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> Everything is a combination of sine waves. No, we hear things as if they were a combination of sinusoidal waves (mostly). That's only one way to represent t

> Everything is a combination of sine waves. No, we hear things as if they were a combination of sinusoidal waves (mostly). That's only one way to represent them; you can just as easily represent them as a series of impulses. Mathematically they're all equivalent models, and none of the models accurately represent acoustic transfer. You can say we perceive things as if they were a linear combination of sinusoidal waves because we have a series of hair cells in the cochlea. Each bundle of hairs responds to waves within a very narrow frequency range, so that's what we mainly respond to. All of our audio perception is filtered through this process first. Since the hair bundles have a specific audio response, they don't respond to instantaneous frequencies- there has to be a wave of a certain duration for us to perceive a frequency. That's even independent of the mathematical fact that shorter wave pulses are more indistinguishable from white noise. Also, all of this is ignoring the other equipment of the ear, like the eardrum and the bone lever[1] that transmits sound to the inner ear. We have a lot of brain circuitry that picks out specific features, which means we can recognize things like square waves or impulses. I don't know much about this stuff but it's important for things like cochlear implants. AFAIK it's similar to some optical illusion/visual perception phenomena- things like how we perceive magenta as a single color, even though it's just two colors together, or how we perceive orange as a distinct color from brown even though it isn't[2]. > The more you have it's as if there are more instruments playing on top of each other, in music they're called "harmonics". Symmetrical clipping and square waves both create odd-order harmonics (3x, 5x, 7x, 9x, etc) which are very unnatural. The brain is good at picking this kind of thing out, and while I find it enjoyable (eg chiptunes), it's not really comparable to normal harmonics in music. It's certainly not something you can simplify down to just the component sinusoids. The perception of sounds has way more to do with stuff happening in the brain than in the air. [1]: https://en.wikipedia.org/wiki/Ossicles#/media/File:Slide1ghe.JPG https://en.wikipedia.org/wiki/Ossicles#/media/File:Slide1ghe... [2]: https://en.wikipedia.org/wiki/Shades_of_orange https://en.wikipedia.org/wiki/Shades_of_orange

sideshowb 6y ago
Related - I have recently been experimenting with musical effects based on breaking down a signal to any basis function of your choice. You can literally build any signal out of (nearly) any other. Turns out not to be a great audio effect as it tends to morph from one to the other via white noise in the middle in the general case, but with the right basis functions it's not so bad. At the extreme, in the case of sinusoidal basis functions ordered in increasing frequency, you've reinvented the filter sweep. I plan to share on the blog at some point https://omnisplore.wordpress.com/category/music-creative/ https://omnisplore.wordpress.com/category/music-creative/
- nitrogen 6y ago
  Sounds cool. I always liked how ZynAddSubFX could use different functions for its additive synthesis.
blincoln 6y ago
> Symmetrical clipping and square waves both create odd-order harmonics (3x, 5x, 7x, 9x, etc) which are very unnatural. What do you mean by "unnatural"? A clarinet has mostly odd harmonics[1], for example. Clarinets don't occur in nature, I suppose, but they're not using electronics or anything either. [1] https://newt.phys.unsw.edu.au/jw/clarinetacoustics.html#harmonics https://newt.phys.unsw.edu.au/jw/clarinetacoustics.html#harm...
- dsego 6y ago
  Probably even harmonics are more rounded or pleasing and less harsh. Compare trumpet vs cornet.
samstave 6y ago
Due to the ear having “hair” in the cochlea, do people with Alopecia have a higher tendency to being deaf? Or fo they hear anything differently?
- mennis16 6y ago
  Hair cells don't actually have anything to do with hair. Not sure why you are being downvoted though, the name is a bit confusing. Jim Hudspeth gives a great talk about the neuroscience of hearing (haven't watched this video but saw him in person ~10 years ago): https://youtu.be/hn8N8p9P5gw https://youtu.be/hn8N8p9P5gw
blincoln 6y ago
> It's certainly not something you can simplify down to just the component sinusoids. Anything a human can perceive as sound can be simplified down to just the component sine waves. > You can say we perceive things as if they were a linear combination of sinusoidal waves because we have a series of hair cells in the cochlea. No. We say this because any waveform can be reproduced by a sufficient number of sine waves at different frequencies and amplitudes. It's not perception, or the physics of the human ear. It's math.[1] [1] http://astro.pas.rochester.edu/~aquillen/phy103/Lectures/D_Fourier.pdf http://astro.pas.rochester.edu/~aquillen/phy103/Lectures/D_F...
- hwillis 6y ago
  Hah, I graduated from UofR- I was even a TA for Physics 142. Math does not have anything to say about sums of sine waves being the true form of functions. The wavelet transform is just as physically representative. In fact you can generate any number of Hilbert bases for a given function. They are ALL equivalent. The Fourier transform has a particular relevance because ears do something similar. Hair cells signal the brain while they are sensing vibrations within their particular frequency range. You could have different ears that signaled when they saw a sharp rise or drop in pressure and worked completely differently, but they would sense square waves just as fine. Or you could have ears that directly sense and measure air pressure. Instead, our ears sense that there are vibrations at 1 Hz, 3 Hz, 5 Hz, 7 Hz etc. and the brain interprets that and realizes it is a square wave. The concept of a real Fourier transform is just as unphysical as a real square wave. A real Fourier transform requires a perfectly defined sound pressure at every instant; because air and sensors have inertia that is not possible. There will always be lag, so any change in frequency is not perfectly transformed or represented from/as a sum of sine waves.
mrob 6y ago
There's nothing more unnatural about odd-order harmonics than even-order harmonics. The brain picks up on both of them because any harmonic sound is good evidence that some living thing is nearby (non-living things like flowing water and falling rocks typically produce inharmonic sounds). The idea that there is something "unnatural" or inferior about odd-order harmonics is propaganda invented by valve-amplifier enthusiasts, because their amplifiers predominantly produce even-order harmonic distortion. A stopped pipe wind instrument produces odd-order harmonics, and they were invented long before chiptunes.
thaumasiotes 6y ago
>> Everything is a combination of sine waves. > No, we hear things as if they were a combination of sinusoidal waves (mostly). That's only one way to represent them Well, but the reason we do our audio processing this way is that the Fourier transform our ear puts out is a high-quality description of the sound. If it didn't work well, we wouldn't do it. > or how we perceive orange as a distinct color from brown even though it isn't Why orange and brown? You can say the same thing about red and blue. Conversely, if orange and brown weren't distinct colors, it wouldn't be possible for us to perceive them differently, and yet we do, very consistently. What exactly are you trying to say by "a distinct color"?
stagas 6y ago
It is a combination of the actual and our perception of it IMO. Even if the wave was a square, our ear hair wouldn't pulsate as square because of the inertia. And as such we wouldn't perceive a perfect square any differently than a "wavy" square, which is why Nyquist theorem/Fourier transform works. My comment was about understanding why the sound becomes richer just by flattening a wave. It is not intuitive that this would be the case but in essence it's as if you are _adding_ more frequencies that didn't exist before to the same sound. More frequencies are interpreted by the ear/brain as more instruments or richer instruments.

sideshowb 6y ago

Related - I have recently been experimenting with musical effects based on breaking down a signal to any basis function of your choice. You can literally build any signal out of (nearly) any other. Turns out not to be a great audio effect as it tends to morph from one to the other via white noise in the middle in the general case, but with the right basis functions it's not so bad. At the extreme, in the case of sinusoidal basis functions ordered in increasing frequency, you've reinvented the filter sweep. I plan to share on the blog at some point https://omnisplore.wordpress.com/category/music-creative/ https://omnisplore.wordpress.com/category/music-creative/

nitrogen 6y ago
Sounds cool. I always liked how ZynAddSubFX could use different functions for its additive synthesis.

blincoln 6y ago

> Symmetrical clipping and square waves both create odd-order harmonics (3x, 5x, 7x, 9x, etc) which are very unnatural. What do you mean by "unnatural"? A clarinet has mostly odd harmonics[1], for example. Clarinets don't occur in nature, I suppose, but they're not using electronics or anything either. [1] https://newt.phys.unsw.edu.au/jw/clarinetacoustics.html#harmonics https://newt.phys.unsw.edu.au/jw/clarinetacoustics.html#harm...

dsego 6y ago
Probably even harmonics are more rounded or pleasing and less harsh. Compare trumpet vs cornet.

samstave 6y ago

Due to the ear having “hair” in the cochlea, do people with Alopecia have a higher tendency to being deaf? Or fo they hear anything differently?

mennis16 6y ago
Hair cells don't actually have anything to do with hair. Not sure why you are being downvoted though, the name is a bit confusing. Jim Hudspeth gives a great talk about the neuroscience of hearing (haven't watched this video but saw him in person ~10 years ago): https://youtu.be/hn8N8p9P5gw https://youtu.be/hn8N8p9P5gw

blincoln 6y ago

> It's certainly not something you can simplify down to just the component sinusoids. Anything a human can perceive as sound can be simplified down to just the component sine waves. > You can say we perceive things as if they were a linear combination of sinusoidal waves because we have a series of hair cells in the cochlea. No. We say this because any waveform can be reproduced by a sufficient number of sine waves at different frequencies and amplitudes. It's not perception, or the physics of the human ear. It's math.[1] [1] http://astro.pas.rochester.edu/~aquillen/phy103/Lectures/D_Fourier.pdf http://astro.pas.rochester.edu/~aquillen/phy103/Lectures/D_F...

hwillis 6y ago
Hah, I graduated from UofR- I was even a TA for Physics 142. Math does not have anything to say about sums of sine waves being the true form of functions. The wavelet transform is just as physically representative. In fact you can generate any number of Hilbert bases for a given function. They are ALL equivalent. The Fourier transform has a particular relevance because ears do something similar. Hair cells signal the brain while they are sensing vibrations within their particular frequency range. You could have different ears that signaled when they saw a sharp rise or drop in pressure and worked completely differently, but they would sense square waves just as fine. Or you could have ears that directly sense and measure air pressure. Instead, our ears sense that there are vibrations at 1 Hz, 3 Hz, 5 Hz, 7 Hz etc. and the brain interprets that and realizes it is a square wave. The concept of a real Fourier transform is just as unphysical as a real square wave. A real Fourier transform requires a perfectly defined sound pressure at every instant; because air and sensors have inertia that is not possible. There will always be lag, so any change in frequency is not perfectly transformed or represented from/as a sum of sine waves.

mrob 6y ago

There's nothing more unnatural about odd-order harmonics than even-order harmonics. The brain picks up on both of them because any harmonic sound is good evidence that some living thing is nearby (non-living things like flowing water and falling rocks typically produce inharmonic sounds). The idea that there is something "unnatural" or inferior about odd-order harmonics is propaganda invented by valve-amplifier enthusiasts, because their amplifiers predominantly produce even-order harmonic distortion. A stopped pipe wind instrument produces odd-order harmonics, and they were invented long before chiptunes.

thaumasiotes 6y ago

>> Everything is a combination of sine waves. > No, we hear things as if they were a combination of sinusoidal waves (mostly). That's only one way to represent them Well, but the reason we do our audio processing this way is that the Fourier transform our ear puts out is a high-quality description of the sound. If it didn't work well, we wouldn't do it. > or how we perceive orange as a distinct color from brown even though it isn't Why orange and brown? You can say the same thing about red and blue. Conversely, if orange and brown weren't distinct colors, it wouldn't be possible for us to perceive them differently, and yet we do, very consistently. What exactly are you trying to say by "a distinct color"?

stagas 6y ago

It is a combination of the actual and our perception of it IMO. Even if the wave was a square, our ear hair wouldn't pulsate as square because of the inertia. And as such we wouldn't perceive a perfect square any differently than a "wavy" square, which is why Nyquist theorem/Fourier transform works. My comment was about understanding why the sound becomes richer just by flattening a wave. It is not intuitive that this would be the case but in essence it's as if you are _adding_ more frequencies that didn't exist before to the same sound. More frequencies are interpreted by the ear/brain as more instruments or richer instruments.