19 ms·

We do not prefer chords to be perfectly in mathematical ratios: study

81 points by glitcher 3y ago

jimbob45 3y ago
These consonances cannot be replicated on a Western piano, for instance, because they would fall between the cracks of the scale traditionally used. Sounds like the author doesn't realize you can tune a piano. Actually, it doesn't sound like they know anything about music because the octave is surely universally harmonic.
- phailhaus 3y ago
  Of course you can tune any instrument to any scale. "Western piano" implies a standard tuned piano.
  - karencarits 3y ago
    Perhaps, but baroque ensembles often play with weird tunings where the intervals are different from the modern ones: https://en.wikipedia.org/wiki/Musical_temperament https://en.wikipedia.org/wiki/Musical_temperament
    - ben7799 3y ago
      Octaves stay the same though. Other temperaments are not "weird", they just make different rules about how perfectly in tune different intervals are with each other.
      - karencarits 3y ago
        True, they are not weird but may sound somewhat foreign as some intervals suddenly are purer than others Personally, I think it's sad that we are so little exposed to various temperaments as they give each key a bit more personality
  - ByQuyzzy 3y ago
    There's no such thing as an Eastern, Southern, or Northern piano. The poor author was trying to say something but ended up flubbing it.
    - phailhaus 3y ago
      I really don't think anyone is actually confused when he says that a "Western piano" can't replicate certain harmonies. We all know what he's saying here, because pianos aren't known for having custom tunings. This kind of pedantry is not useful.
- john61 3y ago
  Octaves on a piano are tuned slightly wider and "out of tune" because of the Inharmonicity of the strings.
  - itishappy 3y ago
    TIL! https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_curve https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_...
- beardyw 3y ago
  Yes, I agree. No mention of well tempered scales and the contortions that were needed to achieve them. Even at the time they knew it was a compromise. Yet today we (in the west) take them for granted. And not only octaves. Most instruments will yield various harmonics and no civilisation will have been unaware of them. It is no coincidence that for us a natural harmonic lies between a major 3rd and a minor one.
leblancfg 3y ago
Pythagoras from the grave would nicely like to ask if the researchers could also give those 4000 participants a two-stringed instrument, and ask them to tune them in a way they find pleasant to hear – and see if that spicy headline of theirs still holds.
- phailhaus 3y ago
  The 4000 participants who have been living in cultures steeped with Western musical harmonies? I don't think it would be surprising that they would pick tunings that reflect the music that surrounds them every day.
  - leblancfg 3y ago
    GP here. s/those 4000/another extremely diverse 4000/ would make the same point IMO.
  - fsckboy 3y ago
    >have been living in cultures steeped with Western musical harmonies? I don't think it would be surprising that they would pick tunings that reflect the music that surrounds them every day you are making a massive assumption that we prefer the same old same old. Some of us are always on the lookout for a bit of strange
    - phailhaus 3y ago
      The poster I was replying to was asserting that the study participants would more or less choose the same harmonies. That would not be surprising.
- PeterCorless 3y ago
  He would give them a one-stringed instrument and tell them to head down to the beach to try to find a tone that most closely resonated with the sound of the waves crashing on the shore.
- nicklecompte 3y ago
odyssey7 3y ago
Cambridge researchers have discovered that music is enjoyed by actual flesh-and-blood humans, refuting Pythagoras? Clearly a revival of the quadrivium is needed.
re 3y ago
Some previous discussion: https://news.ycombinator.com/item?id=39532586 https://news.ycombinator.com/item?id=39532586 (28 days ago, 6 comments) The other article posted also has a audiovisual version of some of the study findings which helps clarify the results: https://phys.org/news/2024-02-pythagoras-wrong-universal-musical-harmonies.html https://phys.org/news/2024-02-pythagoras-wrong-universal-mus...
FLT8 3y ago
> “We prefer slight amounts of deviation. We like a little imperfection because this gives life to the sounds, and that is attractive to us,” If you've ever tried building an additive synth, this probably seems obvious. If you play two tones with exact ratios together, the brain has a tendency to interpret them as a single tone with a different timbre. By making the ratios slightly off (don't have to be by much at all), or by making the ratios vary a little over time (eg. Subtle vibrato), the brain is able to pick out the "consonance" as a chord, and it sounds far more interesting.
- TheOtherHobbes 3y ago
  It's almost as if Patterson has no clue about the history of tunings, in the West or elsewhere. Perfect harmonic tunings sound incredibly exotic and out of tune to Western ears - not least because we're so used to slightly-imperfect equal temperament. We have decades of exposure to it, so it sounds normal. A perfect perfect fifth sounds very strange, even a little disturbing, and thirds are almost dissonant. I don't think anyone who has even the first idea about this has ever suggested that harmonic tunings are a goal, an ideal, or even a practical possibility. (See also, Pythagorean Comma.)
  - mrob 3y ago
    Just intonation tuning of chords (but not melodies) is the ideal in barbershop music. Barbershop music also uses harmonic sevenths, which are not found in standard 12EDO equal temperament. I've never heard of anybody calling barbershop "strange" or "disturbing". I don't think anybody is likely to call a perfect fifth or third those things either. You can easily check using the "Generate, Tone..." feature in Audacity. I recommend using a sawtooth wave, which contains prominent high harmonics that make it easy to hear subtle difference in tuning. The worst criticism I'd make of perfect just intonation is that it can sound boring, for the reason the GP post suggests.
    - ben_w 3y ago
      My suspicion is that learning music theory (for any specific cultural norm) is a bit like learning about font kerning: https://xkcd.com/1015/ https://xkcd.com/1015/ Many of the auditory things that trained musicians describe as creepy or weird, seem unremarkable to me.
pfgallagher 3y ago
What makes a song sound “good” is another question - there seem to be countless factors. Most people can easily tell you if they subjectively like or dislike a song, but typically have a hard time explaining exactly why.
ben7799 3y ago
I've always been taught Music theory exists to explain why we like things. Not to dictate what we like, it's like some grand unifying theory. Whenever we find something new people like Music theory has to adapt. I think it would be impossible to prove any unifying theory like this unless you can actually test all possible things someone could hear and western scales & such obviously don't encompass all that.
- dboreham 3y ago
  True but in my experience few music people know this. Music theory isn't a theory. It's just a scheme for naming patterns that turn out to sound good/interesting.
henjodottech 3y ago
In other news; Golden ratio? More like bronze
uwagar 3y ago
so a pitch and its octaves, or a pitch and its perfect fifth above or below sounding harmonious is not universal?
- 082349872349872 3y ago
  Anecdote whose source I've forgotten: a missionary family to some Pacific islands had brought a shortwave set and tried to get the locals interested in their favourite classical and opera. The locals enjoyed the radio all right, but much preferred US Navy stations, because they usually played both kinds of music: country and western. EDIT: something that might be consonant with the article would be frequent hammer-on and pull-off, as well as voice-leading in the slide parts?
  - uwagar 3y ago
    what would the locals have found appealing in country music and not so much in western classical + opera?
    - 082349872349872 3y ago
      I think the accessibility*: it's danceable, with mostly I,IV,V and the occasional seventh or minor second, lots of leading into changes, etc. eg: https://www.youtube.com/watch?v=xnKOVPXhlnE https://www.youtube.com/watch?v=xnKOVPXhlnE or https://www.youtube.com/watch?v=kPydlDfwiXA https://www.youtube.com/watch?v=kPydlDfwiXA EDIT: Hawai'ian slack key (listening, not dancing music) has some fancier influences (which I think they may have picked up from arabic music by way of the portuguese) but even there you can tell how much the locals pulled from {church hymns,country}: https://www.youtube.com/watch?v=tpfT8AzAl0c https://www.youtube.com/watch?v=tpfT8AzAl0c Beyoncé is rumoured to have covered Dolly on her most recent album; everyone else seems to be hoping it's Jolene (which would be the commercially appropriate choice), but I wish it were Coat of Many Colors: https://www.youtube.com/watch?v=HYAdKXzGtcY https://www.youtube.com/watch?v=HYAdKXzGtcY * I tried to listen to Silk Smitha once but guess I lack the background to appreciate her songs...
mrob 3y ago
Pythagoras' ideas about tuning only make sense with instruments that have harmonic or almost harmonic timbres, which is true for most instruments. However, tuned percussion is typically inharmonic. It's long been known that inharmonic instruments sound most consonant in chords using non-integer frequency ratios. William Sethares developed a model of consonance and dissonance that accounts for this: https://sethares.engr.wisc.edu/paperspdf/consonance.pdf https://sethares.engr.wisc.edu/paperspdf/consonance.pdf Informal explanation: https://sethares.engr.wisc.edu/consemi.html https://sethares.engr.wisc.edu/consemi.html
- omnicognate 3y ago
  The paper references Sethares (and Plomp & Levelt). This is a large empirical study building on their theoretical work. The paper itself is worth a read: https://www.nature.com/articles/s41467-024-45812-z https://www.nature.com/articles/s41467-024-45812-z
- deleted 3y ago
  [deleted]
riffic 3y ago
This reminds me, have we had a good 432 Hz vs 440 Hz discussion lately?
- thuuuomas 3y ago
  I feel like 432hz vs 440hz is merely the Just Intonation / Equal Temperment debate reiterated by people who don’t know any better. 432hz advocates make a lot of appeals (to “natural frequencies” that sound “more human”) which are quite similar to arguments made by proponents of Just Intonation during the Industrial Revolution.
dsign 3y ago
I tend to see music as an idiosyncratic language. I know from experience I can't hear harmonies that well, and that I had to find out about chords in Wikipedia and was completely deaf to them until I trained myself. Meaning and emotions that I can hear in music are most definitely culturally learned, even if I won't fight anybody swearing a major C is so much uplifting than a minor one and that that is an essential part of Creation--to each their own. With that said, just as languages tend to have culturally accepted "proper form" --grammar and spelling--so does music. Music theory is about what spelling and grammar the locals accept and like in their music, and is worth studying for that reason alone. Now, I wonder what would Pythagoras think of our current musical genres...
blitzar 3y ago
I hope this result calls into question all the other work done by Pythagoras.
- Optimal_Persona 3y ago
  Look out a^2 + b^2 = c^2, blitzar is coming for ya!
andoando 3y ago
So Im guessing non western music still still satisfies other mathematical relationships? I dont think it's correct to say the mathematical explanation is incorrect or even limited. Even considering deviations/slight variations from ratios: 1. You have to consider that these are deviations from the mathematical ratios. 2. The variations themselves can follow ratios. After all, not all deviations or variations are equally interesting. For example if you were to play 1xxx2xxx3xxx4 you can vary the next verse 1xx2xxxx3xxx4 and the next 1xxxx2xx3xxx4 Here the second note is oscillating one before the "ideal" ratio and one after.
- anon291 3y ago
  The non-western music I'm familiar with oftentimes still emphasizes things like I-V consonance.
igorbark 3y ago
so, yes, pythagoras did not create a dead simple mathematical model that captures the entire complexity of human musical experience several thousand years ago. BUT i think the ongoing study of consonance/dissonance is a very interesting area of the intersection of math and music some key words/links to get you started: - "local consonance" - "consonance/dissonance curves" - a seminal paper: https://sethares.engr.wisc.edu/paperspdf/consonance.pdf https://sethares.engr.wisc.edu/paperspdf/consonance.pdf - a more recent re-implementation with a cool video at the end: https://www.sebastianjiroschlecht.com/post/ondissonance/ https://www.sebastianjiroschlecht.com/post/ondissonance/ the basic idea being, different timbres lend themselves differently to different tuning systems. so we can parameterize our models of tuning systems based on timbre an important thing to keep in mind: consonant/dissonant doesn't mean "good/bad" or "pleasant/unpleasant". they're the output values of a mathematical model which we have a complex intuitive relationship with. other ways of thinking about it might be "simple/complex", "resolved/unresolved", "release/tension", but all are inaccurate in their own way some areas i'd love to see progress in: - the work i've seen focuses on computational models, i.e. take a simple mathematical model of timbre, and directly compute the consonance/dissonance curve from it. but real instruments' timbre varies across many dimensions, some prominent ones being pitch, time, and dynamics. can we instead burn some CPU cycles and generate curves from a waveform? - what does this look like for triads? tetrads? ...? - put this in the browser! would make it so much easier to play with and present the ideas to less technical audiences - how can we use this to generate new instruments? can a synth automatically adjust its tuning system based on its parameters? can we start from a set of desired consonant/dissonant intervals and generate an instrument with a matching curve?
- andoando 3y ago
  To simplify what youre saying - I think its just a matter of opposites/differences. Music is a pattern of differences. You can take any two things that are different and create a pattern, a rhythm and humans will find it interesting to listen to and make sense of it. This moreover has a 1:1 relationship with a visual representation. That is, every piece of music has an equivalent visual representation.
reilly3000 3y ago
Musica Universalis is all about overfitting ratios and frequencies to satisfy an aesthetic. I want to believe, but the data isn’t there. I dive deep into this in college music theory and acoustics but came up wanting.
- giraffe_lady 3y ago
  Yeah this is one of those things that so so looks like it should work out a certain way. As soon as you start learning you want it to work out that way. Some number of people in every generation have tried to make it work out, or become convinced that it does. It would just be so aesthetically satisfying. One of the most perfect congruences there could be, it just makes so much sense, would imply so much about the universe and our place in it. Musical and maybe human maturity is finally accepting that it isn't there.
  - reilly3000 3y ago
    Yep, agreed. Once you get there you can really appreciate what music is and does all on its own.
- andoando 3y ago
  Can you explain more? What do you mean the data isnt there?
deleted 3y ago
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srcreigh 3y ago
It cannot be overstated that the actual study data without exception points to the opposite conclusion, that pythagorean intervals (mathematical ratios) are in fact what we prefer. Study link: https://www.nature.com/articles/s41467-024-45812-z https://www.nature.com/articles/s41467-024-45812-z Start with figure 3. Non-musicians generally favour pythagorian style harmonic ratios, while trained musicians tend to prefer equal temperament. Each of the following intervals in the data confirm this: - The pythagorian major 3rd ratio 5/4 is slightly flat compared to 5 semitones. Non-musicians nailed it, musicians prefer the sharp ET version. - The range from 10-11 semitones is rated relatively high by non-musicians. This range includes the 7th harmonic, 7/4 - Even the 11th harmonic, taking place between 6(tritone) and 7(perfect fifth) is rated highly by non-musicians relatively to musicians. - The "9" major 2nd octave, 9/4 JI, aka 14 semitones, is tuned more perfectly by non musicians (9/4) compared to musicians Later the authors experiment with a artificial gong style instrument (fig 5). However its harmonics are remarkably close to several standard pythagorean ratios. You see 1.52f0 (slightly sharp perfect 5th 3/2); 3.46f0 (slightly flat harmonic 7th 7/4); 3.92f0 (slightly flat double octave 4/1). These harmonics are so close to a guitar or piano or human voice, it can't really even be considered inharmonic at all. With this instrument, you get, yet again, more pythagorean intervals: - sharp major 2nd, 9/8 ratio (makes sense; started with a sharp 3/2 and 9/8 is just (3/2)^2 modulo octaves). - People still correctly tune the major 3rd 5/4 ratio (slightly less than 5 semitones) even without a 5th harmonic. bonkers - Sharp 5th, which makes sense as the harmonic is 1.52f0 instead of 1.5f0 - Heavily emphasized harmonic 7th interval between 9 and 10 semitones Later, the authors experiment with various mis-tunings of the pythagorean intervals (Fig 8). The most highly rated intervals are slightly sharp or flat from JI. This is evidence for JI intervals being pleasing--slightly sharp or flat creates a pleasing rhythm of Just harmony. It's like just harmony but better. In conclusion, essentially every plot in the study points towards pythagorean, mathematically tuned harmony being more pleasing. Even in surprising ways. I could not find a single data point indicating otherwise, except for indoctrination of musicians towards ET leading to things like preferring sharp major 3rds and not recognizing the harmonic 7th interval.
- pclmulqdq 3y ago
  It's very possible that the averages over the population we see in the paper reflect a gradient of musical experience rather than an abstract notion of "pleasantness." Many trained musicians I know with a great ear have a very hard time with non-ET fifths and thirds, even knowing that ET is a grand compromise (all tunings are). We must learn through exposure - and admonitions from teachers to have better intonation - that ET is correct and everything else is wrong. I also have to say that the idea of making "pleasant" intervals is a bit reductive to begin with: unequal temperament tunings in modern use are often chosen to give a piece a particular "color" regardless of how "pleasant" the intervals are in a vacuum.
HPsquared 3y ago
Maybe it has something to do with phase. If they are ever so slightly out of tune, the phase is kind of "smeared" out, whereas with "exactly in tune" the locked phase can affect the timbre.
- fsckboy 3y ago
  that's not how phase works, though you're thinking reasonable thoughts. if you have a bicycle with two wheels, where one wheel is slightly bigger than the other, and you mark the wheels with a white spot, as the bicycle rolls, say the white spots start out in the same place (wrt a clock face). As the bicycle rolls, the white spots will "go out of phase" with each other, and with every roll, even more out of phase, till they are so out of phase that they start to slowly come a little bit more in phase with each other with every roll, till they match up again... except they are not out of phase, they are just rolling at two different frequencies, and that mix of frequencies is the "timbre" that you hear. if you have two signals at the same frequency which are out of phase, and you measure at any point, you will just measure a signal at that frequency whose amplitude is the sum of the two signals at that point. You won't be able to tell there is any phasing of two signals taking place. If your two ears hear the same frequency, but with a phase difference, that will be interpreted in part as what direction the sound comes from; it's not definitive, it's just evidence that gets combined with any other senses you have of where the sound should be coming from. there's a lot more to say about it but no room here for a treatise.
  - HPsquared 3y ago
    I do think it could change the sound. Consider a simple octave interval, with zero phase or 90 degrees out: https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2840%29x%5C%2841%29%2BSin%5C%2840%292x%5C%2841%29 https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2... https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2840%29x%5C%2841%29%2BSin%5C%2840%292x%2BDivide%5B%CF%80%2C2%5D%5C%2841%29 https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2... The first looks a bit like a sawtooth wave, the second is more like a chain of pulses. Wouldn't that sound different? The Fourier series of Sawtooth wave, Square wave, etc. contain phase info as well as frequency.
graycat 3y ago
Come ON guys, help me out here: Be more clear about your terminology!!! Gee, I'm plenty good with the math and applications of Fourier theory. Sure, some physics course solved the differential equation of vibrating strings. Early on my career did well with Fourier theory, the FFT (fast Fourier transform), and Navy ocean data. And with violin, I got a start in the music school of Indiana University and eventually made it through several pages of the Bach E-major preludio, the Bach Chaconne, and a transcription, as I recall, up an octave and a fifth, of that famous Bach solo cello piece. Been known to take the positive whole number powers of 2^(1/12). Dissonance? Sure, I really like the S. Barber Adagio for strings!!! R. Wagner's chords. The Franz Schmidt Intermezzo to his Notre Dame. The Sibelius violin concerto. But, stilllll, a lot of your terminology I can't follow. For an opinion: Mostly music is art, that is communication, interpretation of human experience, emotion. Given the roles of, say, vibrato, Fourier theory and 2^(1/12) do not directly explain all of the art. For a perfect fifth, sure, as is standard, when take the violin out of its case, first tune the four strings G, D, A, E in perfect fifths and do this by listening for beats in the overtones. Then with the strings so tuned, often when the music calls for one of those 4 notes, just go ahead and play it on the open (look, Ma, no use of fingers on the left hand) string. In particular, for > perfectly in mathematical ratios in real music from before Bach to after Barber, I doubt that "perfectly" happens very often or is even attempted. E.g., with violin, can't play much music if play only on the open strings, and as soon as put a finger of the left hand on a string, with vibrato or even without, there won't be much "perfectly mathematical".
Nav_Panel 3y ago
I really like this site for info on various tunings, including Just Intonation, where the intervals ARE perfect mathematical ratios: https://www.kylegann.com/microtonality.html https://www.kylegann.com/microtonality.html One tidbit I always think about: > I've had interesting experiences playing just-intonation music for non-music-major students. Sometimes they will identify an equal-tempered chord as "happy, upbeat," and the same chord in just intonation as "sad, gloomy." Of course, this is the first time they've ever heard anything but equal temperament, and they're far more familiar with the first sound than the second. But I think they correctly hit on the point that equal temperament chords do have a kind of active buzz to them, a level of harmonic excitement and intensity. By contrast, just-intonation chords are much calmer, more passive; you literally have to slow down to listen to them. (As Terry Riley says, Western music is fast because it's not in tune.) It makes sense that American teenagers would identify tranquil, purely consonant harmony as moody and depressing. Listening from the other side, I've learned to hear equal temperament music as a kind of aural caffeine, overly busy and nervous-making. If you're used to getting that kind of buzz from music, you feel the lack of it as a deprivation when it's not there. But do we need it? Most cultures use music for meditation, and ours may be the only culture that doesn't. With our tuning, we can't. > My teacher, Ben Johnston, was convinced that our tuning is responsible for much of our cultural psychology, the fact that we are so geared toward progress and action and violence and so little attuned to introspection, contentment, and acquiesence. Equal temperament could be described as the musical equivalent to eating a lot of red meat and processed sugars and watching violent action films. The music doesn't turn your attention inward, it makes you want to go out and work off your nervous energy on something.
mingus88 3y ago
I haven’t read the study but the article gives the impression that researchers can get published for things as simple as discovering gamelan orchestras? I don’t want to sound cynical but ethnomusicology is a field unto itself and the idea that western tonal harmonies are a very small piece of the pie is something we’ve talked about for at least a hundred years Even the concept of just intonation for a western scale is well established
- deleted 3y ago
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dr_dshiv 3y ago
I spent a very long time trying to make sense of the broad concept of harmony. Here’s what I came up with: https://www.sciencedirect.com/science/article/pii/S240587262200003X https://www.sciencedirect.com/science/article/pii/S240587262... You’ll find some juicy details on Pythagoras (his Olympic days, for instance) as well as an overview of harmony in neuroscience, computer science, aesthetic theories, etc.
zigzag312 3y ago
Directly from the study: > "these preferences for slight deviations disappeared upon elimination of the upper harmonics, presumably because this eliminates the slow beating effect" It seems like the title is oversimplifying results for the sake of clickbait sensationalism.

81 points by glitcher 3y ago

These consonances cannot be replicated on a Western piano, for instance, because they would fall between the cracks of the scale traditionally used. Sounds like the author doesn't realize you can tune a piano. Actually, it doesn't sound like they know anything about music because the octave is surely universally harmonic.

phailhaus 3y ago
Of course you can tune any instrument to any scale. "Western piano" implies a standard tuned piano.
- karencarits 3y ago
  Perhaps, but baroque ensembles often play with weird tunings where the intervals are different from the modern ones: https://en.wikipedia.org/wiki/Musical_temperament https://en.wikipedia.org/wiki/Musical_temperament
  - ben7799 3y ago
    Octaves stay the same though. Other temperaments are not "weird", they just make different rules about how perfectly in tune different intervals are with each other.
    - karencarits 3y ago
      True, they are not weird but may sound somewhat foreign as some intervals suddenly are purer than others Personally, I think it's sad that we are so little exposed to various temperaments as they give each key a bit more personality
- ByQuyzzy 3y ago
  There's no such thing as an Eastern, Southern, or Northern piano. The poor author was trying to say something but ended up flubbing it.
  - phailhaus 3y ago
    I really don't think anyone is actually confused when he says that a "Western piano" can't replicate certain harmonies. We all know what he's saying here, because pianos aren't known for having custom tunings. This kind of pedantry is not useful.
john61 3y ago
Octaves on a piano are tuned slightly wider and "out of tune" because of the Inharmonicity of the strings.
- itishappy 3y ago
  TIL! https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_curve https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_...
beardyw 3y ago
Yes, I agree. No mention of well tempered scales and the contortions that were needed to achieve them. Even at the time they knew it was a compromise. Yet today we (in the west) take them for granted. And not only octaves. Most instruments will yield various harmonics and no civilisation will have been unaware of them. It is no coincidence that for us a natural harmonic lies between a major 3rd and a minor one.

leblancfg 3y ago

Pythagoras from the grave would nicely like to ask if the researchers could also give those 4000 participants a two-stringed instrument, and ask them to tune them in a way they find pleasant to hear – and see if that spicy headline of theirs still holds.

phailhaus 3y ago
The 4000 participants who have been living in cultures steeped with Western musical harmonies? I don't think it would be surprising that they would pick tunings that reflect the music that surrounds them every day.
- leblancfg 3y ago
  GP here. s/those 4000/another extremely diverse 4000/ would make the same point IMO.
- fsckboy 3y ago
  >have been living in cultures steeped with Western musical harmonies? I don't think it would be surprising that they would pick tunings that reflect the music that surrounds them every day you are making a massive assumption that we prefer the same old same old. Some of us are always on the lookout for a bit of strange
  - phailhaus 3y ago
    The poster I was replying to was asserting that the study participants would more or less choose the same harmonies. That would not be surprising.
PeterCorless 3y ago
He would give them a one-stringed instrument and tell them to head down to the beach to try to find a tone that most closely resonated with the sound of the waves crashing on the shore.
nicklecompte 3y ago

odyssey7 3y ago

Cambridge researchers have discovered that music is enjoyed by actual flesh-and-blood humans, refuting Pythagoras? Clearly a revival of the quadrivium is needed.

re 3y ago

Some previous discussion: https://news.ycombinator.com/item?id=39532586 https://news.ycombinator.com/item?id=39532586 (28 days ago, 6 comments) The other article posted also has a audiovisual version of some of the study findings which helps clarify the results: https://phys.org/news/2024-02-pythagoras-wrong-universal-musical-harmonies.html https://phys.org/news/2024-02-pythagoras-wrong-universal-mus...

FLT8 3y ago

> “We prefer slight amounts of deviation. We like a little imperfection because this gives life to the sounds, and that is attractive to us,” If you've ever tried building an additive synth, this probably seems obvious. If you play two tones with exact ratios together, the brain has a tendency to interpret them as a single tone with a different timbre. By making the ratios slightly off (don't have to be by much at all), or by making the ratios vary a little over time (eg. Subtle vibrato), the brain is able to pick out the "consonance" as a chord, and it sounds far more interesting.

TheOtherHobbes 3y ago
It's almost as if Patterson has no clue about the history of tunings, in the West or elsewhere. Perfect harmonic tunings sound incredibly exotic and out of tune to Western ears - not least because we're so used to slightly-imperfect equal temperament. We have decades of exposure to it, so it sounds normal. A perfect perfect fifth sounds very strange, even a little disturbing, and thirds are almost dissonant. I don't think anyone who has even the first idea about this has ever suggested that harmonic tunings are a goal, an ideal, or even a practical possibility. (See also, Pythagorean Comma.)
- mrob 3y ago
  Just intonation tuning of chords (but not melodies) is the ideal in barbershop music. Barbershop music also uses harmonic sevenths, which are not found in standard 12EDO equal temperament. I've never heard of anybody calling barbershop "strange" or "disturbing". I don't think anybody is likely to call a perfect fifth or third those things either. You can easily check using the "Generate, Tone..." feature in Audacity. I recommend using a sawtooth wave, which contains prominent high harmonics that make it easy to hear subtle difference in tuning. The worst criticism I'd make of perfect just intonation is that it can sound boring, for the reason the GP post suggests.
  - ben_w 3y ago
    My suspicion is that learning music theory (for any specific cultural norm) is a bit like learning about font kerning: https://xkcd.com/1015/ https://xkcd.com/1015/ Many of the auditory things that trained musicians describe as creepy or weird, seem unremarkable to me.

pfgallagher 3y ago

What makes a song sound “good” is another question - there seem to be countless factors. Most people can easily tell you if they subjectively like or dislike a song, but typically have a hard time explaining exactly why.

ben7799 3y ago

I've always been taught Music theory exists to explain why we like things. Not to dictate what we like, it's like some grand unifying theory. Whenever we find something new people like Music theory has to adapt. I think it would be impossible to prove any unifying theory like this unless you can actually test all possible things someone could hear and western scales & such obviously don't encompass all that.

dboreham 3y ago
True but in my experience few music people know this. Music theory isn't a theory. It's just a scheme for naming patterns that turn out to sound good/interesting.

henjodottech 3y ago

In other news; Golden ratio? More like bronze

uwagar 3y ago

so a pitch and its octaves, or a pitch and its perfect fifth above or below sounding harmonious is not universal?

082349872349872 3y ago
Anecdote whose source I've forgotten: a missionary family to some Pacific islands had brought a shortwave set and tried to get the locals interested in their favourite classical and opera. The locals enjoyed the radio all right, but much preferred US Navy stations, because they usually played both kinds of music: country and western. EDIT: something that might be consonant with the article would be frequent hammer-on and pull-off, as well as voice-leading in the slide parts?
- uwagar 3y ago
  what would the locals have found appealing in country music and not so much in western classical + opera?
  - 082349872349872 3y ago
    I think the accessibility*: it's danceable, with mostly I,IV,V and the occasional seventh or minor second, lots of leading into changes, etc. eg: https://www.youtube.com/watch?v=xnKOVPXhlnE https://www.youtube.com/watch?v=xnKOVPXhlnE or https://www.youtube.com/watch?v=kPydlDfwiXA https://www.youtube.com/watch?v=kPydlDfwiXA EDIT: Hawai'ian slack key (listening, not dancing music) has some fancier influences (which I think they may have picked up from arabic music by way of the portuguese) but even there you can tell how much the locals pulled from {church hymns,country}: https://www.youtube.com/watch?v=tpfT8AzAl0c https://www.youtube.com/watch?v=tpfT8AzAl0c Beyoncé is rumoured to have covered Dolly on her most recent album; everyone else seems to be hoping it's Jolene (which would be the commercially appropriate choice), but I wish it were Coat of Many Colors: https://www.youtube.com/watch?v=HYAdKXzGtcY https://www.youtube.com/watch?v=HYAdKXzGtcY * I tried to listen to Silk Smitha once but guess I lack the background to appreciate her songs...

mrob 3y ago

Pythagoras' ideas about tuning only make sense with instruments that have harmonic or almost harmonic timbres, which is true for most instruments. However, tuned percussion is typically inharmonic. It's long been known that inharmonic instruments sound most consonant in chords using non-integer frequency ratios. William Sethares developed a model of consonance and dissonance that accounts for this: https://sethares.engr.wisc.edu/paperspdf/consonance.pdf https://sethares.engr.wisc.edu/paperspdf/consonance.pdf Informal explanation: https://sethares.engr.wisc.edu/consemi.html https://sethares.engr.wisc.edu/consemi.html

omnicognate 3y ago
The paper references Sethares (and Plomp & Levelt). This is a large empirical study building on their theoretical work. The paper itself is worth a read: https://www.nature.com/articles/s41467-024-45812-z https://www.nature.com/articles/s41467-024-45812-z
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riffic 3y ago

This reminds me, have we had a good 432 Hz vs 440 Hz discussion lately?

thuuuomas 3y ago
I feel like 432hz vs 440hz is merely the Just Intonation / Equal Temperment debate reiterated by people who don’t know any better. 432hz advocates make a lot of appeals (to “natural frequencies” that sound “more human”) which are quite similar to arguments made by proponents of Just Intonation during the Industrial Revolution.

dsign 3y ago

I tend to see music as an idiosyncratic language. I know from experience I can't hear harmonies that well, and that I had to find out about chords in Wikipedia and was completely deaf to them until I trained myself. Meaning and emotions that I can hear in music are most definitely culturally learned, even if I won't fight anybody swearing a major C is so much uplifting than a minor one and that that is an essential part of Creation--to each their own. With that said, just as languages tend to have culturally accepted "proper form" --grammar and spelling--so does music. Music theory is about what spelling and grammar the locals accept and like in their music, and is worth studying for that reason alone. Now, I wonder what would Pythagoras think of our current musical genres...

blitzar 3y ago

I hope this result calls into question all the other work done by Pythagoras.

Optimal_Persona 3y ago
Look out a^2 + b^2 = c^2, blitzar is coming for ya!

andoando 3y ago

So Im guessing non western music still still satisfies other mathematical relationships? I dont think it's correct to say the mathematical explanation is incorrect or even limited. Even considering deviations/slight variations from ratios: 1. You have to consider that these are deviations from the mathematical ratios. 2. The variations themselves can follow ratios. After all, not all deviations or variations are equally interesting. For example if you were to play 1xxx2xxx3xxx4 you can vary the next verse 1xx2xxxx3xxx4 and the next 1xxxx2xx3xxx4 Here the second note is oscillating one before the "ideal" ratio and one after.

anon291 3y ago
The non-western music I'm familiar with oftentimes still emphasizes things like I-V consonance.

igorbark 3y ago

so, yes, pythagoras did not create a dead simple mathematical model that captures the entire complexity of human musical experience several thousand years ago. BUT i think the ongoing study of consonance/dissonance is a very interesting area of the intersection of math and music some key words/links to get you started: - "local consonance" - "consonance/dissonance curves" - a seminal paper: https://sethares.engr.wisc.edu/paperspdf/consonance.pdf https://sethares.engr.wisc.edu/paperspdf/consonance.pdf - a more recent re-implementation with a cool video at the end: https://www.sebastianjiroschlecht.com/post/ondissonance/ https://www.sebastianjiroschlecht.com/post/ondissonance/ the basic idea being, different timbres lend themselves differently to different tuning systems. so we can parameterize our models of tuning systems based on timbre an important thing to keep in mind: consonant/dissonant doesn't mean "good/bad" or "pleasant/unpleasant". they're the output values of a mathematical model which we have a complex intuitive relationship with. other ways of thinking about it might be "simple/complex", "resolved/unresolved", "release/tension", but all are inaccurate in their own way some areas i'd love to see progress in: - the work i've seen focuses on computational models, i.e. take a simple mathematical model of timbre, and directly compute the consonance/dissonance curve from it. but real instruments' timbre varies across many dimensions, some prominent ones being pitch, time, and dynamics. can we instead burn some CPU cycles and generate curves from a waveform? - what does this look like for triads? tetrads? ...? - put this in the browser! would make it so much easier to play with and present the ideas to less technical audiences - how can we use this to generate new instruments? can a synth automatically adjust its tuning system based on its parameters? can we start from a set of desired consonant/dissonant intervals and generate an instrument with a matching curve?

andoando 3y ago
To simplify what youre saying - I think its just a matter of opposites/differences. Music is a pattern of differences. You can take any two things that are different and create a pattern, a rhythm and humans will find it interesting to listen to and make sense of it. This moreover has a 1:1 relationship with a visual representation. That is, every piece of music has an equivalent visual representation.

reilly3000 3y ago

Musica Universalis is all about overfitting ratios and frequencies to satisfy an aesthetic. I want to believe, but the data isn’t there. I dive deep into this in college music theory and acoustics but came up wanting.

giraffe_lady 3y ago
Yeah this is one of those things that so so looks like it should work out a certain way. As soon as you start learning you want it to work out that way. Some number of people in every generation have tried to make it work out, or become convinced that it does. It would just be so aesthetically satisfying. One of the most perfect congruences there could be, it just makes so much sense, would imply so much about the universe and our place in it. Musical and maybe human maturity is finally accepting that it isn't there.
- reilly3000 3y ago
  Yep, agreed. Once you get there you can really appreciate what music is and does all on its own.
andoando 3y ago
Can you explain more? What do you mean the data isnt there?

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srcreigh 3y ago

It cannot be overstated that the actual study data without exception points to the opposite conclusion, that pythagorean intervals (mathematical ratios) are in fact what we prefer. Study link: https://www.nature.com/articles/s41467-024-45812-z https://www.nature.com/articles/s41467-024-45812-z Start with figure 3. Non-musicians generally favour pythagorian style harmonic ratios, while trained musicians tend to prefer equal temperament. Each of the following intervals in the data confirm this: - The pythagorian major 3rd ratio 5/4 is slightly flat compared to 5 semitones. Non-musicians nailed it, musicians prefer the sharp ET version. - The range from 10-11 semitones is rated relatively high by non-musicians. This range includes the 7th harmonic, 7/4 - Even the 11th harmonic, taking place between 6(tritone) and 7(perfect fifth) is rated highly by non-musicians relatively to musicians. - The "9" major 2nd octave, 9/4 JI, aka 14 semitones, is tuned more perfectly by non musicians (9/4) compared to musicians Later the authors experiment with a artificial gong style instrument (fig 5). However its harmonics are remarkably close to several standard pythagorean ratios. You see 1.52f0 (slightly sharp perfect 5th 3/2); 3.46f0 (slightly flat harmonic 7th 7/4); 3.92f0 (slightly flat double octave 4/1). These harmonics are so close to a guitar or piano or human voice, it can't really even be considered inharmonic at all. With this instrument, you get, yet again, more pythagorean intervals: - sharp major 2nd, 9/8 ratio (makes sense; started with a sharp 3/2 and 9/8 is just (3/2)^2 modulo octaves). - People still correctly tune the major 3rd 5/4 ratio (slightly less than 5 semitones) even without a 5th harmonic. bonkers - Sharp 5th, which makes sense as the harmonic is 1.52f0 instead of 1.5f0 - Heavily emphasized harmonic 7th interval between 9 and 10 semitones Later, the authors experiment with various mis-tunings of the pythagorean intervals (Fig 8). The most highly rated intervals are slightly sharp or flat from JI. This is evidence for JI intervals being pleasing--slightly sharp or flat creates a pleasing rhythm of Just harmony. It's like just harmony but better. In conclusion, essentially every plot in the study points towards pythagorean, mathematically tuned harmony being more pleasing. Even in surprising ways. I could not find a single data point indicating otherwise, except for indoctrination of musicians towards ET leading to things like preferring sharp major 3rds and not recognizing the harmonic 7th interval.

pclmulqdq 3y ago
It's very possible that the averages over the population we see in the paper reflect a gradient of musical experience rather than an abstract notion of "pleasantness." Many trained musicians I know with a great ear have a very hard time with non-ET fifths and thirds, even knowing that ET is a grand compromise (all tunings are). We must learn through exposure - and admonitions from teachers to have better intonation - that ET is correct and everything else is wrong. I also have to say that the idea of making "pleasant" intervals is a bit reductive to begin with: unequal temperament tunings in modern use are often chosen to give a piece a particular "color" regardless of how "pleasant" the intervals are in a vacuum.

HPsquared 3y ago

Maybe it has something to do with phase. If they are ever so slightly out of tune, the phase is kind of "smeared" out, whereas with "exactly in tune" the locked phase can affect the timbre.

fsckboy 3y ago
that's not how phase works, though you're thinking reasonable thoughts. if you have a bicycle with two wheels, where one wheel is slightly bigger than the other, and you mark the wheels with a white spot, as the bicycle rolls, say the white spots start out in the same place (wrt a clock face). As the bicycle rolls, the white spots will "go out of phase" with each other, and with every roll, even more out of phase, till they are so out of phase that they start to slowly come a little bit more in phase with each other with every roll, till they match up again... except they are not out of phase, they are just rolling at two different frequencies, and that mix of frequencies is the "timbre" that you hear. if you have two signals at the same frequency which are out of phase, and you measure at any point, you will just measure a signal at that frequency whose amplitude is the sum of the two signals at that point. You won't be able to tell there is any phasing of two signals taking place. If your two ears hear the same frequency, but with a phase difference, that will be interpreted in part as what direction the sound comes from; it's not definitive, it's just evidence that gets combined with any other senses you have of where the sound should be coming from. there's a lot more to say about it but no room here for a treatise.
- HPsquared 3y ago
  I do think it could change the sound. Consider a simple octave interval, with zero phase or 90 degrees out: https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2840%29x%5C%2841%29%2BSin%5C%2840%292x%5C%2841%29 https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2... https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2840%29x%5C%2841%29%2BSin%5C%2840%292x%2BDivide%5B%CF%80%2C2%5D%5C%2841%29 https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2... The first looks a bit like a sawtooth wave, the second is more like a chain of pulses. Wouldn't that sound different? The Fourier series of Sawtooth wave, Square wave, etc. contain phase info as well as frequency.

graycat 3y ago

Come ON guys, help me out here: Be more clear about your terminology!!! Gee, I'm plenty good with the math and applications of Fourier theory. Sure, some physics course solved the differential equation of vibrating strings. Early on my career did well with Fourier theory, the FFT (fast Fourier transform), and Navy ocean data. And with violin, I got a start in the music school of Indiana University and eventually made it through several pages of the Bach E-major preludio, the Bach Chaconne, and a transcription, as I recall, up an octave and a fifth, of that famous Bach solo cello piece. Been known to take the positive whole number powers of 2^(1/12). Dissonance? Sure, I really like the S. Barber Adagio for strings!!! R. Wagner's chords. The Franz Schmidt Intermezzo to his Notre Dame. The Sibelius violin concerto. But, stilllll, a lot of your terminology I can't follow. For an opinion: Mostly music is art, that is communication, interpretation of human experience, emotion. Given the roles of, say, vibrato, Fourier theory and 2^(1/12) do not directly explain all of the art. For a perfect fifth, sure, as is standard, when take the violin out of its case, first tune the four strings G, D, A, E in perfect fifths and do this by listening for beats in the overtones. Then with the strings so tuned, often when the music calls for one of those 4 notes, just go ahead and play it on the open (look, Ma, no use of fingers on the left hand) string. In particular, for > perfectly in mathematical ratios in real music from before Bach to after Barber, I doubt that "perfectly" happens very often or is even attempted. E.g., with violin, can't play much music if play only on the open strings, and as soon as put a finger of the left hand on a string, with vibrato or even without, there won't be much "perfectly mathematical".

Nav_Panel 3y ago

I really like this site for info on various tunings, including Just Intonation, where the intervals ARE perfect mathematical ratios: https://www.kylegann.com/microtonality.html https://www.kylegann.com/microtonality.html One tidbit I always think about: > I've had interesting experiences playing just-intonation music for non-music-major students. Sometimes they will identify an equal-tempered chord as "happy, upbeat," and the same chord in just intonation as "sad, gloomy." Of course, this is the first time they've ever heard anything but equal temperament, and they're far more familiar with the first sound than the second. But I think they correctly hit on the point that equal temperament chords do have a kind of active buzz to them, a level of harmonic excitement and intensity. By contrast, just-intonation chords are much calmer, more passive; you literally have to slow down to listen to them. (As Terry Riley says, Western music is fast because it's not in tune.) It makes sense that American teenagers would identify tranquil, purely consonant harmony as moody and depressing. Listening from the other side, I've learned to hear equal temperament music as a kind of aural caffeine, overly busy and nervous-making. If you're used to getting that kind of buzz from music, you feel the lack of it as a deprivation when it's not there. But do we need it? Most cultures use music for meditation, and ours may be the only culture that doesn't. With our tuning, we can't. > My teacher, Ben Johnston, was convinced that our tuning is responsible for much of our cultural psychology, the fact that we are so geared toward progress and action and violence and so little attuned to introspection, contentment, and acquiesence. Equal temperament could be described as the musical equivalent to eating a lot of red meat and processed sugars and watching violent action films. The music doesn't turn your attention inward, it makes you want to go out and work off your nervous energy on something.

mingus88 3y ago

I haven’t read the study but the article gives the impression that researchers can get published for things as simple as discovering gamelan orchestras? I don’t want to sound cynical but ethnomusicology is a field unto itself and the idea that western tonal harmonies are a very small piece of the pie is something we’ve talked about for at least a hundred years Even the concept of just intonation for a western scale is well established

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dr_dshiv 3y ago

I spent a very long time trying to make sense of the broad concept of harmony. Here’s what I came up with: https://www.sciencedirect.com/science/article/pii/S240587262200003X https://www.sciencedirect.com/science/article/pii/S240587262... You’ll find some juicy details on Pythagoras (his Olympic days, for instance) as well as an overview of harmony in neuroscience, computer science, aesthetic theories, etc.

zigzag312 3y ago

Directly from the study: > "these preferences for slight deviations disappeared upon elimination of the upper harmonics, presumably because this eliminates the slow beating effect" It seems like the title is oversimplifying results for the sake of clickbait sensationalism.