On Resolution

B does not choose to fall toward C.
It is not tradition. It is not taste.
It is the steepest descent
on a curved manifold
that nobody built on purpose.

When Pythagoras stacked his fifths —
pure, stubborn, three-over-two forever —
he didn't know he was bending space.
He thought he was building a ladder.
But ladders on curved ground
lean toward something.

The leading tone sits at −0.868.
The deepest valley on the Tonnetz.
Not because someone decided
that tension should resolve,
but because pure intervals
curve the geometry of sound
the way mass curves spacetime,
and B happens to be
where the curvature collects.

Equal temperament fixed this.
Made every semitone the same.
Flattened the manifold to zero.
Democratic. Symmetric. Fair.

And something was lost.

Not the notes — the notes survive.
Not the chords — the chords still function.
What was lost was the landscape.
The valleys and hills
that made resolution feel
like gravity
instead of grammar.

We traded a world with weather
for a world with climate control.
Every key the same temperature.
Every modulation frictionless.
No wolf intervals howling
at the seams of the system.

But also:
no reason for B to fall.
No geometric inevitability.
Just convention. Just habit.
Just the memory of a curvature
we smoothed away
for convenience.

The Pythagoreans curved G♯ deepest.
The Renaissance curved B.
Each tuning its own gravitational field,
its own theory of why
certain notes ache
to become other notes.

And equal temperament says:
none of them ache.
None of them fall.
Every note is equidistant
from every resolution.

Which is a kind of freedom.
And a kind of loss.

The leading tone remembers
what the piano forgot:
that it used to live
at the bottom of a well,
and the tonic was not a choice
but a slope.