Acoustics & Music Theory
why it sounds like that
Generator

How far a wall moves the mean, in spreads

The bias a floor puts into an observed mean, in units of the parent's own spread, against how far the parent sits above the floor. With the mean exactly on the wall the truncated bias is 0.797 spreads and the censored bias is 0.399 — half of it, exactly, because half the mass sits at one point and the other half is an upper half-normal. The earlier essay used the upper figure for a process that produces the lower one, so every bias it quoted is twice what a floor on execution actually causes.
How far a wall moves the mean, in spreads. The bias a floor puts into an observed mean, in units of the parent's own spread, against how far the parent sits above the floor. With the mean exactly on the wall the truncated bias is 0.797 spreads and the censored bias is 0.399 — half of it, exactly, because half the mass sits at one point and the other half is an upper half-normal. The earlier essay used the upper figure for a process that produces the lower one, so every bias it quoted is twice what a floor on execution actually causes.

Drawn above with its standard settings, which is almost never how an essay draws it: an essay states the numbers it is arguing about, so the figure a reader meets there is about that argument rather than about the drawing in general. Every option a placement passes is checked against the ones this function actually reads, because an option it does not read is silently ignored and the figure quietly draws what is above instead.

It makes a noise. 11 of its 11 placements carry sound, built from the same numbers as the drawing, offering these buttons: Sixteen beats exactly on the grid, The same sixteen with 15 milliseconds of scatter, The same sixteen with 15 milliseconds of scatter, and none of it inside 1 of them.

Called by 2 essays

the blast radius of changing it

How far a wall moves the mean, in spreads. The bias a floor puts into an observed mean, in units of the parent's own spread, against how far the parent sits above the floor. With the mean exactly on the wall the truncated bias is 0.797 spreads and the censored bias is 0.399 — half of it, exactly, because half the mass sits at one point and the other half is an upper half-normal. The earlier essay used the upper figure for a process that produces the lower one, so every bias it quoted is twice what a floor on execution actually causes.

The shape a wall leaves behind

A floor on execution biases every statistic computed on swing timing, and the bias was priced with Pearson's truncated-normal formulas. Those are the formulas for a sample with everything below the wall thrown away. A player who cannot execute a short gap does not throw the attempt away — it comes out at the floor. That is a censored sample, its bias is exactly half, and its skew is two thirds larger.

rhythm · Microtiming The bias a wall puts in a mean, against the parent it came from. The bias a wall puts into an observed mean, in spreads, for each of eight standardised parents, with the wall exactly on the parent's mean. The censored values run from 0.354 to 0.433, a range of 0.079; the truncated from 0.582 to 1.000, a range of 0.418. The formula now used is the one that hardly depends on a distribution nobody has measured, and the formula it replaced is the one that depends on it a great deal.

The parent nobody measured

Every figure drawn behind a wall so far assumed a normal parent, and the assumption turns out to matter in exactly the wrong place. The censored bias is half the parent's mean absolute deviation — a theorem, not a coincidence — so it lands between 0.35 and 0.43 spreads for every distribution tried, and the truncated one runs from 0.58 to 1.00. But the third moment proposed as the test moves 2.9 across parents against 0.65 between the two rules, and a censored sample from a slightly left-skewed parent has a skew of 1.007 where a truncated normal has 0.995. The statistic that does work is a count of ties.

rhythm · Microtiming

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