[HN Gopher] We do not prefer chords to be perfectly in mathemati...
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We do not prefer chords to be perfectly in mathematical ratios:
study
Author : glitcher
Score : 65 points
Date : 2024-03-27 17:28 UTC (5 hours ago)
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(TXT) w3m dump (www.cam.ac.uk)
| jimbob45 wrote:
| _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 wrote:
| Of course you can tune any instrument to any scale. "Western
| piano" implies a standard tuned piano.
| karencarits wrote:
| 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
| ben7799 wrote:
| 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.
| ByQuyzzy wrote:
| 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 wrote:
| 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.
| holri wrote:
| Octaves on a piano are tuned slightly wider and "out of tune"
| because of the Inharmonicity of the strings.
| itishappy wrote:
| TIL!
|
| https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_.
| ..
| beardyw wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| GP here. s/those 4000/another extremely
| diverse 4000/
|
| would make the same point IMO.
| fsckboy wrote:
| > _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
| PeterCorless wrote:
| 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 wrote:
| This is irrelevant to the study, because the musical ear is
| attuned to human voices and that's what instruments are trying
| to _emulate._ A specific tuning system is a sacrifice that
| human voices don't have to make (e.g. the barbershop 7th versus
| a dominant 7th on a piano, or wolf intervals in Pythagorean
| tuning).
|
| Pythagorean tuning makes a ton of sense if you're trying to
| tune a fretted stringed instrument (and haven't tried playing
| anything with a key change), but it's an oversimplification of
| how music works. The Pythagorean philosophical mistake is
| treating the tuning system as a theory of music itself, when
| it's really a simple framework for certain types of music.
| BobaFloutist wrote:
| > the musical ear is attuned to human voices and that's what
| instruments are trying to emulate.
|
| That's quite the claim, do you have anything to support it
| beyond your intuition?
| omnicognate wrote:
| They compared people's subjective judgements of consonances
| tuned to perfect ratios to ones slightly off from those ratios
| and found they preferred the latter.
|
| A) Most people wouldn't be able to tune an instrument like what
| you describe accurately enough to contradict the result.
| Practically all the intervals would be slightly off, and
|
| B) The result really does contradict Pythagoras, who postulated
| that musical beauty arose from the mathematical perfection of
| those ratios. Contradicting Pythagoras in this is, of course,
| hardly new. More interesting is the idea that there may be
| entirely new forms of naturally appealing harmony out there to
| explore.
| anigbrowl wrote:
| I disagree with B. People like slightly detuned oscillators
| because it makes the sound thicker and bigger. But they like
| slight detuning _around_ the mathematically perfect ratio.
| The imperfection _emphasizes_ the ratio in the brain 's
| auditory processing.
|
| This is why many subtractive synthesizers have a detune
| parameter, to slightly offset oscillators that are nominally
| tuned to the same frequency. Chorus, phasers, and flangers
| are similarly used to add texture and color to sounds by
| using slight frequency or phase delays to create interference
| signals that make the sound 'move' and make it sound larger
| and more distinct.
| dr_dshiv wrote:
| It's like the "humanize" button on drum machines that will
| make the rhythms slightly off. We still like the small
| integer relations of the drum beats but when they are a bit
| off, they sound warmer and more human.
| buildsjets wrote:
| That sounds more like an experiment that Von Neumann and
| Stanislaw Ulam would have come up with than the product of an
| ancient Greek philosopher. But he probably would have been
| pleased by it.
| odyssey7 wrote:
| 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 wrote:
| Some previous discussion:
| 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-mus...
| FLT8 wrote:
| > "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 wrote:
| 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 wrote:
| 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 wrote:
| My suspicion is that learning music theory (for any
| specific cultural norm) is a bit like learning about font
| kerning: https://xkcd.com/1015/
|
| Many of the auditory things that trained musicians describe
| as creepy or weird, seem unremarkable to me.
| xotesos wrote:
| I would say that is because there is nothing to compare
| barber shop music too.
|
| I am a big fan of Terry Riley's - Harp of New Albion
| exactly because its five-limit just intonation piano sounds
| so incredibly weird to my ears.
| dekhn wrote:
| See also La Monte Young- Forever Bad Blues Band. I
| listened to it and it sounded "different" but not
| particularly weird (I was already listening to Phish, The
| Dead, and indian music, so I think I was prepared for
| blues in just intonation).
| hax0ron3 wrote:
| I don't think everyone is equally sensitive to this. Just
| intonation sounds a bit different to me from equal
| temperament, but it doesn't sound disturbing. Likewise,
| although I have heard a lot of Indian classical music that is
| not in equal temperament, so I am pretty acclimated to it,
| when I hear Indian classical music played on equal
| temperament instruments it does not sound that bad. Some
| subtleties are definitely lost, and I prefer the non equal
| temperament tunings for that kind of music, but I do not find
| it disturbing.
| gnramires wrote:
| Related, a friend likes to say instruments that produce too
| pure sounds (too much like a sine wave) sound somewhat boring,
| because of their lack of timbre characteristics. I think this
| is a somewhat general property; although in general art is more
| of a language. I think a pure sine can sound right in the right
| context (e.g. perhaps how we remember fondly, and still enjoy,
| chiptunes and retro music), and it can have a particular
| meaning within that context that makes sense.
| WorldMaker wrote:
| It is indeed a common complaint of many of the chiptune
| genres that they can sound boring, especially for audiences
| too old or young to have as much nostalgia for the hardware
| whose constraints set the genre constraints. The basic NES
| "instruments" were simple wave generators that were about as
| pure as waveforms get, plus one simple white noise generator.
|
| I've met critics that even think that "pure" chiptune sub-
| genres such as the ones that stay within the bounds of
| physical NES hardware "can't" survive long-term. I think they
| are wrong both because I've heard some extraordinary things
| done within those constraints in my lifetime and for some of
| the reasons that "minimalism" will always be a viable
| subgenre of "Classical" (no matter how boring some people
| find that, too). But I understand where that idea comes from
| of how such a unique set of hardware constraints gave us some
| of the "purest" waveforms possible and why such pure
| waveforms are generally an anomaly in music.
| immibis wrote:
| Ah yes, [simple and
| boring](https://www.youtube.com/watch?v=1lScTUyEsA4). You
| get 3 voices or whatever's on your chip, but you can also
| re-adjust them up to hundreds of times a second any way you
| like. Of course if you just leave them fixed for long times
| they will sound a bit boring.
| vr46 wrote:
| This is intriguing and clearly not new as you say - my strobe
| tuner offers "sweetened" tunings for guitar. Going to have to
| experiment with this variation now...
| pje wrote:
| "Imperfect" tunings are pretty common even in western musical
| instruments.
|
| Fender Rhodes and Wurlitzer electric pianos, for example, which
| are staples of pop and jazz, usually use what's called Stretch
| Tuning, wherein notes an octave apart are _just slightly_
| higher than 2:1 frequency ratios.
|
| https://en.wikipedia.org/wiki/Stretched_tuning
| denotational wrote:
| A "normal" piano with strings uses stretch tuning too.
| StableAlkyne wrote:
| Even playing a single note, having your oscillators a couple
| cents out of tune with each other contributes to a warm sound!
|
| Old polyphonic synths like the venerable Oberheim OB-Xa would
| have their voices go slightly out of tune as the instrument
| warmes up. It's subtle, but once you hear it you start to
| notice the color it adds
| pfgallagher wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| In other news; Golden ratio? More like bronze
| uwagar wrote:
| so a pitch and its octaves, or a pitch and its perfect fifth
| above or below sounding harmonious is not universal?
| 082349872349872 wrote:
| 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?
| mrob wrote:
| 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
|
| Informal explanation:
|
| https://sethares.engr.wisc.edu/consemi.html
| omnicognate wrote:
| 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
| riffic wrote:
| This reminds me, have we had a good 432 Hz vs 440 Hz discussion
| lately?
| thuuuomas wrote:
| 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 wrote:
| 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 wrote:
| I hope this result calls into question all the other work done by
| Pythagoras.
| andoando wrote:
| 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 wrote:
| The non-western music I'm familiar with oftentimes still
| emphasizes things like I-V consonance.
| igorbark wrote:
| 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
|
| - a more recent re-implementation with a cool video at the end:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| Yep, agreed. Once you get there you can really appreciate
| what music is and does all on its own.
| andoando wrote:
| Can you explain more? What do you mean the data isnt there?
| srcreigh wrote:
| 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
|
| 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 wrote:
| 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.
| srcreigh wrote:
| Agreed. Western musicians have a sort of
| indoctrination/familiarity towards ET, leaving the untrained
| folks better equipped to recognize Just intoned harmony.
|
| Also agreed re: pleasant intervals. My favourite example
| (which I have posted before) is this Mozart piece in 6th
| comma meantone. The back and forth between dissonance and
| pure harmonic resolution with great 3rds tuning is
| extraordinary. Anyone, give it one listen, you will be
| convinced.
|
| https://youtu.be/lzsEdK48CDY?si=rtBE-M0cCRQsDHNx&t=700
|
| (Note the last, cheerful section was added after mozart's
| death.)
| pclmulqdq wrote:
| I don't personally like the tuning on that - it feels a
| little too rough. However, many classical and even
| romantic-period composers had pianos tuned in Werckmeister,
| Kirnberger, or Vallotti temperaments, which had toned-down
| versions of similar dissonances you hear here (similar to
| the second rendition of the Mozart in that video).
| anigbrowl wrote:
| Quite, and this has been known for years - any good
| ethnomusicology textbook addresses it chapter 1. Equal
| temperament and 'western harmony' are not all that.
| HPsquared wrote:
| 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.
| graycat wrote:
| 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 wrote:
| 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
|
| 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 wrote:
| 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
| dr_dshiv wrote:
| 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/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.
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