Triangle Wave Explorer

a JavaScript music demo

Downward Bias		Upward Bias
Negative Bias		Positive Bias
Deämping Bias		Amping Bias
Low Pitch		High Pitch
Low Amplitude		High Amplitude

What is this?

This is an audio generator tool to explore the timbral quality of the triangle wave family of waveforms, including both symmetric and asymmetric variants. The top box is an oscilloscope view which visualizes the waveform, and the bottom box is a harmonic spectrum view.

Three different symmetries of the wave are parameterized and can be controlled to "bias" the wave away from symmetrical. These symmetries / biases are:

downward–upward bias — In a symmetric triangle wave, there is equal representation in the portions of the waveform which have an upward (positive) slope and those which have a downward (negative) slope. A negative bias skews representation towards the downward-sloping portion. A positive bias on this control skews representation towards the upward-sloping portion of the waveform. At the extremes of this bias, the waveform becomes a sawtooth wave.
negative–positive bias — In a symmetric triangle wave, there is equal representation of positive and negative values. A negative bias on this control skews representation towards negative values. A positive bias on this control skews representation towards positive values.
deämping–amping bias — In a symmetric triangle wave, there is equal representation of value movement away from zero (amping up) and value movement towards zero (deämping or amping down). A negative bias on this control skews representation towards deämping. A positive bias on this control skews representation towards amping up.

In addition, you can change the pitch (frequency) and total amplitude of the note being played. Adjusting these can help discern the various patterns of the displays.

See the source.

Items of note

At many frequencies, you can observe harmonics that are not even multiples of the fundamental frequency. For example, if you ramp up the pitch slowly, you can see these harmonics "bounce off the wall." These are aliasing artifacts which are produced because the period (single cycle) of the waveform isn't a whole number of samples. The demo code reduces — but does not eliminate — this effect by oversampling, that is, by producing samples at a higher rate than the output sample rate. In this case, those samples are simply averaged together, a tactic which serious audio engineers would probably scoff at but which is both effective and efficient for the current use case.