APU-like Triangle in WebAudio

PeriodicWave

We can define OscillatorNode for any periodic function f(t), defined by the domain [0, 2π), using PeriodicWave:

const ω = new OscillatorNode(
    audioContext,
    {
        type: "custom",
        frequency: frequency,
        periodicWave: new PeriodicWave(
            audioContext,
            {real: a, imag: b}
        ),
    }
);

where a and b are Float32Arrays.

APU-like Triangle

NES's pseudo-triangle wave repeats FEDCBA9876543210 and 0123456789ABCDEF:

begin	end	value
0	π/16	1
π/16	π/8	13/15
π/8	3/16 π	11/15
3/16 π	π/4	3/5
π/4	5/16 π	7/15
5/16 π	3/8 π	1/3
3/8 π	7/16 π	1/5
7/16 π	π/2	1/15
π/2	9/16 π	-1/15
9/16 π	5/8 π	-1/5
5/8 π	11/16 π	-1/3
11/16 π	3/4 π	-7/15
3/4 π	13/16 π	-3/5
13/16 π	7/8 π	-11/15
7/8 π	15/16 π	-13/15
15/16 π	π	-1

As a result, we obtain follows:

$$\begin{aligned} a_{0} &= 0 \\ a_{k} &= \frac{4}{15\pi{k}} \sum_{n=1}^{15} \sin\frac{\pi{kn}}{16} \\ b_{k} &= 0 \end{aligned}$$