Harmonics Explorer

This is really cool. I used to do a lot of overtone (&quot;harmonic&quot;) throat singing and playing with this tool reminded me of those days.<p>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.<p>e.g. <a href="https:&#x2F;&#x2F;www.open.edu&#x2F;openlearn&#x2F;health-sports-psychology&#x2F;health&#x2F;from-sound-meaning-hearing-speech-and-language&#x2F;content-section-2.3" rel="nofollow">https:&#x2F;&#x2F;www.open.edu&#x2F;openlearn&#x2F;health-sports-psychology&#x2F;heal...</a>

I like the thing, but it misses what I enjoyed teaching about these most: phase. Many people know white noise is nominally &#x27;all frequencies at the same intenisty&#x27;, 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.

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)<p>But interestingly, we still have big open gaps in our scientific models of consonance and dissonance.<p>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&#x2F;dissonance, so far as I know. This tool looks like a good way to generate stimuli for experimentation, thanks!

Nice visualization! A few improvement suggestions -- I noticed that it is easy to clip the &#x27;master&#x27; output, a &#x27;master fader&#x27; to control its output (or a checkbox to rescale visualization based on maximum value).<p>Also, implementing a phase control for each harmonic would also be interesting for visualization.<p>Finally, why not add a wavetable synth to allow you to hear the resulting waveform?

If you want to go above 13 overtones or make other waveforms, I quickly whipped this up for square&#x2F;triangle&#x2F;sawtooth&#x2F;impulse trains:<p><a href="https:&#x2F;&#x2F;www.desmos.com&#x2F;calculator&#x2F;eioaj93rzr" rel="nofollow">https:&#x2F;&#x2F;www.desmos.com&#x2F;calculator&#x2F;eioaj93rzr</a>

This is very cool.<p>If the creator is reading these comments, my one piece of feedback would be that I think it would be more interesting&#x2F;useful if the harmonics were expressed as multiples or ratios of the fundamental.

The effect when switching from sine to square wave, as the harmonics are added, is very nice.

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.<p>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.<p>Lovely!

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&#x27;t &quot;there&quot;, your ears can still hear it.

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.

It&#x27;s wonderful when an interaction makes you question that which you thought you knew.<p>My understanding was that, in order to produce a triangle or sawtooth wave, you need to have a phase control. This is because of the (-1)^k term in the Fourier expansion, as seen in Wikipedia.<p>After seeing this site produce a sawtooth wave with no phase control, my mind is blown apart, into tiny little pieces.

My tinnitus does not thank you

Nice, I built a similar toy with RNBO - <a href="https:&#x2F;&#x2F;knobs-gallery.vercel.app&#x2F;harmonics" rel="nofollow">https:&#x2F;&#x2F;knobs-gallery.vercel.app&#x2F;harmonics</a><p><a href="https:&#x2F;&#x2F;rnbo.cycling74.com&#x2F;" rel="nofollow">https:&#x2F;&#x2F;rnbo.cycling74.com&#x2F;</a>

This is great. I wish the left side showed the frequency ratio as well as the raw frequency

My similar project, with a bit of a spirograph mixed in: <a href="https:&#x2F;&#x2F;merely.xyz&#x2F;waves" rel="nofollow">https:&#x2F;&#x2F;merely.xyz&#x2F;waves</a>

Nice. Would be even nicer to be able to move the base frequency

Well, that was fun, I&#x27;ve got headphones on, so I heard it all the way down to 16 Hz sine wave.<p>Getting a triangle wave with 4n+1 harmonics wasn&#x27;t easy.

I thought this might be a map of the positions of various harmonics on e.g. guitar strings, but still very interesting and cool.

should check Tero&#x27;s other works: <a href="https:&#x2F;&#x2F;teropa.info&#x2F;" rel="nofollow">https:&#x2F;&#x2F;teropa.info&#x2F;</a><p>another comment:<p>if you want to use any number of sine waves of any freq, you can use code to do this:<p><a href="https:&#x2F;&#x2F;glicol.org&#x2F;tour#mixjs2" rel="nofollow">https:&#x2F;&#x2F;glicol.org&#x2F;tour#mixjs2</a>