[HN Gopher] The Fine Art of Combining Harmonics
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The Fine Art of Combining Harmonics
Author : flabber
Score : 129 points
Date : 2021-06-22 06:39 UTC (16 hours ago)
(HTM) web link (whatmusicreallyis.com)
(TXT) w3m dump (whatmusicreallyis.com)
| xavriley wrote:
| Harmonic intervals are interesting but they are also
| misunderstood. Humans are able to distinguish out of tune notes
| down to a value of about 1%. To get more accurate tuning we tend
| to listen for beating (a kind of amplitude modulation) instead.
| This means we can tolerate tuning systems other than just
| intonation. Another thing to consider - the missing fundamental
| phenomenon suggests that the ear/brain is actually doing
| something like autocorrelation. This makes more sense than the
| idea that we have a template for the harmonic series wired in our
| brains. Finally auto correlation works for chords too, not just
| intervals. Every chord has a fundamental period of repetition -
| shorter periods are widely ranked as more consonant. There are
| lots of grand music theories that fixate on the harmonic series.
| The maths is fun, but it can get in the way of more effective
| alternatives for organising sounds.
| SeanFerree wrote:
| Very cool! Excellent visuals in this article
| fit2rule wrote:
| Ctrl-F: harmonic bundle
|
| .. hmm ..
|
| Ctrl-F: conjugate
|
| .. hmm.
| seph-reed wrote:
| This is really cool, but -- as someone who's been researching
| just tuning for a while -- I think a lot of very important
| aspects of human psychology have been overlooked here.
|
| Frankly, familiarity is a vastly more important aspect of music
| than any micro-tonal artist would like to admit. And while the
| overtone series is (in many many ways) the root of all music, not
| every overtone is equal.
|
| For instance: 9/8 (a major second) is just (3 * 3)/(2 * 2 *2) and
| is generally more consonant (like dull, boring, unmoving: an
| octave or perfect fifth) than anything with a 5 prime number in
| it (eg 5/4 a major 3rd). AFAICT, the order of simplicity
| (dullness -> dissonance) on intervals is 2/1, 4/1, 3/2, 4/3, 3/1,
| 9/8, 16/9, 5/4, 8/5, 6/5... it's not exactly clear what the math
| is here.
|
| Also, it's always really, really telling to me when someone
| shares a music theory without sharing a recording of that theory
| in action. The site I'm working on lets people use their keyboard
| to play with every scale, so you can verify that it's not just
| number play.
| necrotic_comp wrote:
| yep - I came in here to talk about "familiarity" as the bedrock
| of how we listen to tunes. In my estimation, music is a
| constant juggling act between familiarity and novelty, and
| bending too much on one side or the other trends towards
| boredom.
|
| I would argue that some of the pure intonation music (i.e.
| Michael Harrison's Revelations) or alternate tuning (i.e.
| Lamonte Young's Well Tuned Piano) is striking initially because
| of how alien it sounds, but to my ear a lot of it doesn't feel
| like it does too much more than that both as a function of the
| tuning and the difficulty in building a moving composition in
| something so foreign.
|
| The standard tunings in Western Music are well-worn, but they
| can give a rich vocabulary for dissonance and consonance and
| have the psychological familiarity to build up emotional
| abstractions that some of the more adventurous scales do not.
| PaulDavisThe1st wrote:
| I found the first 2/3 of this mostly acoustic-woo, but by the
| time it got to the actual 2D "HarmoniComb" I was quite excited by
| the concept of this as a playing surface.
|
| However, then I decided to go visit another page at the same
| site, the one on "Tuning". It has a section on digital sample
| rates that is just so completely incorrect that it made me wonder
| about everything else I had read. The page linked above is
| _specifically_ about "combining harmonics". However, the author
| doesn't appear to understand how the exact same concept (more
| specifically, how any waveform can be represented as the sum of a
| (potentially infinite) series of sinusoidal waves) makes their
| musings on digital audio totally wrong.
| klysm wrote:
| Yeah a lot of the explanations have a pseudo-scientific flavor
| to them with questionable mathematical hand waving.
| seph-reed wrote:
| Holy cow! I just came up with this theory and started proving it
| like... 2 months ago. Crazy how these things line up sometimes.
|
| One thing not included in here: given tests on human response
| rates to sound, it is very likely that grouping frequencies
| together based off a harmonic series is done "before the brain."
| (ie, that bird is this set of frequencies, that tree in the wind
| is this other set)
| chipuni wrote:
| Please, try playing your harmonic ideas with real sounds.
|
| Here's some things to try:
|
| - How bad or good do two synthesized violins sound together at
| 800 and 900 hertz? Think about them as overtones: Does adding a
| tone at 100 hertz resolve the sound? Think of them as undertones:
| Does adding a new tone at 7200 hertz resolve that sound?
|
| - Does the instrument change the harmony? What happens to harmony
| when the instrument is a clarinet? What happens to harmony when
| the instrument is a sine wave? What happens to harmony when the
| instrument is a tuned tympani?
|
| - Try to play together the overtone series, for example, 1000 hz,
| 2000 hz, 3000 hz, ... How does that sound?
|
| - Try to play together the undertone series, for example, 2520
| hz, 1260 hz, 840 hz, 630 hz, 504 hz, ... How does that sound?
| klysm wrote:
| This is incredibly dismissive of any harmony that is based on
| equal temperament, or anything that isn't the harmonic series. I
| don't think that's justified - a lot of jazz harmony only sounds
| good in equal temperament. For instance, minor 6 chords are going
| to sound terrible.
| cousin_it wrote:
| Huh? To me Dm6 in the just intonation A minor scale sounds
| fine.
| deeviant wrote:
| I'm sorry, but this is a pile of mumbly-bumbly.
| twic wrote:
| Time Cube, but for sound!
|
| I know next to nothing about music theory, but this felt like an
| abstruse statement of the bleeding obvious up until the section
| "What Tuning Really Is: Subsets of the HarmoniComb", which was
| interesting. I have no idea if it's accurate.
|
| Incidentally, the author seems to use some strange 'I' character
| (a capital I with a dot over it) a lot. I'm not sure why.
| king_magic wrote:
| Ah, Time Cube - instantly what I thought as well.
| deeviant wrote:
| > Incidentally, the author seems to use some strange 'I'
| character (a capital I with a dot over it) a lot. I'm not sure
| why.
|
| This is because the author is actually a fractal within a
| 420-dimensional LSD hypercube, the 'I' denotes membership of
| the set of infinity|UniTY<>Triome.
|
| Also, you nailed in one, definitely timecube vibes going on
| here.
| kortex wrote:
| My immediate thought on reading the first paragraph is, "this
| is like Time Cube if it actually made complete sense under the
| word salad." It's really, honestly rather obnoxiously, obtuse,
| but I get what they are getting at.
|
| It feels like when academic ML papers use the abstract to try
| to boozle and astound the reader with tons of jargon, because
| we all know a paper wins more Academia Points (TM) the more
| they can make other smart people feel dumb.
| mkl wrote:
| "I" is from some Turkic languages:
| https://en.wikipedia.org/wiki/Dotted_and_dotless_I
| streamofdigits wrote:
| Beautiful visuals. Ever since the pythagoreans there is a
| mystical fascination with harmonic ratios and harmonic perception
| but after reading Philip Ball's "music instinct" I am not sure
| its justified. I don't know if there is something more updated
| since 2010 (for non-brain neurologists)
| bsedlm wrote:
| I have been thinking very much this for over a decade now. Down
| to even using the times and the division signs the same way (or +
| and - given they are more easily typed).
|
| An interesting thing is that 2 is very special musically, but not
| mathematically, because it makes all notes musically the same
| (establishes pitch classes).
|
| A very funky thing (kinda annoying really) is as follows:
|
| Given a note, any note, as a tonal center or starting point (I
| call it O for origin) you 'make' a new note from this one by
| multiplying by 3 (O+3) [note 1]. Similarly we can make O+5.
|
| O+5 is in traditional western music closest to the major third
|
| AND O+3 corresponds to a 12-tet perfect fifth (flat 2 cents).
|
| In short +3 is the fifth and +5 is the third...weirdly annoying.
|
| note 1: Here's were 2 (which defines octaves) comes into play
| because it allows to say that O+3 defines a pitch-class no matter
| the octave.
| bigbillheck wrote:
| From the 'Tuning' page:
|
| > In the case of the human voice, these overtones will all be
| harmonics, because they display relationships based on perfect
| integers. On non-biologic instruments (which display slight
| deviations from perfect numbers due to mechanical attributes like
| stiffness), the whole matrix will get stretched or compressed
| according to the deviation (or "inharmonicity") factor
|
| I'm not sure I understand an instrument made mostly of meat and
| cartilage and maybe a little phlegm can be more 'perfect' than a
| mechanical one.
| iainctduncan wrote:
| If you want the goods on this stuff from someone who actually
| understands it, read Kyle Gunn's "The Arithmetic of Listening".
| auiya wrote:
| Music producer Andrew Huang does a fantastic job demonstrating
| the harmonic series concepts in a video from last year:
| https://www.youtube.com/watch?v=Wx_kugSemfY
| mrob wrote:
| >There is of course a questionable degree of dissonance that can
| be tolerated, but the most obvious fact is that the brain can
| well be conditioned to accept and even enjoy these dissonances,
| as long as they are part of the only music it has ever
| experienced.
|
| I disagree. I have listened to a fair amount of music in just
| intonation, and I am capable of hearing the tuning flaws of 12
| equal temperament, but I am still capable of enjoying dissonance,
| and of appreciating the artistic flexibility that those tuning
| flaws give you.
|
| This article presents a very limited view of music. Just
| intonation does have artistic merit (check out the works of Harry
| Partch), but it's not the only valid form of music. The human
| brain doesn't count frequencies, and integer ratios are not
| fundamental to perception of consonance. They just happen to work
| well with a common class of timbres. But for other timbres, e.g.
| tuned percussion, other tuning systems can sound more consonant.
| You can even hear this in Western classical music: pianos are
| tuned with non-integer octaves to compensate for the
| inharmonicity of their strings. See:
| https://en.wikipedia.org/wiki/Stretched_tuning
|
| William Sethares published a more general model of consonance
| perception that handles all these cases:
|
| https://sethares.engr.wisc.edu/paperspdf/consonance.pdf
|
| I previously posted about this on HN with some more background
| and references:
|
| https://news.ycombinator.com/item?id=23638307
| lmilcin wrote:
| That's right. If you spend too much time eating sweet chocolate
| you might start enjoying something more savory, too.
|
| I am learning to play Irish trad on Irish flute and I have
| learned some time ago that dissonance is a real tool that can
| be used to create certain kind of moods, especially in slow
| airs.
| bsedlm wrote:
| I based my bachelor's graduation project on Setahres' work.
|
| The one thing I wish we could find is the drum version of this.
| As in instead of starting from a string (which leads to
| harmonic series), start from a circular membrane (which leads
| to a very complicated mathematical result based on bessel
| functions ircc).
| eezurr wrote:
| +1 for Harry Parch. Here's a good introduction for new people
| [1]. I'd add in Lou Harrison [2] and Tristan Murail [3]
|
| Lou Harrison was heavily influenced by Gamelan music, and
| Tristan Murail is one of the founders of spectralism, which
| uses spectrograms of individual instruments to build distinct
| harmonies by having orchestral instruments play the harmonic
| series as shown on the spectrogram. They stretch this idea even
| further by adding in "harmonics/overtones" that are not shown
| on the spectrogram to create dissonance.
|
| [1] https://youtu.be/kCuYcS_Lcro?t=372
|
| [2] https://www.youtube.com/watch?v=f7IwH01YFAI
|
| [3] https://www.youtube.com/watch?v=q6WXzOIsBuQ
| jcpst wrote:
| And Gerard Grisey.
| TheOtherHobbes wrote:
| Sethares and Tymoczko are the go-tos on this.
|
| But there's a _lot_ more to creating interesting musical
| structures than creating chords out of mathematical structures
| that are based on the harmonic series.
|
| The more time I spend trying to understand music, the less I
| understand it.
|
| That's what makes it so endlessly fascinating.
| iainctduncan wrote:
| I've read quite a bit on this, but not Sethares, do you have
| a recommendation for starting on his work? thanks!
| qmmmur wrote:
| > as long as they are part of the only music it has ever
| experienced.
|
| So noise music is only enjoyable if listened to from birth in
| isolation?
| crawfordcomeaux wrote:
| I accidentally abandoned many of my preferences
| (likes/dislikes) and automated judgments. I took this newfound
| perspective into music, embodying the idea of "there are no
| wrong notes." I find deep joy in sitting at a 120+ year old
| pump organ, holding a mishmash of dissonant notes, including
| some out of tune ones, and wiggling one of the keys to learn to
| spot it in the mashup. It gives me a chance to witness the
| internalized feelings conditioned from classical musical
| training and listening to a ton of western music throughout my
| life, as well as to watch those feelings fade away into the
| joy.
|
| We can learnjoy anything, which is why choosing to do anything
| without joy doesn't make sense to me anymore.
| chestervonwinch wrote:
| > I accidentally abandoned...
|
| It sounds like you made a conscious and intentional decision.
| How does one drop their preconceived judgements by accident?
| tomc1985 wrote:
| Psychedelics, perhaps?
| crawfordcomeaux wrote:
| I was aiming to abandon judgments of things and had no idea
| it meant how my body reacts to things would change, that
| I'd effectively disable disgust in myself, that country
| music would become rockin (and that I'd enjoy all other
| forms of music, food, smells, drinks, and people...children
| went from obnoxious to adorable in weeks).
|
| The intention was to try something very broad that would
| likely cover moral judgments. I did make a conscious
| decision, but the side effects were for sure happy
| accidents.
| egonelbre wrote:
| I like to think that in an alternate world, somebody wrote:
|
| > There is of course a questionable degree of consonance that
| can be tolerated, but the most obvious fact is that the brain
| can well be conditioned to accept and even enjoy these
| consonances, as long as they are part of the only music it has
| ever experienced.
| [deleted]
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