Music Frequency to Note Converter

Pitch perception is logarithmic, so naming a frequency requires a logarithmic map rather than a linear one. Twelve-tone equal temperament divides the octave (a 2:1 frequency ratio) into twelve identical steps, each a ratio of the twelfth root of 2, about 1.059463. Inverting that relationship gives the converter its core expression: the number of semitones above or below the reference A4 equals 12 times the base-2 logarithm of the measured frequency divided by the reference. Adding 69 to that value yields the MIDI note number, because the MIDI specification fixes A4 at note 69 and middle C at note 60. The fractional remainder, multiplied by 100, is the deviation in cents, since one semitone is defined as exactly 100 cents and one octave as 1200 cents. Practical ranges matter when reading the output. Concert A commonly sits at 440 Hz under ISO 16, but many European orchestras tune to 442 or 443 Hz, and historically informed ensembles use 415 Hz for Baroque repertoire and sometimes 392 Hz for French Baroque. Trained listeners detect roughly 5 to 10 cents of error on sustained tones, so deviations under about 2 cents are effectively inaudible while anything past 25 cents is a quarter-tone away from the target. Two caveats limit the result. Real instruments produce inharmonic partials, so a frequency analyzer may lock onto an overtone rather than the fundamental, and piano tuning deliberately stretches octaves by 20 to 30 cents at the extremes, meaning a correctly tuned piano will not read as zero cents everywhere.

Standard pitch is a much younger idea than notated music. Through the 17th and 18th centuries, A varied by more than a whole tone between cities and even between the organ and the orchestra in the same town, roughly 392 to 465 Hz depending on place and instrument. The physics needed to fix a number came from Marin Mersenne, whose Harmonie universelle of 1636 laid out the laws relating string length, tension and frequency, and from Joseph Sauveur, who around 1700 measured absolute frequencies by counting acoustic beats and coined the term acoustics. Equal temperament as a tuning scheme was described mathematically in the late 16th century by Zhu Zaiyu in China and Simon Stevin in the Netherlands, though keyboards in Europe only migrated to it widely during the 19th century. Standardization arrived in stages. An 1859 French commission legislated a diapason normal of A at 435 Hz; the 1885 Vienna conference endorsed it, but pitch inflation continued. The American Standards Association adopted A equals 440 Hz in 1936, a 1939 international conference in London recommended the same figure, and the International Organization for Standardization published it as ISO 16, with the current edition dated 1975. The digital layer came later: the MIDI 1.0 specification, agreed between Dave Smith of Sequential Circuits, Roland and other manufacturers in 1983, assigned integer note numbers to semitones and made the exponential frequency formula used here a routine calculation in synthesizers, tuners and audio software.