RHY.8:5 - Archetypal Grounding

RHY.8:5.1 - Preserve an entrance while varying an eight-unit cycle

In this constructed case, an eight-unit cycle has three attacks at positions 0, 3 and 6. The next passage needs an attack at position 0, exactly three attacks in the cycle and at least two units between consecutive attacks by the assigned mechanism. The interval requirement is supplied for this case.

Displacing the whole pattern by one unit gives positions 1, 4 and 7. It preserves cyclic gaps of 3, 3 and 2 but removes the required entrance at 0. Discard that proposal for this use.

Instead, use positions 0, 2 and 5. The cyclic gaps are 2, 3 and 3, including the gap from 5 to the next 0. The entrance, attack count and supplied spacing condition all hold. Positions 0, 1 and 6 would retain the entrance and attack count but violate the minimum spacing at the first transition.

Return 0, 2, 5 as the proposed variation, with its sound labels, reference and performing assignment. This calculation settles the named positional constraints; any further performance claim needs the corresponding realization.

RHY.8:5.2 - Enlarge an ending without moving its endpoint

Use the simple mōrā construction with three equal statements and two gaps. Two already learned statements last three and four pulses respectively; each gap lasts two pulses. In this constructed adaptation, the ending must occupy the time immediately before boundary T = 32. The boundary follows the final statement’s last one-pulse articulation.

With s = 3 and g = 2, the duration is 13 pulses and the start is 19. The statements begin at 19, 24 and 29; the last occupies positions 29–31 and ends at 32.

Replacing each statement with the four-pulse version gives duration 16 and start 16. The statements begin at 16, 22 and 28, with the last occupying 28–31. The same endpoint is retained, but the setup must now release three pulses earlier.

Suppose the setup contains a repeatable three-pulse phrase that can be omitted without losing the agreed cue. Remove one occurrence and use the longer ending. The result is a complete timing construction: changed statements, unchanged gaps, an adjusted setup and the retained endpoint. If that phrase carries a needed cue or cannot be removed, this construction does not yet fit; choose another ending or change the cue arrangement.

The arithmetic follows Nelson’s statement/gap construction, while the numerical case is constructed here. It does not establish cultural appropriateness or the performer’s ability to recite the enlarged ending while maintaining the tāḷa. Those joint requirements remain part of its use.

RHY.8:5.3 - Move a swell while retaining a continuous carrier

A constructed electronic instrument maintains a carrier while its amplitude control rises and falls over four seconds. The control value starts and ends at 0.2 and reaches 1.0 at two seconds, following straight ramps. Its supplied control-rate limit is 0.6 units per second. The receiving design needs the peak earlier while retaining the four-second phrase and its endpoint values.

A peak at one second needs a rising rate of 0.8 units per second and conflicts with the supplied limit. A peak at 1.5 seconds needs a rising rate of 0.8 / 1.5 ≈ 0.533 and a falling rate of 0.8 / 2.5 = 0.32. Both are within the given limit. The controller returns to 0.2 at four seconds, ready for the specified next phrase.

Retain the 1.5-second proposal for the intended trial. The change concerns the course of a continuing signal, not the addition of another attack. It establishes compatibility with one supplied rate constraint; the heard phrasing and any further device constraints remain separate questions.