How pitch, wavelength, temperature, and tempo fit together
Sound Lab combines musical tuning with physical acoustics and studio timing. Frequency describes how many pressure oscillations occur each second, but the musical note we perceive also depends on tuning convention, harmonic content, duration, and listening context. The calculators expose the numerical relationships without treating pitch and frequency as interchangeable in every situation.
From piano key to frequency
The note catalog uses twelve-tone equal temperament, in which every octave doubles frequency and is divided into twelve equal logarithmic steps. With A4 assigned to 440 Hz, adjacent semitones differ by the constant ratio 2^(1/12). This produces A5 at 880 Hz and A3 at 220 Hz, while every other piano note follows the same exponential relationship.
A4 = 440 Hz is the reference specified by ISO 16, not a claim that all music must use it. Historical performance, orchestras, period instruments, and some modern ensembles may adopt another reference pitch. The Web Audio tone is a clean synthesized reference; real instruments add overtones, attack, decay, and resonances that determine timbre.
Frequency is not acoustic wavelength
Acoustic wavelength is calculated from λ = v/f. Frequency is established by the source, while wavelength depends on the propagation speed of the medium. At approximately 20°C, sound travels through ordinary air near 343 m/s, giving A4 a wavelength of roughly 0.78 m. Lower notes have longer wavelengths, which is why bass control requires larger rooms and careful loudspeaker placement.
Air temperature changes molecular speed and therefore acoustic velocity. The temperature calculator uses an idealized dry-air relationship suitable for education and everyday estimates. Humidity, atmospheric composition, altitude, wind, and strong temperature gradients can shift real measurements, so precision field work should include local environmental data.
Converting tempo into milliseconds
Tempo and pitch use the same unit—cycles per second—but describe different structures. At a tempo of 120 BPM, one quarter-note beat lasts 60,000 / 120 = 500 ms. Subdivisions divide that duration; dotted values multiply it by 1.5, while triplets divide two ordinary note values into three equal parts. These timings are useful for delays, reverbs, gates, compressors, LFOs, and synchronized modulation.
Choosing the right tool
- Note to frequency: compare pitches, piano keys, MIDI values, and wavelengths.
- BPM to milliseconds: synchronize musical effects and modulation with tempo.
- Speed of sound: estimate acoustic velocity and wavelength as air temperature changes.