Partial Pitch Calculator

Pull out a brass instrument and blow a note. It sounds right. At least you think it does. You check your tuner: four cents sharp. So you tweak your embouchure to correct it, but now your tone has gone stuffy or went flat, in a whole other direction.

No, this isn’t just a matter of bad technique. It’s equal temperament versus physics. Run the calculator above and it’ll show you how frequency of a harmonic partial compares to the piano key that is supposed to match it. Turns out they hardly ever quite line up.

Why Brass Instruments Sound Out of Tune

Brass instruments are essentially tubular resonators that rely on the harmonic series for their sound. This means that when you blow into it, you don’t create just a single note, but also a whole series of overtones or partials. Each partial is based off an integer multiple of fundamental frequency. So if there’s a fundamental at 220Hz, there will be a partial at 440Hz (a perfect octave). There will also be another at 660Hz (a fifth above the octave). They are all pure intervals which neatly match the natural sound of instrument itself.

But whenever we try to fit these pure numbers into standard piano or synthesizer tuning, things start to become mucky. This is where the calculator does all the hard work. It then compares the nearest tempered note to the partial you have selected. The example above show the fifth partial. In the harmonic series, this major third is about fourteen cents flat compared to a piano.

The problem arise when you tune that D sharp to be perfect for a keyboard. What you’re really doing is going against grain of how your instrument naturaly sounds. You’ll sound like a hero to the piano player. However, you’ll be out of tune with everyone else in brass section and out of tune with yourself.

Many players miss this because we follow direction of the tuner’s needle. We don’t realize that they is measuring us according to a different set of rules. It’s fair to say that this has more to do with air temperature. When it is warm the air move faster and the pitch of every partial in tube rises uniformly. That means that if you are rehearsing outside on a cold day, you will need an entirely different embouchure approach than a hot stage bathed in bright light.

You can use tool to adjust for ambient temperature. However, unless you take this variable into account, you will still find your slots drifting even if you feel you’re playing in tune. Pulling your tuning slide out to compensate for cold room may result in you being flat again when instrument heats up to the warmth of your breath. Temperature changes fight against musical intent in a never-ending struggle.

Then there are the troublesome partials. One such color tone is the seventh harmonic, which occurs approximately thirty-one cents lower then the equal-tempered minor seventh. You can’t play it in tune with a piano without bending it significantly, and even then, it sounds unique. It also indicates that you need to be aware of these cent offsets when composing close harmony for brass instrument.

As you go higher up the register, trumpet players is aware that the upper partials cluster more closely together. This gives them fewer options for intonation. The bottom line with brass playing is that it’s all about breaking rules when needed. It’s tuned by ear not by machine.

The machine give you data on which notes do not work well together or why a note feels unstable. Use this to see if you have a tendency to slide too much into one particular slot. Then, put down the phone and listen. Your ear makes the decision of where to stay, but the numbers indicates where the pitch wants to go.