "equal-tempered scale"; the gap between each note is the same ratio, and you have a simple geometric progression upwards.

Except we don't actually have an equal-tempered scale. If you try to play on an equal-tempered scale, it'll sound subtly "off", and certain chords will result in "beats" (pulsing) where the frequency ratios are off just enough to cause an unpleasant modulation in loudness.

The modern diatonic scale is based on the circle-of-5ths [1], where the fundamental ratio is the 5th at 3/2 the frequency. It works like this because now chords are an even multiple of frequencies, while you would get an irrational number with the equal-tempered scale. Going up from the root (C), the next 5th up is G at a ratio of 3/2. Then you go up to D (9/4); when you reduce this to lowest terms because you've ascended a full octave, it gives a ratio of 9/8, which is one whole tone above. Next 5th up is A (27/16), which is the ratio in frequencies of a 6th. And then you get E (81 / 32 = 81/64), a major 3rd. And so on. The frequency ratios of the diatonic scale come from repeatedly reducing powers of 3/2 to lowest terms after dividing out the octave.

[1] https://en.wikipedia.org/wiki/Circle_of_fifths

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twobitshifter an hour ago | parent | next [-]

We do have an equal temperament scale! That’s what most music uses. What we don’t have is just intonation which uses simple ratios/intervals for the notes. It’s just intonation without the beating, equal temperament, which was listen to all day has the beating but we’re adjusted to it.

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nostrademons an hour ago | parent [-]

Do we? My impression was that strings, woodwinds, choirs instinctively tend to use just intonation, and Wikipedia entries for both just intonation [1] and equal temperament [2] seem to back that up. That's why symphony orchestra players will often have a different flute, clarinet, or oboe for different tunings. It's just fretted instruments like guitars that are by nature equal-tempered.

On a side note, both Wikipedia entries reinforce my original point that the mathematics of this is fascinating.

[1] https://en.wikipedia.org/wiki/Just_intonation

[2] https://en.wikipedia.org/wiki/Equal_temperament

	▲	fl4regun 18 minutes ago \| parent [-]
		Not just fretted instruments, pianos as well. Anything which lacks ability to adjust tuning on its own, while being played (things that wind instrumenst and non-fretted strings can do), for example a steel pan drum, would be equally tempered (assuming you want to be able to play in all possible keys). >That's why symphony orchestra players will often have a different flute, clarinet, or oboe for different tunings. Not sure what you are referring to here? Clarinets don't come in different "tunings" unless you mean different keys - like Eb or Bb clarinet, but those aren't there for intonation, they play in different ranges of pitch than one another. Edit: in addition, you don't HAVE to equally temper a guitar. You can choose just intonation. The problem is that you can only have just intonation on a single KEY for that instrument. So if you tune justly to C major, a key like B major, will sound horrendous!

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klaff an hour ago | parent | prev [-]

You've got that a bit backwards.