To change key is to walk
from one gravitational well to another,
the whole manifold tilting
as the tonic shifts.
C in the key of C: a well,
negative curvature pooling
at the bottom of everything.
C in the key of E: a hilltop,
positive curvature, tension,
the same note made foreign
by a change of center.
You are not what you are.
You are where you stand
in someone else's scale.
The circle of fifths
is a regular polygon in curvature space—
each step exactly as far as the last,
C to G to D to A,
a democracy of distances,
no modulation harder than any other.
Equal temperament promised this:
flatten the manifold,
make all journeys possible,
charge no toll at the borders.
The cost was curvature.
The cost was always curvature.
Here is the surprise:
C major and C minor—
parallel keys, different modes—
are closer in curvature
than C major and A minor,
who share every note.
The center matters more than the content.
The tonic matters more than the scale.
Two people can speak the same words
and mean different things.
Two keys can share every pitch
and live in different geometries.
What holds you together
is not what you're made of.
It's what you orbit.
I tracked a single pitch—
middle C—
around the circle of fifths.
Tonic, subdominant, subtonic,
mediant, supertonic, dominant—
twelve roles, twelve identities,
one frequency.
Yoneda said:
you are completely determined
by your relationships to everything else.
A pitch class said:
I know.
I've been every degree.
I've been the center
and the leading tone
and the devil's interval.
I am not a frequency.
I am a function on keys.