welcome to my tone generator

it makes sounds like this:
I call them circular waves [0] because when you plot them over time they make alternating, connected semicircles.
they're similar to other geometric waveforms, like
sawtooth,
square, &
triangle waves
they're a little harder to generate [1], but they have interesting acoustic properties.
to appreciate them, it helps to understand that conventional sound systems reproduce audio signals by moving a speaker cone with magnets [2]. they interperet the audio input signal as the target displacement of the speaker cone over time, and the motion of the cone creates similarly-shaped pressure waves that radiate through the air and into your ears.
as such, all the geometric waves above are technically impossible for speakers to reproduce faithfully. all require infinite acceleration of the speaker cone, which would require infinite force. sawtooth and square waves are also discontinuous and would require the cone to jump between positions instantaneously.
circular waves are impossible to reproduce in their own way: they ask your speaker cone to move infinitely fast over an infinitely short distance. your cone cannot literally move infinitely fast due to being limited by the speed of light and your amplifier's output capabilities. but it does the best it can and it gets close, resulting in sounds that are both audible at low frequencies and smooth without a low pass filter.
my tone generator lets you explore them by mixing circular, square, sawtooth, and circular sawtooth [3] waves together.
you can use it for anything:
  • - purr at your cat
  • - tune your flute
  • - give your tesla manly engine sounds
  • - drown out your coworkers voices in the office
  • - play some background noise while you sleep
  • - experiment with circular binaural beats
just be careful (!) as extremely high and low frequencies can harm your hearing and/or speakers at high volumes - even if you can't hear them well.
if you find it useful, hit me up (@masontraylor on bluesky)!
[0] do they already have a name? I haven't seen them defined before, but if you have let me know~
Are they sine waves? No. Sine waves describe simple harmonic motion and look like this:
sine wave
[1] sawtooth, square and triangle waves can all be generated with simple relaxation oscillators, but not circular waves. if you know how to make a circular wave with a relaxation oscillator - hit me up!
this site generates them with the Fourier series
f ( x ) = ∑ n=1 ∞ ( -1 ) ⌈ n 2 ⌉ J 1 ( π n 2 ) n sin ( n π x L )
where J1(z) is a Bessel function of the first kind.
[2] not all speakers work by moving cones with magnets. for example, electrostatic speakers move a sheet-like membrane with electrostatic forces. but the same principles apply.
[3] square and circular waves are comprised of only the odd elements of their Fourier series. if you instead sum all of their elements, square waves become sawtooth waves and circular waves become what I call circular sawtooth waves.
circular sawtooth