Why does an A note sound different across instruments?
omarshehata.me
omarshehata.me
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.
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.
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)
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.
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.
Now what happens when I play a chord and get overtones out of the interaction between two strings or a choir? What's happening there?
Nothing. Sound superposition is linear. There's no interference between different frequencies. By playing several strings together you obtain the sum of the sounds played by each of them separately. No new frequencies can appear.
The beats have a frequency and are audible, but their frequency is not a pitch.
You can deconstruct any given sound wave into its partial sine waves. This is typically done using a Fourier Transform algorithm (FT).
Of course, we can also do it the other way around, create a signal out of many sine waves. In practice, this is called additive synthesis.
Instruments not only sound different because of the timbre. Another thing to look at is the loudness over time, e.g. when plucking a string. We usually do this with an ADSR representation (Attack, Decay, Sustain, Release).
Knowing these chracteristics is enough to recreate an instrument with a synthesizer. Of course, it gets more complex when there are inharmonics and if they are irregular (different depending on each tone). That's why synthesizing instruments realistically is a pretty time consuming science.
Since you mention "octave" here I want to point out that this is a common misconception. Harmonics are not just octaves of the fundamental. The octave scale is logarithmic but harmonics are linear and include all integer multiples.
If your fundamental is 100, the octaves are 200, 400, 800, 1600, .... But the harmonics are 200, 300, 400, 500, 600, ... There are many extra harmonics that aren't overtones.
This is important for many reasons, but a fun one is that you can use this in sound design by relying on a clever thing our brains can do. We are so good at doing frequency analysis in our heads that we can figure out what fundamental must be present even when it isn't. If you play sine waves at 200, 300, 400, 500, 600, etc. your brain can figure out that those would all be multiples of a 100-Hz fundamental, even though that fundamental isn't present [1].
This lets you do a neat trick where you hi-pass a sound to remove some of the lowest frequencies in order to make room in the mix for other bass sounds. Even though the sound loses its fundamental, listeners will still hear it as "functionally" having a bass register. (This is also why when you listen to music on a crappy tiny speaker, you still hear the bass as bass even though it's actually quite tinny and high-frequency.)
Overtones are any partials other than the fundamental. While overtones CAN be non-harmonic (notably in bells), I think it's fair to say that most of them, or at least the most important ones, are usually harmonics. This is because the terms "fundamental" and "overtone" are historically music terms, and are generally applied to sounds we perceive as tonal or musical: and such sounds are largely composed of harmonics.
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.
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.
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.
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.
The simple sine wave is exactly one dominant frequency in a spectrogram, a line. Instruments such as a trumpet will have upwards of 12 overtones, parallel lines, lessening in strength.
One interesting idea that came to me last night was trying to reproduce the physical 3D model of an instrument based on its spectrographic fingerprint. With enough samples, this ought be possible, and with a 3D printer one might even be able to create interesting physical instantiations of instruments based on spectrographic fingerprints. One could even create never-before-seen instruments based on a generated spectrogram, in an interesting radar-to-ocean operation (as opposed to ocean-to-radar, how radar normally works). Maybe topography-from-radar is a clearer way to state the same.
Generating audio from spectrograms is an open problem and I would love to see more open-source work in this domain.
In case you haven't already read it, this might be of interest to you:
Mark Kac: "Can One Hear the Shape of a Drum?"
https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum
https://www.maa.org/sites/default/files/pdf/upload_library/2...
Not to mention, two different pianos or two different violins can sound very different.
Many synthesizers use a sampled recording of the actual instrument for the attack, then synthesize the sustained portion of the instrument.
Actually probably like 10% at most of the battle. My understanding is attack is overwhelmingly dominant in our perception of timbre.
Was a lot of fun when I was young.
I'm a guitar player who took a few months of trumpet lessons when I was a kid. I recall that you can produce several different notes with the same fingering on the trumpet depending on the shape of your mouth. is this similar to the natural harmonics you can produce with a guitar by covering (but not fretting) the strings at certain nodes?
edit: here's a fantastic video on pinch harmonics: https://www.youtube.com/watch?v=eTWxCdoyol0
On a trumpet, the embouchure will affect the frequency of the vibration of the air compressed in the tube, and simply drop out lower harmonics, as can be confirmed via spectrogram.
The same thing happens on a guitar, leetcrew I encourage you to try the spectrogram linked at that site with your guitar to note the effect [0].
[0] https://musiclab.chromeexperiments.com/Spectrogram [1] I am under the impression that the fundamental tone of the string requires the whole string-length to resonate, and if it is clamped, pinched, or otherwise muted all you will hear are resonant harmonics that can exist on smaller string segment lengths.
One of these is true but I’m not clear on whether this means actually both of them are true?
My understanding of how this works is that the length of the trumpet's tubing (at any given fingering) permits the air to resonate in standing waves only at one of the frequencies in a harmonic series. The player's lips can vibrate at any frequency on their own, but the big column of air inside the trumpet will essentially lock the column of air into vibrating at the closest frequency in that set.
To elaborate/review, your lips are the guitar strings in this equation, and naturally will behave much like a string on a chamber instrument or fretless guitar (as is obvious from "free buzzing" and mouthpiece buzzing). The length of the tubing then dictates which frequencies will resonate with your lips, meaning your lips will want to "settle" into something in harmonic resonance with that length of tubing.
The key difference here is that your lips themselves are basically "fretted" to the harmonics (though with practice you can bend that quite a bit), since the corners of your lips are moving (slightly; it's a short string!) in and out to go higher or lower (respectively), and since they'll want to vibrate at a harmonic (the vibrating metal and air impart a force on your lips for the same reason your vibrating lips impart a force on the metal and air, so it takes much more effort to buzz against that harmonic than it does to just ride it and keep that feedback loop going). Further, the mouthpiece itself is basically a capo in this context, so your lips are always "fretted" to the mouthpiece's constraints (this is a big part of the reason - if not the entirety of it - why trumpets have tiny mouthpieces and tubas have giant mouthpieces).
I suspect that if you were to replace the body of an acoustic guitar with a really long pipe, you'd see/hear similar dynamics at play: a string tuned or fretted to one of that pipe's harmonics will keep vibrating for a good while, and a string tuned/fretted to something else would stop vibrating sooner as the destructive interference sucks energy out of it. And the former would likely be much more audible than the latter.
Content-less comments that derail the conversation, comments that are needlessly inflammatory - these are the kinds of meta comments that are not wanted.
It's not even about which frequency is dominant. I'm not an expert on psychoacoustics from the "sciency" side, but basically our brains can figure out the fundamental note based on the harmonics alone, even if we don't hear the fundamental frequency itself. De-emphasizing the fundamental frequency is sometimes used in synthesis just to create an interesting sound, but most notably this phenomenon is heavily relied on in modern heavy bass electronic music and down-tuned metal. A really common trick is to distort the bass track, so it can be still heard even if speakers can't reproduce that frequency, as distortion generates more harmonics. I don't mean distortion in literal sense, but in audio effect sense, so effects like saturation, overdrive, fuzz, clipping, etc.
The fundamental is always the lowest frequency. All overtones are some (almost always integer, or _nearly_ integer) multiple of that.
Not an undertone, it's fundamental frequency. Harmonics/overtones follow a very specific pattern:
https://en.wikipedia.org/wiki/Harmonic_series_(music)
...so in most cases there isn't really any ambiguity on what the actual fundamental frequency is. The best way to demonstrate it is probably with a high-pass filter (aka. low-cut filter). High-pass filter allows only higher frequencies to pass through, or in other words it cuts out lower frequencies. On the example below you can hear that as the lower frequencies are getting removed from the signal, it's still the same note:
https://www.youtube.com/watch?v=50lRE2Bgag0
I wish the filter sweeps were slower, but that's the best example I could find
I guess this is valid for trained musicians. For me, I can't possibly identify the same note in different instruments, as all these sound very different to me.
The only thing I seem to be able to do is to identify a song based on the very first second or two. Because they are different sounds, not just notes.
Of course, with such a complicated and underconstrained system you might need to basically tell it what a human vocal system roughly looks like and let it calculate parameters based on the model. Maybe not though, neural networks are surprising sometimes.
How does a person match the pitch of the piano? I could hear a few different pitches when one note was played (in a confused way, I would zero in on different parts of the sound), any of which might have been the target pitch to be matched.
And was I supposed to make my voice sound more like the piano? Was that part of “matching the note?”
Complicating things was the fact that my own voice had different pitches in it. Which part of my voice was supposed to match the note?
What a time. Now I know I was noticing the fundamental of the piano note at times and overtones at some others. Also, changing the timbre of your voice can mirror the overtones of the piano better, but that isn’t normally the goal of a singer.
A percentage of monks heard a different fundamental pitch than their brethren, so they sang one of the harmonics. Leading to polyphonic hymns and then to formal western harmony.
(Shaped by equal temperament along the way)
I think one of the most interesting things about pitch is that it's not well defined, it's a psychological phenomenon. If you could extract it from people's brains, you would likely get different values from different people. This is compounded by the fact that harmonics produced by real instruments are not exact ratios of each other, yet they affect the perceived pitch.
The way we distinguish between musical instruments and notes is because of timbre/tone color. Which has nothing to do with fourier transforms per se and you can use wavelet for that matter. DFT/DTFT are the most common approaches to quantize and convert back to analog and they can be completely left out of the discussion for such a title.
This is pretty well studied, but kudos to the author for trying to explain it again, it's an odd topic. But I suggest looking up "timbre" at least and perhaps updating the article with the terms used by actual musicians to mean exactly this.
Timbre - "the quality of tone distinctive of a particular singing voice or musical instrument"
(Yeah, OK, that was terribly said, sorry 'bout that.)
For timbre, see https://en.wikipedia.org/wiki/Timbre e.g.
FFTs, etc., give us visualization tools, but they miss the point. Different materials resonate differently across the auditory spectrum, emphasizing or diminishing various harmonics, resulting in complex sound profiles that make each instrument distinctive.
Or, to put it most simply: Different materials react to sound differently, and each instrument's materials and construction are what give it its distinctive timbre.
On an unrelated note, Daniel Levitin, former music producer and director of the Grammys, and current neuroscientist at McGill, was once asked what makes each musical era distinctive: timbre was, in his opinion, the single most important factor (source: one of his books, probably still in a moving box in my basement, otherwise I'd look it up).
That's a fascinating idea; I googled and found what might be the story you're looking for:
[quote]
In the best seller “This is your brain on music” by Daniel Levitin, he talks about John R. Pierce (inventor of the travelling wave vacuum tube and the first telecommunications satellite) who, interested to discover rock music, asked him to summarize the genre in a concise list of six songs. Levitin ended up with a list of songs from Little Richards, the Beatles, Jimi Hendrix, Eric Clapton, Prince and the Sex Pistols.
Interestingly, while listening, Pierce was not really interested by the songs themselves, their melodies, their harmonic structures or their rhythm characteristics, but he said he found the “timbres” to be remarkable and described them as being new, unfamiliar, and exciting.
Levitin concludes his story by saying: “The way in which instruments were combined to create a unified whole - bass, drums, electric and acoustic guitars, and voice – that was something he (Pierce) had never heard before. Timbre was what defined rock for Pierce. And it was a revelation for both of us.”
Quoted from "An Overview of the Concept of Timbre and its Use in Contemporary Music and Record Production" by Mathieu Bedwani
Anyone interested in this might enjoy the paper about the "Scanning the Dial" experiment. (It's about contemporary music rather than historical eras, but the idea is related)
https://www.researchgate.net/publication/248906443_Scanning_...
The punchline is that listeners can typically assign a genre to a recording after hearing a single quarter-of-a-second clip, but the paper is worth reading for its notes on genre and timbre in general.
Andrew Huang's video on the harmonic series does a really cool dive into this
This was my attempt to show you how you can derive the answer from first principles, just by analyzing the sound, and forming your own hypothesis/getting to these conclusions yourself.
The links at the end do have resources for the physics and theory behind it.
It's like that popular Monad tutorial that has you implementing Functors and Monads in order to solve a problem without ever telling you until the end that what you just created were Functors and Monads.
Starting off with the well-known terminology kind of colors the discussion from the beginning--even folks who don't really know what harmonics or timbre or monads or applicatives are probably have some general impression, and that impression could be wrong in a way that prevents them from learning.
No reason that learning a fairly interesting word's definition can't be part of the lesson...
https://github.com/kevinacahalan/piano_waterfall
It's portable to Linux and Windows at least. It won't run well in a virtual machine (including a ChromeBook) because it needs a GPU that can scroll the window fast enough.
There are 3 windows. One just shows the selected waveform. The others show an 8192-bucket FFT in red, a 1024-bucket FFT in green, and the active MIDI notes in blue. It's live, scrolling up at 93.75 pixels per second.
The QWERTY row becomes the white keys, and the number row becomes the black keys. F1 through F4 choose the type of sound. Left and right arrows change the octave in use; your speakers probably don't handle the full range very well. The program turns out to be a great speaker test, especially if you change the sound to a sine wave. It's also a great keyboard test; see how many keys you can hold down before your keyboard won't register any more. Individual colors in either window can be toggled with the 2x3 keypad that has Insert, Delete, Home, End, PgUp, PgDn. (the screenshot has green toggled off)
To make a trombone sound, first switch to a type of sound with lots of harmonics, like a sawtooth wave. Pick a low note, then find notes to line up well with the first two harmonics. Switch to the sine wave, and play all three of your chosen notes. For more of a clarinet sound, release the middle of the three that you have selected.
The sweet spot is between #222 and #333 in my opinion.
Distortion on a guitar makes an identical phrase sound much richer, and it's not just the wavelength limiting - it's the much louder harmonics relative to the fundamental.
Real life sawtooth: violin
[1] https://www.youtube.com/watch?v=FOpZYlI-F1g
[2] https://en.wikipedia.org/wiki/Karplus–Strong_string_synthesi...
There's a music cognition paper about it somewhere.
edit: found it here: https://experiments.withgoogle.com/sound-maker
Another synth that does this is Chrompahone by AAS:
https://www.applied-acoustics.com/chromaphone-3/
In fact it was used by Richard Devine to produce UI sounds for Google.
https://en.wikipedia.org/wiki/Hurdy-gurdy
Andrey Vinogradov playing his https://www.youtube.com/watch?v=wwyznoWJDHI
So, it doesn't really explain anything. It's kinda circular. Timbre is itself the word for "sounding different" (without being different in pitch, loudness, or location).
My simple answer: "different frequency spectrum + consistent patterns of change over time in spectrum, loudness, and/or pitch"
E.g. it's not the loudness of trumpet vs piano, but it is partly the fact that trumpet doesn't consistently have the loud to quiet fade timbrel temporal pattern of piano
The question is clearly not, "what's the musical term for why instruments sound different when playing the same pitch?" (timbre) it's, "what is the fundamental reason for that?" — and for most people, they have a mental model that an instrument plays a single frequency, so you have to show them that that model is broken, and then it becomes very clear, very fast what is going on.