[HN Gopher] Harmonics Explorer
       ___________________________________________________________________
        
       Harmonics Explorer
        
       Author : udit99
       Score  : 257 points
       Date   : 2024-01-29 09:51 UTC (13 hours ago)
        
 (HTM) web link (teropa.info)
 (TXT) w3m dump (teropa.info)
        
       | mikewarot wrote:
       | Well, that was fun, I've got headphones on, so I heard it all the
       | way down to 16 Hz sine wave.
       | 
       | Getting a triangle wave with 4n+1 harmonics wasn't easy.
        
       | mcqueenjordan wrote:
       | This is really cool. I used to do a lot of overtone ("harmonic")
       | throat singing and playing with this tool reminded me of those
       | days.
       | 
       | For anyone curious, vowels are mostly just how we perceive
       | different harmonic distributions. Put differently, harmonics are
       | the basis of what it means to pronounce a different vowel. The
       | human voice is basically just a harmonic chord, with different
       | distributions of the 2nd, 3rd, 4th, etc. harmonics.
       | 
       | e.g. https://www.open.edu/openlearn/health-sports-
       | psychology/heal...
        
         | lioeters wrote:
         | That reminds me, I saw a video recently of a choir practice
         | where they sang "brighter" and "darker" based on the
         | conductor's hand position.
         | 
         | It was fascinating how the singers could control the brightness
         | of their voice while holding the same note and frequency. When
         | they went bright, it sounded closer to "eee" or "iii". When
         | they went dark, it sounded like "uuu" and "ooo".
         | 
         | From that, I learned that the lyrics of a song, in particular
         | the vowels, can be chosen consciously (or not) for their
         | harmonic effect.
        
           | xeonmc wrote:
           | You may find this interesting:
           | https://www.youtube.com/watch?v=vC9Qh709gas
           | 
           | EDIT: also this https://www.youtube.com/watch?v=FdldD0-kEcc
        
             | brk wrote:
             | You may also find this interesting:
             | https://www.youtube.com/watch?v=3oxe4mlsQos&t=120s
        
             | divan wrote:
             | Thanks for sharing! Didn't know human voice can do this.
        
           | AlecSchueler wrote:
           | A lot of great music has been written with this in mind, I
           | would highly recommend Stimmung, for six vocalists and six
           | microphones, by Karlheinz Stockhausen.
           | 
           | Really the whole piece is created from a framework of
           | phonetics, loose vowel sounds as well as names taken from the
           | "magical of otherworldly" traditions of various cultures as
           | well as words taken from the composer's own poetry.
        
             | lioeters wrote:
             | Ooh nice. I'd heard of Stockhausen - attended a performance
             | of his works once - but this is new to me. Very strange
             | music with a wide range of harmonics produced by
             | vocalizations of vowel sounds. Sometimes nasal, other times
             | chant-like, machine-like, and even reminiscent of insects
             | at night.
             | 
             | https://www.youtube.com/watch?v=3hPkJW95jsw
        
           | kevindamm wrote:
           | Reminds me of pink trombone.
           | 
           | https://dood.al/pinktrombone/
        
         | klysm wrote:
         | Is this related to formants? I don't actually know what that
         | term means but I've heard it used in this context
        
         | srcreigh wrote:
         | 90 second video demonstration:
         | https://www.youtube.com/watch?v=VnC8I3d2MXQ
         | 
         | Lots of different notes present. Perfect 5th, major 2nd, major
         | 3rd, major 7th are all found in the harmonic series. In
         | addition there's some beautiful non-piano intervals, notably
         | the 7th harmonic (slightly flat minor 7th) and the 11th
         | harmonic (flat tri-tone)
        
       | d--b wrote:
       | My tinnitus does not thank you
        
       | dr_dshiv wrote:
       | The earliest known scientific hypothesis test was a Pythagorean
       | investigation of whether the mathematical model for consonance in
       | stringed instruments generalized to chimes -- so rather than 1:2
       | as a ratio of string length, whether a ratio of 1:2 in chime
       | thickness also produces an octave. It does. (This experiment was
       | conducted by Hippasus and recorded by Aristoxenus, a student of
       | Aristotle)
       | 
       | But interestingly, we still have big open gaps in our scientific
       | models of consonance and dissonance.
       | 
       | Consonant tones involve a large number of shared harmonics. That
       | alignment appears to be important in the perception of consonance
       | and dissonance. Yet, harmonic alignment is not currently a
       | mechanism used in the algorithmic detection of
       | consonance/dissonance, so far as I know. This tool looks like a
       | good way to generate stimuli for experimentation, thanks!
        
         | mrob wrote:
         | William Sethares developed a model of consonance and dissonance
         | based around alignment of harmonics (or partials; it
         | generalizes to inharmonic sounds).
         | 
         | Original paper:
         | 
         | https://sethares.engr.wisc.edu/paperspdf/consonance.pdf
         | 
         | Informal explanation:
         | 
         | https://sethares.engr.wisc.edu/consemi.html
        
       | Prcmaker wrote:
       | I like the thing, but it misses what I enjoyed teaching about
       | these most: phase. Many people know white noise is nominally 'all
       | frequencies at the same intenisty', yet those taught Fourier
       | mathematics are also taught that the same recipe makes a pulse.
       | The difference is all in the phase information, and why I
       | maintain to this day the Nyquist-Shannon sampling theorem, as
       | typically applied, is incorrect.
        
         | laszlokorte wrote:
         | Yes phase information is really important. Try this:
         | 
         | 1. Fourier Transform an Image 2. Set all magnitues the the
         | spectrum to 1.0, but do not change the phase 3. Inverse
         | Transform and look at the result 4. Now try the same, but this
         | time keep the maginutes unchanged but change all phases to 0deg
         | 
         | Spoiler: When changing all amplitudes the image is still
         | regocognizable, when changing all phases, it is not. See
         | example: [1]
         | 
         | But in what sense are you saying the Nyquist-Shannon theorem is
         | incorrect (when applied)? It only says something about the most
         | general case of perfectly reconstructing a signal.
         | 
         | For getting an playful and intuitive understanding of
         | time/frequency transformations my fourier-cube visualization
         | might be useful [2]
         | 
         | [1]: https://static.laszlokorte.de/phase.png [2]:
         | https://static.laszlokorte.de/frft-cube/
        
           | rcxdude wrote:
           | I'm not sure the original poster meant, but the sampling
           | theorem is often misunderstood, there's a good article I
           | recommend to most anyone who has the choose a sampling rate
           | which goes into those misconceptions: https://neuron.eng.wayn
           | e.edu/auth/ece4330/practical_sampling...
        
           | roelschroeven wrote:
           | Phase information is important, but as far as I understand
           | it, it is not important in audio: our ears are insensitive to
           | phase.
           | 
           | (Phase is important when combining different sinuses of the
           | same frequency, because the sum of those will be different
           | depending on their relative phase, but that's a different
           | matter and not relevant here.)
           | 
           | Changing the phases of the different frequencies will result
           | in a waveform that looks different, but it will sound the
           | same. Our ears are like a spectrum analyzer that only records
           | the volume of each frequency, and is unable to record the
           | phase.
        
             | xeonmc wrote:
             | It's insensitive to _individual_ phase of audible
             | frequencies, but the concept of phase itself is very
             | important in audio in the form of time delays /echoes, if
             | you are dealing with long sample lengths.
             | 
             | See my sibling comment explaining how translation
             | corresponds to ramping phase shift/"fast-forwarding" each
             | frequencies such that the shifted distance are the same
             | across the spectrum.
        
             | wholinator2 wrote:
             | To expand on the other comment. You wouldn't be able to
             | tell the difference in a single sine wave with phase set to
             | either 0 or 180 degrees. But if you add in another sine
             | wave at 0 degrees, the two 0's will add up and the 0 and
             | 180 will completely cancel.
             | 
             | Phase makes a huuuuge difference in audio engineering.
             | There isn't a single song that gets mixed without intense
             | consideration of phase interactions between the different
             | tracks. Getting it wrong can result in catastrophic damage
             | to the audio signal that reaches your ears. If you have a
             | speaker capable, try switching the leads that feed the
             | signal on one of the speakers and see how it sounds!
             | Everything that's exactly the same between the two speakers
             | will sound hollow and tinny, the frequency balance will
             | completely degrade
        
             | bongodongobob wrote:
             | Phase is hugely important and is part of how we perceive a
             | sound in space. Making sure the phase is correct when using
             | multiple mics to mic a drum kit, for example, is critically
             | important.
        
           | xeonmc wrote:
           | Explaining concretely: a uniform spatial displacement of the
           | image corresponds to a ramping phase shift across the
           | frequency spectrum.
           | 
           | i.e. if you shift an image by 1cm, then the 1 rad/cm
           | frequency component gets its phase "fast forwarded" by 1rad,
           | the 1.5 rad/cm component forwarded by 1.5rad, and 2 rad/cm by
           | 2rad and so on.
           | 
           | By subtracting each frequency's phase from their original
           | distribution, you are basically displacing them each by a
           | different distance from one another, decohering the image
           | entirely.
        
           | ubavic wrote:
           | Tangential: Your Fourier Cuboid is very cool project. I have
           | added it to awesome-interactive-math [1] list.
           | 
           | [1]: https://github.com/ubavic/awesome-interactive-math/
        
         | rock_artist wrote:
         | Without entering the broader discussion in the comment. I've
         | also missed the ability to change phase for each harmony.
        
         | bigbillheck wrote:
         | In the domains that I'm familiar with we never get to measure
         | phase, only intensity.
         | (https://en.wikipedia.org/wiki/Phase_retrieval)
        
       | _nivlac_ wrote:
       | I love these. My favourite part is that you can hear the
       | fundamental frequency when you add up the non-octave frequencies
       | (i.e. increase all harmonics except 1, 2, 4 and 8). Even though
       | the fundamental frequency isn't "there", your ears can still hear
       | it.
        
       | xeonmc wrote:
       | If you want to go above 13 overtones or make other waveforms, I
       | quickly whipped this up for square/triangle/sawtooth/impulse
       | trains:
       | 
       | https://www.desmos.com/calculator/eioaj93rzr
        
         | djmips wrote:
         | Very nice.
        
       | edoardo-schnell wrote:
       | Nice. Would be even nicer to be able to move the base frequency
        
         | quercusa wrote:
         | Look for the arrows on either side of C4 on the top bar.
        
       | quercusa wrote:
       | The effect when switching from sine to square wave, as the
       | harmonics are added, is very nice.
        
       | elevaet wrote:
       | This is very cool.
       | 
       | If the creator is reading these comments, my one piece of
       | feedback would be that I think it would be more
       | interesting/useful if the harmonics were expressed as multiples
       | or ratios of the fundamental.
        
       | waffletower wrote:
       | Nice visualization! A few improvement suggestions -- I noticed
       | that it is easy to clip the 'master' output, a 'master fader' to
       | control its output (or a checkbox to rescale visualization based
       | on maximum value).
       | 
       | Also, implementing a phase control for each harmonic would also
       | be interesting for visualization.
       | 
       | Finally, why not add a wavetable synth to allow you to hear the
       | resulting waveform?
        
         | chankstein38 wrote:
         | Master volume fader, please. This is cool but I have to change
         | my computer volume to adjust the volume and that's not a very
         | great experience. Especially when I click Square and it just
         | starts screaming at me.
        
       | superb-owl wrote:
       | This is great. I wish the left side showed the frequency ratio as
       | well as the raw frequency
        
       | KyleBrandt wrote:
       | It might be interesting if there is more fine tuning towards the
       | lower end of the volume. So the higher harmonics can be present
       | but much softer.
        
       | jefurii wrote:
       | I thought this might be a map of the positions of various
       | harmonics on e.g. guitar strings, but still very interesting and
       | cool.
        
       | miggol wrote:
       | Wow, what a lucky find. This is incredibly useful to me for
       | equalizing speakers to match a room. I was using Websynths
       | Microtonal before but this almost seems designed for the purpose.
       | 
       | All it might need is the ability to manually enter the base
       | frequency yourself or do an automatic sweep. But I could probably
       | bodge that into the source myself.
       | 
       | Lovely!
        
       ___________________________________________________________________
       (page generated 2024-01-29 23:00 UTC)