7 ms·

This is a really interesting article because the author clearly figured out some stuff but also hasn't filled in all the missing pieces or learned the terms yet

This is a really interesting article because the author clearly figured out some stuff but also hasn't filled in all the missing pieces or learned the terms yet. They are absolutely correct that the thing that makes different instruments playing the same pitch sound different is additional higher-frequency components. In particular, frequencies that are integer multiples of the lowest fundamental frequency are called harmonics. The set of harmonics and their relative amplitudes determines an instrument's timbre (usually prounounce "tamber" in English) or its characteristic sound. There are also inharmonics—frequencies that aren't multiples of the fundamental. Those tend to die out quickly because they don't form standing waves in the resonating body. These transient sounds form an important part of the very beginning of the sound. Some instruments, like bells, have more or longer-lasting inharmonics.

titzer 6y ago
I spent hours playing with Friture, which is a continuously-running audio spectrum analyzer. It's really cool to see the characteristics of a musical instrument live and connect the visual cortex to the auditory.
hashkb 6y ago
Can you clarify harmonic vs overtone?
- SeanLuke 6y ago
  All sound waves can be defined as the sum of a (possibly infinite) set of different sine waves. Each such sine wave naturally has a frequency (a pitch), an amplitude, and a phase. If you break a wave into its constituent sine waves like this, each sine wave is known as a PARTIAL. Sound waves that we perceive as tonal -- as musical -- commonly consist with partials which follow a certain pattern. Namely, there is one lowest partial, and most or all of the higher partials have frequencies which are INTEGER MULTIPLES of the this lowest partial's frequency. For example, if the fundamental is at 200Hz, perhaps the next lowest partial is at 400Hz, and the next one might be at 600 or 800Hz, and so on. When partials are organized like this, they are known as HARMONICS. The lowest such partial -- the lowest harmonic -- is called the FUNDAMENTAL, and the remaining (higher) harmonics are known as the OVERTONES. It is common, but not always the case, that the fundamental (1) defines the pitch of the sound (2) is the loudest harmonic. Overtones instead tend to add color to a sound.
  - hashkb 6y ago
    So all overtones are harmonics. All harmonics except the fundamental are overtones? Edit: I never realized the fundamental was a harmonic. I thought all harmonics had to be above the fundamental. I thought the overtones were the multiples (e.g. higher octaves) and harmonics were other intervals produced by the instrument (organs being the most extreme example and maybe oboe being the least)
    - schoen 6y ago
      Might be a terminological ambiguity -- like in mathematics you can distinguish "subsets", "proper subsets", and "nontrivial" (or "nonempty") subsets. Or "divisors" and "nontrivial divisors" and "proper divisors". Even though the terminology can be defined in order to make these distinctions clear, there's an arbitrariness in terms of which definition you prefer (in the past, some mathematicians treated 1 as prime, which makes the definition of a prime simpler, but makes many theorems about primes more complicated to express). And there's a likelihood that even experts will sometimes use the simple term informally when they technically mean a more specific thing (like occasionally saying "divisors" instead of "proper divisors", or something). I imagine that acoustics experts have a definition available that definitively states whether the fundamental "is" a harmonic, but in certain contexts it intuitively makes sense either to include or exclude it, regardless of that. A similar case might be "animals"; taxonomically humans are animals (and apes), which is very important sometimes and confusing other times.
      - hashkb 6y ago
        The fundamental being in or out of the set is less interesting to me than the (useful, to me in my day to day) distinction between overtones and harmonics. Technical misunderstandings really mess up rehearsals so I try to be as accurate as possible with the objective stuff so I can use it to communicate the subjective stuff.
    - enriquto 6y ago
      > So all overtones are harmonics. Not at all! It's the other way round. Harmonics are those overtones that are integer multiples of the fundamental. You can have other, non-harmonic, overtones.
enriquto 6y ago
> There are also inharmonics—frequencies that aren't multiples of the fundamental. Those tend to die out quickly because they don't form standing waves in the resonating body. This is only true for one-dimensional vibrations on strings and the air inside a long tube. Two and three-dimensional bodies have overtones with arbitrary ratios to the fundamental, depending on the shape of the object. Bells need to be carefully tuned to have harmonic spectrum, but this is an artificial construction based on western music tastes (who wants octaves to not be dissonant). Other percussion instruments (e.g., the indonesian gamelan) are deliberately tuned to a non-harmonic overtone sequence adapted to the local music tastes. You can certainly have inharmonic overtones that don't die out quickly! And they can form standing waves in the resonating body, just like the fundamental.
- hashkb 6y ago
  This helps answer the question I just asked under another comment. Thank you!
- munificent 6y ago
  Ah, great comment, thanks! I'm still learning too.
olau 6y ago
I would like to add to this that real instruments are much more complicated in their sound. If you take a look at the frequency histogram of one of those, you'll realize that what you might call a theory of pure frequencies, while perhaps adequate for explaining melody (several notes put together) is nowhere enough for explaining sound. Just like salty/fatty/sweet/sour is nowhere enough for explaining taste. This is also why it is so incredibly difficult to make a realistic sounding synthesizer. If you want to play with this, search for a sample pack and try running a couple of the sounds from that through sox to get a histogram.
- alanbernstein 6y ago
  I'm not saying this is wrong, but the Nyquist-Shannon sampling theorem states that a "theory of pure frequencies" is sufficient to reconstruct a band-limited signal from samples. What's the missing element?
  - yoz-y 6y ago
    I'd hasard a guess that the problem is not that you can't perfectly reproduce a sound of an instrument being played. However when you simulate it using samples you reduce the sound to a sum of independent recordings, whereas a real instrument will behave differently when you play multiple notes because of the material.
    - andybak 6y ago
      Yes. Plus a huge amount of other stuff. A naive sampler misses: 1. (as you say) How playing multiple notes at the same time changes the way the instrument responds 2. How playing at different intensities changes how the instrument responds. 3. The many subtle ways your physical interaction with the instrument change the sound 4. The way playing notes in succession at different rates can alter the sound 5. The physical space or choice of amplification can affect the instrument - even an acoustic guitar can "feed back" on itself to some degree 6. A bunch of other things I haven't thought of. Sophisticated samplers (and sophisticated sample libraries) can simulate some of the above. But physical modelling synths are probably a better way forward.
TheOtherHobbes 6y ago
More than that, the sound is defined by how the overtones change over time, and for acoustic instruments that's defined by various resonant modes and how they're excited. This article makes it sound as if timbre is static. It isn't. It's the changes that make instruments recognisable. A static slice of a violin timbre doesn't sound much like a violin. It's also wrong about having to use a 9ms slice. FFTs apply a windowing function which fades a slice to zero at the edges. Otherwise you get discontinuities which introduce spurious high frequency overtones which don't really exist. And so on. These are all things that some slightly deeper background reading would have revealed.
temporallobe 6y ago
I play several instruments and this is a correct analysis, but I would also add that resonance plays a huge part in the emphasis of certain frequency ranges. An acoustic guitar resonates through the body to emphasize and amplify the vibrations of the guitar strings, and in fact the shape and composition of the body will emphasize different ranges in completely different ways. The strings also cause sympathetic vibrations in each other, further adding to the resonance and contributing to the tonal quality (timbre) of even a single note.

titzer 6y ago

I spent hours playing with Friture, which is a continuously-running audio spectrum analyzer. It's really cool to see the characteristics of a musical instrument live and connect the visual cortex to the auditory.

hashkb 6y ago

Can you clarify harmonic vs overtone?

SeanLuke 6y ago
All sound waves can be defined as the sum of a (possibly infinite) set of different sine waves. Each such sine wave naturally has a frequency (a pitch), an amplitude, and a phase. If you break a wave into its constituent sine waves like this, each sine wave is known as a PARTIAL. Sound waves that we perceive as tonal -- as musical -- commonly consist with partials which follow a certain pattern. Namely, there is one lowest partial, and most or all of the higher partials have frequencies which are INTEGER MULTIPLES of the this lowest partial's frequency. For example, if the fundamental is at 200Hz, perhaps the next lowest partial is at 400Hz, and the next one might be at 600 or 800Hz, and so on. When partials are organized like this, they are known as HARMONICS. The lowest such partial -- the lowest harmonic -- is called the FUNDAMENTAL, and the remaining (higher) harmonics are known as the OVERTONES. It is common, but not always the case, that the fundamental (1) defines the pitch of the sound (2) is the loudest harmonic. Overtones instead tend to add color to a sound.
- hashkb 6y ago
  So all overtones are harmonics. All harmonics except the fundamental are overtones? Edit: I never realized the fundamental was a harmonic. I thought all harmonics had to be above the fundamental. I thought the overtones were the multiples (e.g. higher octaves) and harmonics were other intervals produced by the instrument (organs being the most extreme example and maybe oboe being the least)
  - schoen 6y ago
    Might be a terminological ambiguity -- like in mathematics you can distinguish "subsets", "proper subsets", and "nontrivial" (or "nonempty") subsets. Or "divisors" and "nontrivial divisors" and "proper divisors". Even though the terminology can be defined in order to make these distinctions clear, there's an arbitrariness in terms of which definition you prefer (in the past, some mathematicians treated 1 as prime, which makes the definition of a prime simpler, but makes many theorems about primes more complicated to express). And there's a likelihood that even experts will sometimes use the simple term informally when they technically mean a more specific thing (like occasionally saying "divisors" instead of "proper divisors", or something). I imagine that acoustics experts have a definition available that definitively states whether the fundamental "is" a harmonic, but in certain contexts it intuitively makes sense either to include or exclude it, regardless of that. A similar case might be "animals"; taxonomically humans are animals (and apes), which is very important sometimes and confusing other times.
    - hashkb 6y ago
      The fundamental being in or out of the set is less interesting to me than the (useful, to me in my day to day) distinction between overtones and harmonics. Technical misunderstandings really mess up rehearsals so I try to be as accurate as possible with the objective stuff so I can use it to communicate the subjective stuff.
  - enriquto 6y ago
    > So all overtones are harmonics. Not at all! It's the other way round. Harmonics are those overtones that are integer multiples of the fundamental. You can have other, non-harmonic, overtones.

enriquto 6y ago

> There are also inharmonics—frequencies that aren't multiples of the fundamental. Those tend to die out quickly because they don't form standing waves in the resonating body. This is only true for one-dimensional vibrations on strings and the air inside a long tube. Two and three-dimensional bodies have overtones with arbitrary ratios to the fundamental, depending on the shape of the object. Bells need to be carefully tuned to have harmonic spectrum, but this is an artificial construction based on western music tastes (who wants octaves to not be dissonant). Other percussion instruments (e.g., the indonesian gamelan) are deliberately tuned to a non-harmonic overtone sequence adapted to the local music tastes. You can certainly have inharmonic overtones that don't die out quickly! And they can form standing waves in the resonating body, just like the fundamental.

hashkb 6y ago
This helps answer the question I just asked under another comment. Thank you!
munificent 6y ago
Ah, great comment, thanks! I'm still learning too.

olau 6y ago

I would like to add to this that real instruments are much more complicated in their sound. If you take a look at the frequency histogram of one of those, you'll realize that what you might call a theory of pure frequencies, while perhaps adequate for explaining melody (several notes put together) is nowhere enough for explaining sound. Just like salty/fatty/sweet/sour is nowhere enough for explaining taste. This is also why it is so incredibly difficult to make a realistic sounding synthesizer. If you want to play with this, search for a sample pack and try running a couple of the sounds from that through sox to get a histogram.

alanbernstein 6y ago
I'm not saying this is wrong, but the Nyquist-Shannon sampling theorem states that a "theory of pure frequencies" is sufficient to reconstruct a band-limited signal from samples. What's the missing element?
- yoz-y 6y ago
  I'd hasard a guess that the problem is not that you can't perfectly reproduce a sound of an instrument being played. However when you simulate it using samples you reduce the sound to a sum of independent recordings, whereas a real instrument will behave differently when you play multiple notes because of the material.
  - andybak 6y ago
    Yes. Plus a huge amount of other stuff. A naive sampler misses: 1. (as you say) How playing multiple notes at the same time changes the way the instrument responds 2. How playing at different intensities changes how the instrument responds. 3. The many subtle ways your physical interaction with the instrument change the sound 4. The way playing notes in succession at different rates can alter the sound 5. The physical space or choice of amplification can affect the instrument - even an acoustic guitar can "feed back" on itself to some degree 6. A bunch of other things I haven't thought of. Sophisticated samplers (and sophisticated sample libraries) can simulate some of the above. But physical modelling synths are probably a better way forward.

TheOtherHobbes 6y ago

More than that, the sound is defined by how the overtones change over time, and for acoustic instruments that's defined by various resonant modes and how they're excited. This article makes it sound as if timbre is static. It isn't. It's the changes that make instruments recognisable. A static slice of a violin timbre doesn't sound much like a violin. It's also wrong about having to use a 9ms slice. FFTs apply a windowing function which fades a slice to zero at the edges. Otherwise you get discontinuities which introduce spurious high frequency overtones which don't really exist. And so on. These are all things that some slightly deeper background reading would have revealed.

temporallobe 6y ago

I play several instruments and this is a correct analysis, but I would also add that resonance plays a huge part in the emphasis of certain frequency ranges. An acoustic guitar resonates through the body to emphasize and amplify the vibrations of the guitar strings, and in fact the shape and composition of the body will emphasize different ranges in completely different ways. The strings also cause sympathetic vibrations in each other, further adding to the resonance and contributing to the tonal quality (timbre) of even a single note.