A little more context for those who aren't familiar with how sound works:
Every note an instrument makes is composed of a sine wave at the fundamental frequency of the note plus a number of sine waves at integer multiples of the note, called overtones. The amplitudes of those overtones determine the timbre or sound of a particular instrument. The difference between a guitar playing A2 at 110Hz and clarinet playing A2 is in the relative loudnesses of their different overtones.
So an A2 will be composed of sine waves at 110Hz, 220Hz, 330Hz, 440Hz, 550Hz, 660Hz, 770Hz, and so on. The amplitudes diminish as the overtones go up in frequency and it eventually peters out.
Notes an octave apart are also integer multiples. An A3 is at 220Hz with overtones at 440Hz, 660Hz, 880Hz, etc. As you can see, there are a lot of overlapping overtones. So it seems like you shouldn't be able to fake a lower note by shaving off the fundamental. If you take an A2 and remove the 110Hz fundamental, you're left with 220Hz, 330Hz, 440Hz, 550Hz, 660Hz, 770Hz. That looks quite a lot like an A3.
However, our brains are smart enough to note that there are extra overtones in there that are not integer multiples of A3's fundamental 220Hz. The presence of 330Hz, 550Hz, 770Hz, etc. are enough for our brain to realize there must be a lower fundamental that we aren't hearing that leads to all of these extra overtones. Another great example of how our brains that fill in missing data by perceiving patterns in the data it receives.
This is an important technique in dance music production. On a good sound system, especially in a club, you want the bass to have a deep low fundamental that users can feel in their chest, lower than 100Hz even. But listeners are often using earbuds, in their car, or in other places with smaller speakers that can't reproduce that fundamental. So when doing sound design for the bass, you ensure the note has some overtones above that will still be preserved.
In practice, the user experience in many synthesizers goes in the other direction where they pick a fundamental that is in the reliably audible range and then add in a "sub" oscillator that makes a clean sine tone an octave below.
Every note an instrument makes is composed of a sine wave at the fundamental frequency of the note plus a number of sine waves at integer multiples of the note, called overtones. The amplitudes of those overtones determine the timbre or sound of a particular instrument. The difference between a guitar playing A2 at 110Hz and clarinet playing A2 is in the relative loudnesses of their different overtones.
So an A2 will be composed of sine waves at 110Hz, 220Hz, 330Hz, 440Hz, 550Hz, 660Hz, 770Hz, and so on. The amplitudes diminish as the overtones go up in frequency and it eventually peters out.
Notes an octave apart are also integer multiples. An A3 is at 220Hz with overtones at 440Hz, 660Hz, 880Hz, etc. As you can see, there are a lot of overlapping overtones. So it seems like you shouldn't be able to fake a lower note by shaving off the fundamental. If you take an A2 and remove the 110Hz fundamental, you're left with 220Hz, 330Hz, 440Hz, 550Hz, 660Hz, 770Hz. That looks quite a lot like an A3.
However, our brains are smart enough to note that there are extra overtones in there that are not integer multiples of A3's fundamental 220Hz. The presence of 330Hz, 550Hz, 770Hz, etc. are enough for our brain to realize there must be a lower fundamental that we aren't hearing that leads to all of these extra overtones. Another great example of how our brains that fill in missing data by perceiving patterns in the data it receives.
This is an important technique in dance music production. On a good sound system, especially in a club, you want the bass to have a deep low fundamental that users can feel in their chest, lower than 100Hz even. But listeners are often using earbuds, in their car, or in other places with smaller speakers that can't reproduce that fundamental. So when doing sound design for the bass, you ensure the note has some overtones above that will still be preserved.
In practice, the user experience in many synthesizers goes in the other direction where they pick a fundamental that is in the reliably audible range and then add in a "sub" oscillator that makes a clean sine tone an octave below.