RHY.6:5 - Archetypal Grounding

RHY.6:5.1 - Positions survive while sound classes disappear

This constructed percussion exercise has two attacks in one beat. Let D and T denote two distinct sound classes under a supplied local convention. They are not a claim about a particular named iqa‘.

The target preserves the two attack positions but cannot distinguish A from B. It is sufficient for asking where the attacks fall. To reproduce the sound-class order, retain (D, T) or (T, D) associated with those occurrences.

Now shift A’s two attacks forward by one quarter of the beat, without changing their sound classes. Their new positions are 1/4 and 3/4, yielding the position reading ka–mi under the four-part convention. D remains with the first shifted event and T with the second. Repeating ta–di after the shift would preserve the old positions, not the requested edit.

The edit can also originate in the target. Suppose the user changes ta–di to ka–mi while keeping the two occurrences and their associated D/T order. Under the selected four-part convention, reconstruct D at 1/4 and T at 3/4. Translating that revised source yields ka–mi; leaving ta–di unchanged leaves D at 0 and T at 1/2 unchanged.

If the user instead inserts a third attack, the two-label companion supplies no sound class for it. Return that missing assignment when the receiving task needs the sound-class phrase; the three positions alone can still serve a positional question. If a companion also demands that the old positions remain fixed, it conflicts with the requested ka–mi edit: resolve which positional requirement changes instead of silently retaining incompatible instructions.

This is a bounded construction of positions and labels. Whether a changed phrase still belongs to a particular musical prototype needs that practice’s identity conditions.

RHY.6:5.2 - A phrase is not a string of independent stroke commands

Nelson describes learning spoken patterns and their instrumental realizations in parallel, without a universal one-to-one correspondence between syllables and strokes. Suppose the receiving task is to realize a supplied phrase on an instrument.

Retain the phrase’s cycle placement and obtain its applicable instrumental realization from the prepared performer or lesson. Align the phrase portions that matter to the receiving use. If two realizations preserve the phrase’s timing but differ in technique or sound, keep that choice with the performance decision instead of hiding it in a guessed dictionary.

The translation may support rhythmic analysis before every instrumental choice is settled. It cannot then be presented as complete instructions for an unprepared player.

RHY.6:5.3 - Rotating a cyclic picture changes a cue

A constructed eight-unit pattern has attacks at 0, 3 and 5. A comparison identifies all rotations as the same shape. A target result chooses a rotation by two units, giving positions 2, 5 and 7 under the original cycle reference.

Returning only “the same rhythm” loses the information needed by an entering performer. Return the displacement and origin when the use requires those positions. If the task compares shapes regardless of phase, keep the coarser answer.

If the target instead changes traversal direction, recover the new order separately. Rotation and reversal are different operations unless the declared comparison deliberately identifies both.

RHY.6:5.4 - Keep a sustained beat distinct from a silent beat

Reuse the two-beat instructions from RHY.5:5.4. The source supplies an onset at position 0 and either an endpoint at position 2 (A), or an endpoint at position 1 followed by a rest until position 2 (B). Units are beats; the interval ends at 2.

An onset-only target gives ta for both, losing the sustain/stop answer. Under Cha’s explicitly selected extension, translate A as ta–ah and B as ta (ta). Reading back through that convention recovers the required continuation or rest. A sustained syllable plus a beat gesture and an explicit endpoint can supply the same distinction without using this extension.

If the received source is only the untimed string ta, neither A nor B can be recovered uniquely. Keep the onset information and ask for duration only if the receiver must decide sustain versus silence. For an onset-count question, the available information already suffices.

The translation therefore ends in one of two useful results: a complete instruction for the supplied duration-sensitive source, or a qualified onset-only result for the underdetermined source. No experiment is needed to discover this information loss; the two constructed cases exhibit it.

RHY.6:5.5 - Reconstruct between samples only within the admitted family

Reuse trace A from RHY.5:5.5, now represented by samples (time, position): (0, 0), (1, 1), (2, 0). The receiving question asks for the position at time 1/2. Select, for this constructed source family, straight-line interpolation between successive samples. The first segment then gives position 1/2; the target answer returns to the source’s time unit and position axis.

The same samples also fit a different trace whose first segment is position = time squared. That trace gives position 1/4 at time 1/2, while keeping positions 0 and 1 at the sampled endpoints. If the source family admits both traces, the sampled target cannot determine the requested answer. Retain the actual segment description or obtain the needed intermediate observation; otherwise return the answer as unresolved.

This is a local reopening: the shared samples still answer their sampled-position questions, and the time-1 side distinction remains intact. Only the unsupported between-sample reconstruction loses its warrant. Actual movement requires a basis for the chosen reconstruction; the calculation alone does not establish its physical course.