RHY.10:5 - Archetypal Grounding

RHY.10:5.1 - A placement difference and accumulating drift

A constructed reference has event times 0.00, 0.50, 1.00 and 1.50 seconds. One response gives 0.08, 0.58, 1.08 and 1.58: its intervals match, with a constant 0.08 displacement. Another gives 0.00, 0.52, 1.04 and 1.56: its intervals are 0.52 and its displacement grows.

Suppose a controller is intended to coincide with the reference, its event identification is sound, and its configuration permits re-entry at the future 2.00 landmark. For the first response, retain the 0.50 interval and correct the entry placement. For the second, change the interval to 0.50 and re-establish entry at that landmark. These are different repairs.

The series alone does not establish why a human performed either pattern. If the 0.08 displacement were intended phrasing, the first series would already meet that relation.

RHY.10:5.2 - Two complete corrections can undo each other

Consider a constructed pair of ideal controllers producing matched events with the same period. B is 0.10 seconds later than A. A delays its next event by a fraction a of the difference; B advances its next event by a fraction b. With no other disturbance, their next difference is (1 - a - b) × 0.10.

If both correct the whole difference, a = b = 1, the difference becomes −0.10: the order reverses, without reducing its magnitude. Under these stipulated conditions, choosing a = b = 0.5 removes the difference on the next event.

This is a calculation about the selected controller, not a universal optimum for people. Delivery delay, noise, preparation and intended expression can change a useful choice. The practical result is to inspect the combined correction instead of demanding a complete correction from every participant.

RHY.10:5.3 - Continue through a silent or sustained span

A constructed four-beat phrase has beats at 0.0, 0.5, 1.0 and 1.5 seconds and a new phrase at 2.0. Its first sound starts at 0.0. The supplied score says it continues for one second, followed by a one-second rest.

An onset-only recitation marks the first sound and the next phrase but leaves the intervening duration unspecified. A familiar four-beat gesture maintains beat and cycle position; the score or timed demonstration supplies the sustain and rest. Together they specify when to stop the sound and when to re-enter.

Suppose the learner, already able to sustain and release that sound, performs the stated durations and enters at the demonstrated next phrase while using the gesture. Retain this supported coordination. Whether the learner can continue after the gesture is withdrawn is a separate RHY.13 question.

RHY.10:5.4 - A changing delivery delay resembles a changed pace

In a constructed remote-cue case, the receiver obtains events at 0.10, 0.62, 1.14 and 1.66 seconds. Their 0.52-second intervals fit both a source whose period is 0.52 with constant delivery delay and a source whose period is 0.50 with growing delivery delay. The intended coordination is with the source performance.

An already available source-side record, aligned to the same time reference, gives 0.00, 0.50, 1.00 and 1.50. Subtracting these values from the received times gives delays of 0.10, 0.12, 0.14 and 0.16. Within the stipulated event matching and clock accuracy, the growing difference belongs to delivery; it does not justify changing the source’s continuing pace.

The selected move is to try an available cue channel with stable delay and establish the intended entry relation while retaining the 0.50 period. Its usability still needs a joint attempt. The calculation does not establish a human response or identify which component causes the delay.

Had the source-side times instead been 0.00, 0.52, 1.04 and 1.56, the same received series would have a constant 0.10 delay. The next question would concern the source pace and whether its change was intended. Without a usable second reference, keep both explanations open and choose a familiar cue contrast that could distinguish them.