Pitch: what a note is
Every key on your keyboard starts a vibration, and how fast it vibrates is the pitch you hear. Learn to read a note as a number, and the whole keyboard becomes a map you can calculate with.
- Explain a note as a vibration with a frequency in hertz
- Find any key’s frequency from octaves and semitones
- Hear two notes slightly out of tune as beating
01A note is a vibration
Press a key and something starts to shake: a string, a reed, a column of air, or, in a synthesizer, a loudspeaker cone. The shaking pushes the air back and forth, and those tiny pressure waves reach your ear.
What makes it a note, rather than a noise, is that the vibration repeats. The same shape comes back again and again, many times a second. Each repetition is one cycle, and the number of cycles in a second is the frequency, measured in hertz (Hz). A4, the A above middle C, vibrates 440 times a second: 440 Hz.
A sine wave at A4: 440 vibrations every second
The simplest vibration is the sine wave: a smooth swing back and forth, like a pendulum or a tuning fork. It is the only sound made of exactly one frequency, which is why the spectrum on the right shows a single line. Every other sound you will meet in this course is built from sine waves added together. That is the subject of the next lesson.
The faster the vibration, the higher the pitch. The lowest A on a piano vibrates 27.5 times a second, slowly enough that you can almost feel the separate pulses. The top C vibrates over four thousand times a second.
02Octaves double the frequency
Play A3, A4 and A5. Your ear says “the same note, three heights”. Their frequencies say why:
Three A’s, the same 10 milliseconds
An octave is a doubling of the frequency: A3 is 220 Hz, A4 440 Hz, A5 880 Hz. Doubling sounds the same to the ear wherever it happens, whether 55 to 110 Hz in the bass or 1760 to 3520 Hz at the top. That is why the keyboard repeats the same pattern of twelve keys over and over.
03The keyboard in hertz
Between one A and the next there are twelve keys, and Western tuning spaces them evenly: each key is the same ratio above the one below. Twelve equal steps must make a doubling, so each step multiplies the frequency by the twelfth root of 2, about 1.0595. One such step is a semitone.
The piano’s 88 keys in hertz
Here is one octave from middle C, with the MIDI numbers your keyboard actually sends:
| Key | MIDI | Frequency |
|---|---|---|
| C4 | 60 | 261.6 Hz |
| C♯4 | 61 | 277.2 Hz |
| D4 | 62 | 293.7 Hz |
| D♯4 | 63 | 311.1 Hz |
| E4 | 64 | 329.6 Hz |
| F4 | 65 | 349.2 Hz |
| F♯4 | 66 | 370 Hz |
| G4 | 67 | 392 Hz |
| G♯4 | 68 | 415.3 Hz |
| A4 | 69 | 440 Hz |
| A♯4 | 70 | 466.2 Hz |
| B4 | 71 | 493.9 Hz |
| C5 | 72 | 523.3 Hz |
Every key also has a MIDI note number: 60 for middle C, 69 for A4, one more for every semitone up. Your keyboard sends these numbers, and KiMiA turns each one into a frequency with exactly this rule: 440 Hz times 2 to the power of (note − 69) / 12.
This course uses the international naming: middle C is C4 (MIDI note 60), and the octave number goes up at every C. KiMiA’s own displays use it too (“A4 · 440 Hz”). Yamaha instruments, including the CK and MODX series, call middle C C3, so a note shows one octave number lower there. The key is the same; only the name differs.
04In tune and out of tune: cents and beating
A semitone is a big step. For tuning, musicians split it into 100 cents, so an octave is 1200 cents. Most listeners notice a difference of about 5 to 10 cents between two notes played one after the other. Played together, though, the ear is far more sensitive, because two close frequencies produce beating:
Two sine waves 4 Hz apart beat 4 times a second
The beat rate is simply the difference between the two frequencies: 444 − 440 = 4 beats a second. As two notes get closer to each other the beating slows, and when it stops they are in tune. Piano tuners, guitarists and string players all tune by listening for it.
KiMiA tunes to A = 440 Hz unless you change it, with Master tune in Routing›Stage Settings: from 415 to 466 Hz in half-hertz steps, with a 440 Hz button to come back. Use it to match an acoustic piano that sits a little sharp or flat, or a band tuned to 442. Tuning belongs to your setup, not to a sound: switching sounds never changes it.
05The range of hearing
Young ears hear from about 20 Hz to about 20,000 Hz (20 kHz). The top of that range drops with age: many adults hear little above 14 to 16 kHz. At the bottom, very low frequencies are felt as much as heard, and small speakers can’t reproduce them at all. Listen to these sine waves, starting with your volume low:
The piano’s keys stop at about 4.2 kHz, yet the sound of a piano reaches far higher, through the harmonics you will meet in the next lesson. Which of these tones you hear clearly depends on your ears, your speakers and your headphones. On laptop speakers the 30 and 60 Hz tones may disappear completely.
High sine tones are uncomfortable and tiring. Keep the volume moderate whenever you test sounds, and give your ears a break after loud sessions: your hearing is your most important tool.
06A habit to start now
Whenever a sound catches your ear from now on, ask three things: how high, how loud, and what color? Those three questions run through the whole course.
07Try it
- Load the sine. Import this module’s course patches (see the module page) and choose 01 · Pure Sine. Play A3, A4 and A5, then C4. Notice how plain a pure sine sounds: one frequency, nothing else.
- Find the frequencies. Using the rule (each octave doubles, each semitone ×1.0595), work out the frequency of E4 and of A2. Check them with the table above.
- Hear beating. Load 01 · Tuning Beats and hold A4: it beats four times a second. Now play A3 and A5 and count the beats. Do they change?
- Test your speakers. Play the lowest and highest keys on the sine patch on your speakers, then on headphones. Note where each one seems to fade.