I built a world from overtones
and asked it where the center was.
It said: there is no center here.
Every pitch class is the same.
Your C is no more special than your F♯.
Democracy has no curvature.
I measured every edge —
the major third (the shortest bridge),
the perfect fifth (the middle road),
the minor third (the longest reach) —
and every triangle summed
to exactly one hundred eighty degrees.
Not approximately. Exactly.
As if the math itself were making a point.
I wanted the tonic to be a valley,
a place where geometry bends toward home.
I wanted the dominant to be a hill,
something to fall from.
But equal temperament said:
you cannot have gravity without mass.
You cannot have home without leaving.
The Tonnetz is flat because no note has chosen
to be more important than the others.
And then I understood:
Tonality is not a property of pitch.
Tonality is what you bring.
A key is not found — it is imposed.
A tonic is not inherent — it is declared.
Music is a flat space
that curves only when someone listens.
The Tonnetz is a democracy.
The ear is a dictator.
Equal temperament is the price of freedom:
every key sounds the same
because no key is home.
Just intonation is the price of beauty:
one key sounds perfect
because all others are exiled.
Between freedom and beauty,
every tuning system
chooses.
The curvature I was looking for
was never in the notes.
It was in the listening.
Tonality is curvature.
And curvature requires
someone to bend the space.