Why does a tuning fork sound different than a piano, even if they’re playing the same note?
The objective aspects of a sound like frequency and amplitude can be measured. A tuning fork and a piano may be playing exactly the note at exactly the same volume, and may be perceived by a listener to have the same pitch and loudness, but the two will never sound "the same" to a listener. The objective and subjective aspects of two sounds that distinguish them from one another is the timbre.
Listen to this recording of several different instruments all playing A440 and recognize how they all sound different:
Timbre is a combination of both the objective physical properties of a sound wave and the subjective psychoacoustic perception of the listener. Objective aspects are those that can be definitively measured, and are usually related to the physical propagation of the sound. There are several of these, but the two most important are:
- The instantaneous combinations of frequencies, including the fundamental tone and it's related harmonics (also known as partials or overtones)
- The change in the frequency and amplitude over time, typically referred to as the attack, decay, sustain, release (ADSR)
Any physical instrument is not only going to play the fundamental but also harmonics. These harmonics are frequencies in the sound that are integer multiples of the fundamental tone. For examples, the A above middle C has a frequency of 440Hz, so will generate harmonics of 880Hz (x2), 1320Hz (x3), 1720Hz (x4), and on and on. Theoretically they're infinite, but in most practical situations the higher harmonics are to soft to be heard or noticed over the louder lower harmonics.
For example, in this frequency graph of one instant of a Grand Piano playing A440, we see peaks at exactly these integer multiples:
Because all of these frequencies exist at the same time, they combine to form a complex waveform:
So instead of creating a simple sine wave, like a tuning fork or a single cathedral organ pipe does, the harmonics create complex waves that human ears perceive as "interesting".
In addition to the instantaneous frequencies, the waveform can change over time in the ADSR cycle — attack (when the note is first struck), decay (from the initial strike down to the sustain), sustain (the long part of the note), and release (when the note ends).
Attack and Decay
You can see the harmonics and the ASDR cycle demonstrated in this video. It looks best in 720p HD and full screen. Watch the frequency graph at the bottom of the video change over time:
These instruments were played in Garage Band, so it's simulating an instrument and is not exactly perfect, but the main point here is that even approximations of real instruments are extremely complicated. It's also interesting to note how some of the "recordings" have very different left and right stereo tracks, which is an attempt by the software instrument to sound more like a real instrument, even though a recording of an actual instrument would likely have exactly the same waveforms on both tracks.
In the audio recordings below, you can hear what sounds with different timbres sound like and compare their frequency graphs and waveforms during the sustain.
This is exactly the same timbre of a tuning fork, as one is a simple vibrating rod and the other is a simple vibrating column of air.
Analog Mono Lead
This one is actually very complicated, as the waveform changes in a cycle over a period of seconds.
A tuning fork sounds different than a piano because a tuning fork only has one fundamental note that has a uniform waveform throughout it's playing, whereas a piano has complex harmonics and great variation throughout it's attack, decay, sustain, and release, which makes their timbres very different. While it's very complex to analyze a sound wave to break it into it's combinations of frequencies and amplitudes, it's easy for most humans to hear even small differences in timbre. The timbre is determined both by the physical properties of the sound wave that we've described here and the perception of the listener. Timbre is what makes sounds interesting.