[HN Gopher] Harmonics Explorer
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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!
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