The tuning
In tune
with what?
Most people think tuning is one setting. It’s two decisions: the reference pitch, and the tuning system. Most instruments take the default for both. I chose both on purpose, and everything I play is built on them.
Same chord, two tunings. Use headphones or decent speakers. Press a button to play, press it again to stop.
Decision 1 · Reference pitch
Where the
notes start.
The reference pitch fixes one note. Everything else is measured from it. The modern standard puts A at 440 Hz.
I use scientific pitch, which puts C at 256 Hz. Every C is then a power of two: 32, 64, 128, 256. Tuned in just intonation from that C, A comes out at 432 Hz.
Decision 2 · Tuning system
How the other
notes relate.
Equal temperament makes every step the same size. It was built so a piano could play in every key and sound acceptable in all of them. It’s a compromise. It’s useful for an orchestra and unnecessary for a drone in a quiet room.
Just intonation sets each note by a whole-number ratio to the root, the way the harmonic series does.
The harmonic series
One note
is many.
Play one note and you are hearing a stack: the fundamental, plus overtones at 2×, 3×, 4× and 5× its frequency. Every acoustic sound does this. A flute, a bowl, your voice. It’s physics.
The gaps between those overtones are the intervals. Tune a scale to those exact ratios and you have just intonation. The intervals lock, because their overtones line up.
One string, four ways it vibrates at once: whole, in halves, in thirds, in quarters. 1× is the note you name. 2×, 3× and 4× are its first overtones.
- Octave2 : 1
- Fifth3 : 2
- Fourth4 : 3
- Major third5 : 4
- Equal-tempered fifth2.996 : 2. Close, but the overtones now rub against each other. That rub is the shimmer, or beating, you hear in a chord. In just intonation it stops.
In a session
What it changes.
Sustain
Notes ring longer.
When intervals are whole-number ratios, the overtones reinforce each other. I play less and the room does more.
Blend
A chord becomes one sound.
Just-tuned notes merge into each other instead of sitting side by side.
Stillness
Nothing wobbles.
With no beating between overtones, there is nothing in the chord pulling at your attention. That is the space in “sound creates space.”
What I use
The numbers.
- ReferenceC = 256 Hz, scientific pitch.
- SystemJust intonation, on the harmonic series.
- A432 Hz, just intonation: 256 × 27/16.
- DroneOne low root note for the whole session, set to the room.
- Acoustic instrumentsTuned by hand and measured. They sit a few cents either side of the target, and I leave that in.