RHY.7:5 - Archetypal Grounding

RHY.7:5.1 - Equal interval entropy, different entrances

Take two constructed eight-unit cycles. A has onsets at 0, 1, 2 and 4; B at 0, 1, 3 and 4. Their cyclic successive gaps are respectively (1, 1, 2, 4) and (1, 2, 1, 4). Each histogram gives probability 1/2 to gap 1 and 1/4 each to gaps 2 and 4.

The Shannon entropy of either histogram is 1.5 bits. This equality concerns the two chosen distributions; it does not make the ordered patterns interchangeable.

The receiving task requires a third attack at position 2. Inspecting ordered positions gives A at 2 and B at 3. A meets that positional requirement; B does not. No more elaborate complexity measure or listening experiment is needed to answer it. For a later question about the experience of either pattern, retain that separate question.

RHY.7:5.2 - The same pattern under two allocations

A constructed controller must produce four attacks at positions 0, 2, 4 and 6 of an eight-unit cycle. Its supplied mechanism specification requires at least three units between attacks by the same actuator. Treat that limit as an input to this calculation, not as a general physiological fact.

One actuator receives a gap of two units between every pair, including the cycle boundary; the proposed allocation conflicts with the supplied limit. Alternating two actuators assigns 0 and 4 to one, 2 and 6 to the other. Each then has four units between its own attacks, satisfying that particular constraint.

The onset pattern is unchanged while the allocation comparison changes. The result is a compatible allocation under the stated limit, not a claim that an untested device or human performer has achieved the rhythm. RHY.9 arranges the remaining rhythmic actions and timing cues; use MDPE.3 if the wider performing configuration must change.

RHY.7:5.3 - A cue can help entry without supplying the wanted phrasing

In a constructed partnered exercise, variant A makes the recurring reference easy for the receiving partner to locate. Variant B preserves a desired continuous articulation but gives a less usable entry cue. Suppose those differences have already been established in the relevant practice; no numerical scores are supplied.

Neither observation cancels the other. For entry training, A supplies the needed advantage. For a performance that requires B’s articulation, investigate whether an independent cue can retain the reference without changing that articulation. RHY.3 and RHY.9 construct that combination.

The comparison returns a trade-off and a concrete design question. Adding imagined “clarity” and “artistry” numbers would not resolve it.

RHY.7:5.4 - Equal endpoints, different usable peaks

Two constructed four-second sound-control envelopes begin and end at level 0.2 and reach level 1.0. Each follows straight segments between its specified points. A reaches its peak at 1.5 seconds; B reaches it at 2.0 seconds.

The receiving construction requires the peak by 1.75 seconds. Comparing endpoint levels and peak level leaves a tie; comparing peak time selects A and rejects B for this condition. Retain the specified courses for any later question about their rates or intermediate values.

This settles a property of the proposed envelopes. Whether either realized sound provides a usable cue to the intended listener remains a different comparison.