RHY.2:5 - Archetypal Grounding

RHY.2:5.1 - Equal interval counts, different entrances

Consider a constructed repeated cycle of eight equal time units with identical short sounds. Version A has attacks at 0, 1, 2 and 4; version B at 0, 1, 3 and 4. The next cycle starts at 8.

The cyclic intervals are respectively (1, 1, 2, 4) and (1, 2, 1, 4). Both have two intervals of length 1, one of length 2 and one of length 4. A histogram therefore cannot distinguish them. Yet an instruction to enter with the third attack places the entrance at 2 in A and 3 in B.

The needed account preserves ordered attacks relative to the cycle start. The histogram remains usable for questions about interval frequencies. No listener preference or perceived meter follows from this arithmetic alone.

RHY.2:5.2 - A contact trace leaves out the load change

A constructed dance recording shows a foot contacting the floor before a transfer becomes usable by the partner. For a question about foot placement, contact timing may be enough. For a question about responding to the transfer, the account also needs the load change and the partner’s response.

Select those relations from an appropriate observation or bounded trial. If the video cannot show them, return the unresolved relation rather than labeling the contact “weight arrival.” RHY.4 develops the timing comparison.

RHY.2:5.3 - A smooth sound has a rhythmic shape

A continuously sounding tone has a changing amplitude envelope. Consider two constructed envelopes over two seconds. A completes one smooth rise-and-fall cycle; B completes two. Both remain audible throughout, with the same beginning and end of the tone.

The receiving question is which modulation repeats once per second. A list containing only the tone’s start and stop gives the same answer for both and cannot resolve the question. Retain the course of amplitude change, or its modulation period when that summary suffices: two seconds for A and one second for B. B has the required repetition period. The tone’s attack list remains useful for onset questions.

This construction establishes the stated envelope difference, not what a listener feels as a beat. For a question about that response, retain the listening conditions and obtain the response relation; the envelope period alone does not supply it.