Definition
Pitch is the perception of how high or low a sound is. It corresponds, to a good approximation, to the fundamental frequency of a periodic vibration, measured in hertz (Hz) = cycles per second. The human ear covers about 20 Hz – 20 kHz (the upper limit drops with age); the sense of musical pitch is sharp roughly between 30 Hz and 4–5 kHz.
Octaves and ratios
- Doubling the frequency = going up one octave (2:1 ratio). A2 = 110 Hz, A3 = 220, A4 = 440, A5 = 880.
- Perception is logarithmic: from 100 to 200 Hz is an octave, from 1000 to 1100 Hz is less than two semitones.
- In equal temperament a semitone is the ratio 2^(1/12) ≈ 1.05946.
Frequency of a MIDI note n: f = 440 · 2^((n − 69)/12). Inverse: n = 69 + 12 · log2(f / 440).
The tuning pitch
A4 at 440 Hz is the international standard (London conference of 1939, then ISO 16 in 1975). Many European orchestras tune to 442–443 Hz for a brighter sound; Baroque music on original instruments often uses 415 Hz (about a semitone lower) and part of the Classical repertoire 430 Hz. The French “diapason normal” of 1859 set 435 Hz. Claims about the supposed benefits of 432 Hz have no scientific basis.
Reference table (12-TET, A4 = 440 Hz)
| Note | Hz | Note | Hz |
|---|---|---|---|
| E1 (low string of the bass) | 41.20 | C4 (middle C) | 261.63 |
| A1 | 55.00 | E4 | 329.63 |
| C2 | 65.41 | A4 | 440.00 |
| E2 (low string of the guitar) | 82.41 | C5 | 523.25 |
| A2 | 110.00 | A5 | 880.00 |
| C3 | 130.81 | C6 | 1046.50 |
| G3 | 196.00 | C8 (last piano key) | 4186.01 |
Pitch, timbre, and harmonics
A real musical sound contains the fundamental and many harmonics (integer multiples: 2f, 3f, 4f…) that determine the timbre. The brain reconstructs the pitch even if the fundamental is missing (missing fundamental): this is why an 808 at 45 Hz can be “heard” even on a smartphone if it is saturated and has harmonics at 90, 135, 180 Hz. See “The Harmonic Series and Timbre”.
The other properties of sound
- Amplitude → perceived intensity (dB SPL in air, dBFS in digital).
- Envelope (attack, decay, sustain, release) → character of the articulation.
- Spectrum → timbre.
- Duration → rhythm.
The wavelength in air is λ = 343 / f meters: 50 Hz ≈ 6.9 m, 1 kHz ≈ 34 cm. It explains why low frequencies are hard to control in a small room (room modes).
Practical use for the producer
- Tuning kick and 808: find the fundamental with an analyzer (Fruity Parametric EQ 2, Voxengo SPAN) and transpose it to the tonic or the fifth of the track. A kick tuned to F at 43.65 Hz is ideal for a track in F minor.
- Musical EQ: a bass in A has fundamentals at 55 or 110 Hz: a high-pass at 100 Hz on that track removes half of the line.
- Pitch and speed: slowing a sample by 50% lowers it by an octave; transposing by +1 semitone means multiplying the speed by 1.0595.
Example in a song
In dubstep drops and in many Hans Zimmer soundtracks the bass goes below 40 Hz: the perception depends largely on the harmonics generated by distortion. In “Bad Guy” (Billie Eilish) the synth bass line lives mostly below 100 Hz and remains audible on small speakers thanks to saturation.
Exercise
- In FL Studio load a sine wave (3x Osc) and play scientific A3, A4, A5 (A4, A5, A6 in FL's Piano roll): verify 220, 440, 880 Hz with Wave Candy.
- Calculate the frequency of the tonic of your latest track in octaves 1, 2, and 3 and note where it falls relative to the high-pass on your pads.
- Lower a drum loop by 12 semitones without time-stretch and verify that it lasts twice as long.
Links
Note Names and Octaves; Equal Temperament and Cents; The Harmonic Series and Timbre; EQ by Frequency Zone.