why don't we hear beats when different keys on the piano are played at the same time?

Answer 1

You *can* hear destructive interference, if you play a minor 2nd, (for example A and A-flat.) You may also be able to hear faint beats in a major third (C, E)

Most common intervals and chords you will hear played on a piano are "consonant," meaning the frequencies tend to "line up" and not strongly interfere with each other. Two pitches are "consonant" if their frequencies form an exact ratio of whole numbers. For example, in an octave, the simplest interval, the ratio of the frequencies is 2:1

Modern pianos are tuned using "twelve tone even temperament", or "12-TET." Specifically, the ratio between the frequencies of any two keys on the piano is

f2 / f1 = 2^(n /12)

where n is how far apart the two keys are(considering both black and white keys.)

For a major third to be *exactly* consonant, it needs to have a frequency ratio of exactly 5/4 = 1.25. But using even temperament, the ratio between the notes C and E (for example) is 2^(4/12) = 1.2599, so on a piano, major thirds tend to be slightly sharp. If you listen carefully, you can hear the dissonance in thirds, even on a well tuned piano. The interference in minor seconds is simply because the notes are so close together.

Even temperament gives relatively good consonance for seconds, fourths, fifths, and sevenths, but causes thirds and sixths to be slightly out-of-tune.......a bit of a musical compromise. However, most piano music has a relatively large number of notes played at the same time, and is played quickly enough, that any dissonance is hard to distinguish from background noise. In practice, even temperament tends to sound more "harmonious" than other systems where the intervals would be exact.

Hope that's not too confusing,
~W.O.M.B.A.T.

Answer 2

The simple answer to this is that to obtain beats of a frequency you can hear, the two notes involved have to be very much closer together than any two musical notes would be on a piano
The most likely time to hear beats is when two motors are running constantly at very near speeds such as in a twin engine plane. This is then heard as a droning sound
The notes of a piano do not in fact have a long enough duration to allow the beats to happen as the further apart the two notes are the less the beat frequency is.

Answer 3

hear beats keys piano played time

Answer 4

Because the waveforms are too rich (timbre). If they were closer to pure tones, e.g. a pitchfork, then you would.

Answer 5

What do you mean "beats"? Can you be more specific as to what you are referring to?