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Comment by twobitshifter | Hacker News Reader

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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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

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!

Not everyone tunes their piano equal temperament. I use an alternative tuning ebvtiii which I think is a better compromise. There are a ton of well-tempered tunings with various compromises. I would like a piano that has 15 keys per octave so I can tune it in quarter comma mean tone. (i've seen pipe organs done this way, but never piano.)

Wikipedia has an entry for well tempered as well https://en.wikipedia.org/wiki/Well_temperament

Most popular music we hear outside is based on guitars and pianos, as I play the guitar I always think of music that way. You are right that we naturally sing in just intonation and woodwinds have difficulty with equal temperament based on their physics, however it’s very rare that you will hear a specific song in just intonation. You can search YouTube for performances, it’s pretty interesting to hear the differences.

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