Hyperphysics: Musical Instruments | Hacker News Reader

Hyperphysics: Musical Instruments

hyperphysics.phy-astr.gsu.edu

68 pointsbrudgers19 comments

Fun fact: the reason you hear distortion applied to stringed instruments like a guitar, but not wind instruments like a flute, is because of the harmonics involved. Overdriving a signal generates a chain of overtones related to whatever the fundamental is- 3rd, 4th, 5th harmonic, etc. But if you play two unrelated notes and then overdrive the signal you get weird extra frequencies related to the sum and difference of the two notes.

Now with a stringed instrument, the natural harmonics of a vibrating string are multiples of the original frequency (since a string is vibrating in one dimension only). So the artificial harmonics from the overdrive work together with the natural ones in a way that produces a pleasing sound.

But with a two dimensional resonating surface like a bell or a three dimensional volume like a flute, there are all kinds of extra frequencies that aren't clean multiples of the fundamental. So when you overdrive that signal you get a splash of noisy frequencies that are not very musical.

That's why you hear overdriven guitars, but not overdriven flutes. And, if they have discovered the trick of overdriving a musical signal on Proxima Centauri b, they are probably doing it on a stringed instrument.

So, in summary: space rock and roll is a plausible thing.

My understanding is that the purpose of ring-modulation in a synthesizer signal path is emulation of the non-harmonic overtones of bells and similar instruments.

But I thought a flute was considered fairly close to a sine wave.

An early pioneer in the scientific study of musical sounds was Hermann von Helmholtz@; his mid-1880s work (short name Sensations of Tone) is a classic. [https://archive.org/details/onsensationston01helmgoog/page/n...]

Short story, he used 'resonators' to pick out the partial tones that are found in complex timbres, more here: [https://en.wikipedia.org/wiki/Harmonic_series_(music)#Partia...] I read parts of it closely to grasp the details of what's meant by 'timbre' ... why a trumpet sounds different from a violin (or, for that matter, one violin from another!) Really useful if you want to get into sound design.

I absolutely love this website <3

So many times in my life has it been an excellent jumping point for research.

Same here. Superb summary of all the core concepts

The interface of this with Music Theory is equal temperament, as in [1]. The musical hardware provides white piano keys giving intervals with rational frequency ratio, so harmonious (called just intonation). With that you can play in only one key (or relative minor). The problem is what to do with the other keys. The solution was equal temperament, that suddenly alowed to play all keys at once without retuning the instrument. That new technology was showcased by Bach in his 'Well tempered clavier', that was a set of etudes each one in a different key, ranging over all possible keys. One could sit down and play them all in a row. In equal temp. one can, even inside the piece, do modulations (local key changes) that one couldn't in just intonation. But the price was to abandon the rational frequency ratios of intervals, turning to a system based on multiplying by 2^(1/12) (irrational, except at the octave, 12 semitones/multiplications away, that is at doubling frequency), hence dropping some of the good properties of just intonation. One can see that frequencies of notes in both systems are similar, but end up not really matching.

[1] https://pages.mtu.edu/~suits/scales.html

My Clavinova has buttons for changing temperament – by default it is equal (fairly obviously) but it is wonderful to actually be able to try out mean tone / pythagorean and various other obscure temperaments, particularly when bashing around with strings or singers. Playing Bach's well-tuned klavier -- a piece written to celebrate equal temperament -- in a pythagorean temperament is also just fun. The difference is subtle, but decidedly there.

Minor note (plz pardon pun) on Bach: While it’s still debated what tuning he used for this work, it’s generally currently thought that he did not use equal temperament. Tons of ink spilled on this topic.

Ah you're right, modern scholars are leaning as you say. Let me repair my comment saying that Bach could have played all WTC in equal temperament had he wanted. Thanks for completing.

Wow, this website is a blast from the past. Pretty sure I owe a lot of my physics degree down to this website

Boy, you don't really a lot of unstyled <table> elements anymore.

And how many <map> do you find out there?

isn’t piano considered a percussion instrument?

Scientists still do not quite agree to which species the piano belongs ;-), see https://en.wikipedia.org/wiki/Musical_instrument_classificat...

That would be musicology, not science. I have personally never heard the piano classified outside the percussion instruments by any non-layman.

So we're back to the old question what is science and what is not; there is definitely a different perspective depending on whether you come from US or Europe; here in Europe, we are much more (i.e. too) liberal with the term "science"; so there is e.g. "Musikwissenschaft" or "Geisteswissenschaft", and in parallel an eternal discussion whether it's indeed "Wissenschaft" (science) or not (and whether it makes sense for a society to enable so much people to study it). I myself play piano for nearly fifty years (even as a professional musician for some years) and never met any professional subsuming it under percussion; rather, it is a category "sui generis".

I am also a long-term pianist. I have always heard it categorized as percussion.

That being said, percussion isn't necessarily the most useful category of a piano for purposes of physical modeling: after all, it's just a traveling wave generator along harmonic strings and an amplifier board. If anything it's more like a hammered dulcimer or hammering a guitar.

In which country are you? Have you heard that from your teacher?

In my music encyclopedias, pianos and percussion instruments are always different categories, or see e.g. here: https://www.britannica.com/art/piano https://www.britannica.com/art/percussion-instrument

But of course it's just language, which is "the source of all misunderstandings", as they say. The physical modeling is a bit more complicated than you envisioned; e.g. https://www.modartt.com, which is a great simulation, even has different physical models for different piano brands, taking into account the specific differences in materials and construction methods.

Classification of musical instruments into these sorts of categories gets tricky in some areas (especially with regard to percussion). Really, the percussion and keyboard categories (when people acknowledge them) kind of become weird catchall categories, especially percussion. Also, depending on our goal, it's ok to let one instrument belong to multiple categories.

*As an exercise:* do you classify based on the means of playing the instrument or by the actual source of the sound?

If it's by the means, then the *piano* is a keyboard instrument, but if by the source of the sound, it's percussion... or is it a string instrument (chordophone) being played by means of percussion which is being triggered by means of keyboard? Is percussion only ever a means of playing? If so, what are drums, membrane instruments? And are cymbals a different category?

And then what about a *harpsichord*? It's another strung-keyboard instrument, but its strings are plucked rather than hammered. How should it be classified?

And then there's *bass guitar*, clearly an electric chordophone unless it's being slapped in which case it's obviously percussion... but its sound is actually reproduced by a speaker cone at the end of an electrical path that varies in complexity... unless it's being recorded directly to tape/digital without a speaker being used at all. Does the classification of a bass guitar depend on listening format?

It's kind of like when people say, _"Actually, a tomato is a fruit,"_ or, _"There's no such thing as a fish."_ Botanically/taxonomically, sure, those people are absolutely correct, but then a ton of other things that we refer to as vegetables (most of them, off the top of my head) are also technically fruit. In fact, botanically speaking, there's no such thing as a vegetable (huh, kind of like fish... I guess we could consider them seafood).

*To sum things up*, I guess my point is that categorizations are somewhat flexible (in many cases even subjective). More importantly, they're only meaningful when they help us to solve a problem. By extension, they only apply to a particular context. A tomato is both a fruit and a vegetable; you just need to decide whether you're a botanist or a chef.

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