Generator

Frere Jacques, and how much of it is one chord

Frere Jacques at quaver resolution — 64 slots, 8 bars — with every slot whose pitch belongs to I marked. 81.3 per cent of the tune lies inside that one triad. eight bars of four-four, sung as a four-part round with entries two bars apart.

Drawn above with its standard settings, which is almost never how an essay draws it: an essay states the numbers it is arguing about, so the figure a reader meets there is about that argument rather than about the drawing in general. Every option a placement passes is checked against the ones this function actually reads, because an option it does not read is silently ignored and the figure quietly draws what is above instead.

It makes a noise. 5 of its 5 placements carry sound, built from the same numbers as the drawing, offering these buttons: Frere Jacques, against itself two bars later, Frere Jacques, alone, Twinkle, twinkle, against itself two bars later, Twinkle, twinkle, alone.

Called by 1 essay

the blast radius of changing it

Every delay, scored — a round and a tune that is not one. Mean Plomp-Levelt roughness of the simultaneities a tune makes against a copy of itself entering a whole number of bars later, for Frere Jacques and Twinkle, twinkle. The two do not overlap: the worst delay of the first is smoother than the best delay of the second. The model sees roughness and nothing else — no voice leading, no parallels, no distinction between a passing dissonance and a structural one.

A melody that can accompany itself

Whether a tune works as a round is decidable before anyone sings it. Score every simultaneity it makes against a delayed copy of itself, at every delay, with the roughness model already in use, and two nursery tunes separate completely — every delay of one is smoother than every delay of the other. What the scan does not do is pick out the entry the tradition uses, and that refusal is the most informative thing in it.

harmony · Voice-leading

All figures · What can be heard