The Supersaw

What it is

A stack of the saws from part one, spread a few cents either side of the note, from one voice up to twelve. Seven of them over thirty cents is the supersaw, the sound of every trance lead and a good share of bassline, and the thing producers argue about is how many voices it takes.

Part four was two saws, one pair, one clean beat. Add a third and there are three pairs beating at three rates. By seven there are twenty one and the swell has become a shimmer. This page measures three things about that shimmer as voices are added: how much the level moves, how long before the whole shape comes back, and how tall the peaks stand over the average.

The answer to how many voices turns out to be the wrong question. The right one is how they are spaced.

How it works

Each voice is a saw of twelve harmonics, and the voices sit across plus and minus fifteen cents of the note. Evenly spaced puts them at equal steps. Unevenly spaced nudges each one off its step by a different amount from a seeded generator, so no two spacings share a ratio. The stack is divided by the voice count, so the average level doesn’t change as voices are added and only the movement around it does.

The movement is measured off the level, the RMS in a fifty millisecond window, hopping every ten. Its flutter is the standard deviation of that level in dB. Its repeat time is the first lag at which the whole envelope matches itself point for point to within a quarter of its spread, or never if it doesn’t within the record. The crest is the tallest peak over the average, and the page reports it against a single saw’s.

The real stack of Web Audio oscillators, each started a fraction of its period early to land on the phase the maths gives it, was rendered offline and measured the same way. Flutter 1.99, 1.52, 2.54 and 2.60 dB against the maths’ 2.00, 1.52, 2.52 and 2.57. Repeat 0.5 s, 3.1 s, never and never against 0.5, 3.1, never and never. Crest 8.9, 9.9, 10.5 and 11.8 dB against 8.8, 9.9, 10.6 and 11.8.

What surprised me

The movement doesn’t shrink. I expected more voices to steady the level the way more coins steady an average, and they do not. Two voices flutter by 1.97 dB, five by 2.37, seven by 1.56, twelve by 2.38, and the starting phases move those numbers about as much as the voice count does. The sum of many sines at random phases has an envelope with a fixed shape, and that shape doesn’t tighten with more of them. Seven voices move exactly as much as two.

What changes is whether it comes back. Two voices repeat every half second, which you hear as a beat. Evenly spaced, every count repeats exactly, on a period of one over the smallest pairwise beat: 1.0 s for three voices, 2.1 for five, 3.1 for seven, 4.2 for nine, 5.8 for twelve, each measured to the decimal against that prediction. Seven evenly spaced voices are a 3.1 second loop, and once you know that you can hear it. Spaced unevenly, three voices stretch the repeat to 6.3 s and five or more never come back within 24 seconds, on every seed I tried. That’s the fatness, and it’s a property of the spacing rather than the count. The JP-8000, which is where the sound comes from, spaces its seven voices unevenly, and this is why.

I got uneven wrong first. My nudges came from the golden ratio, which is the usual way to get something irrational, and consecutive golden fractions differ by only two values, so seven voices got exactly two spacings, 3.7 and 7.1 cents, one almost double the other. It repeated nearly as well as even did. The nudges come from the seeded generator now and all six spacings are different.

I also measured the wrong thing first. The obvious test for repeating is the autocorrelation of the envelope, and its tallest peak read 0.99 to 1.00 for everything, even and uneven alike, because a peak there only says there is a slow component in the movement, and every supersaw has one. It doesn’t say the shape comes back. Asking whether the envelope matches itself point for point at some lag is the honest question, and it’s what separates 3.1 seconds from never.

The cost is real and it’s the other number. A single saw peaks 6.0 dB above its average. Two voices peak 8.9, seven around 10, twelve around 11.5. Now and then every voice lines up and the peak is the sum while the average hasn’t moved, so a supersaw at the same loudness as a saw is four to six dB closer to the limiter, which anyone who has mixed one already knows in their hands.

What I would do next

Part eight is the wobble, an LFO on the filter from part two, and the measurement is what tempo sync actually does to it.

The spread here is fixed at fifteen cents and the voices all at one level. Real supersaws taper the outer voices down, and the JP-8000’s curve is asymmetric as well as uneven. Measuring the repeat time and the flutter for that exact curve against a plain uneven spread would say how much of the original’s character was in the shape of the curve and how much is just in the spacing not being even.

The other thing to measure is the click from part three. Twelve voices started at twelve phases means twelve different clicks at once, and a supersaw’s attack is famously soft. Whether that’s the envelope or the phases averaging out is a question this page can already ask.