More often than not you want to know the exact frequency of a certain pitch. That’s when a frequency chart is a big help. It is a table that contains the corresponding frequency for any pitch within the audible range (about 20 Hz to 20 kHz).
Let’s start with an example: You hit a Middle C on your keyboard and wonder what frequency that might be. Is there a correlation between a pitch and its frequency value? Yes, there is. To better understand this correlation, it’s important to have a look at some scientific terms first.
The science behind
What is sound? Well, sound is defined as a vibration which propagates through the air or any other medium. It propagates as an audible wave of pressure.
Frequency is a physical term that describes the number of vibrations per second. It is measured in hertz (Hz).
This leads us to the following phenomenon: A sound with fast vibrations is perceived as a sound with a high frequency. According to this, a bass sound has a low frequency.
OK. But how to find out the exact value? Lucky for us, in the 20th century some people decided to define a standard. The pitch of A above Middle C is tuned to 440 Hz. This pitch (which corresponds to A3 on your MIDI keyboard) is also called concert pitch.
Still, that leads to another question: What is the mathematical correlation between the different pitches on your keyboard? The answer to this question is pretty simple. If you jump up an octave, the frequency will be multiplied with the factor 2. So, the pitch of A4 on your MIDI keyboard is 880 Hz. With that being said, it’s pretty easy to calculate all the A’s on your keyboard. To calculate all the other pitches, we have to take a look at…
The chromatic scale
This is a scale which contains all available pitches (i.e. all the 12 white and black keys on your keyboard). What’s so special about this scale? It’s the distance between the pitches which is one semitone. This means: It takes 12 semitones to get up an octave. And, with that in mind, we can calculate the mathematical factor of a semitone. It’s the 12th root of 2 which is 1,059.
Cool! There we are! We have the magical number to calculate the frequency of any pitch. Have a look at the chart in the picture above. All the values are rounded. For example, Middle C has a pitch of 262 Hz.
Let’s check this with the help of our DAW and its tools.
A spectrum analyzer is a tool which shows you all the frequencies a sound contains. Now, let’s load a virtual piano into our DAW and let’s play a Middle C via the MIDI keyboard. And let’s analyze the sound which should be at 262 Hz…
Wait a minute?! Something must have gone wrong because there are many other frequencies within that sound, too…
Don’t worry! Any sound is the sum of several frequencies. The deepest component of a tone is called fundamental frequency, while the components above it are known as overtones. Both together, fundamental frequency and overtones, are called partials. If the frequencies of those partials are numerical integer multiples of the fundamental, they are called harmonics. A sound with harmonics appears clean and rich. On the other hand, inharmonic partials make up for a noisy sound. The noise generator in any synthesizer would be an appropriate example.
If you want to understand the advanced mathematics behind, I recommend the Wikipedia text about the Fourier transform (FT).
Let’s have a look at the spectrum analysis above. The fundamental frequency of the sound is at 262 Hz. Consequently, a frequency chart tells you only the fundamental frequency of a certain pitch.
What do we need such a chart for?
In the following section I want to show you three applications of a frequency chart:
Kick drum tuning
Mostly, I use the chart when I tune my electronic kick drums which must have a correct pitch. For example, a track in the scale of C major needs to have a kick with either the pitch C (tonic), G (dominant) or F (subdominant) to sound good. Honestly, any pitch within the scale is OK. But you should avoid non-diatonic pitches.
For EQing purposes it’s also nice to have a frequency chart at your fingertips. Say, you have recorded a piano, and the lowest pitch within that sequence is a Middle C. Hence, you could set your low cut filter to 262 Hz or even higher. There’s something really interesting about our brain. It can “calculate” the missing fundamental just by having the harmonics of a sound.
Emulating real sounds
Recently, I created the sound of a German emergency car using only virtual synthesizers. Therefore, I needed to know which notes to program into my MIDI editor.
A frequency chart is a handy tool that every sound engineer or sound designer needs to have in his or her studio. The usage is diverse and can range from drum tuning over EQing to sound emulation.