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 2 hours 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 2 hours 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!