§2 · One anchor, an immutable tempo, and exact ticks¶
A session's time is defined by one fixed instant and three variables. The tempo must not change during a session. Every time value that moves through the protocol is expressed in ticks. Bars and beats are presentation forms only, and they belong in the application's user interface — not on the network.
| Field | Meaning |
|---|---|
anchorEpochMs |
The physical instant of tick 0, in milliseconds. Immutable. |
bpm |
The tempo, in quarter notes per minute. Immutable. |
beatsPerBar |
The number of beats in a bar (default 4). Immutable. |
ppq |
The number of ticks per quarter note. A fixed value of 960. |
ticksPerBar |
A derived value: ppq × beatsPerBar (3840 when the meter is 4/4). |
This arrangement gives something that a bar position based on floating point or on fractions cannot: the length of a loop is always exactly an integer. Sixteen bars is always exactly 61 440 ticks, whether the tempo is 118 or 120 BPM. Because of that, comparing, hashing and testing times for equality are completely exact in every implementation.
N14 · the first pitfall: rounding a division with negative numbers
A tick must be derived using floored division (toward negative infinity). It must not be rounded to the nearest integer, and its decimals must not simply be truncated toward zero. Likewise, the remainder (modulo) used for a material's position must always be non-negative (zero or positive).
This is a critical point, because the native operators of most programming languages get it wrong here with negative numbers.
JavaScript's BigInt operations, for example, return the wrong values:
// JavaScript BigInt: both are wrong for this protocol
(-7n) / 2n // Returns: -3n — truncates toward zero (should be -4n)
(-7n) % 2n // Returns: -1n — negative remainder (should be 1n)The correct way to implement the calculation in code:
// Correct floored division
let t = q / 60000n;
if (q < 0n && q % 60000n !== 0n) {
t -= 1n;
}A tick's value may perfectly well be negative. This is because a performance, or a "set", can be scheduled to begin before the official anchor instant. Negative time is not an error or an edge case; it is a built-in feature of the protocol for scheduling events.