Scientific pitch

Scientific pitch, also known as philosophical pitch, Sauveur pitch or Verdi tuning, is an absolute concert pitch standard which is based on middle C (C₄) being set to 256 Hz rather than approximately 261.63 Hz, making it approximately 31.77 cents lower than the common A440 pitch standard. It was first proposed in 1713 by French physicist Joseph Sauveur, promoted briefly by Italian composer Giuseppe Verdi in the 19th century, then advocated by the Schiller Institute beginning in the 1980s with reference to the composer, but naming a pitch slightly lower than Verdi's preferred 432 Hz for A, and making controversial claims regarding the effects of this pitch.

Scientific pitch is not used by concert orchestras but is still sometimes favored in scientific writings for the convenience of all the octaves of C being an exact round number in the binary system when expressed in hertz (symbol Hz). The octaves of C remain a whole number in Hz all the way down to 1 Hz in both binary and decimal counting systems. Instead of A above middle C (A₄) being set to the widely used standard of 440 Hz, scientific pitch assigns it a frequency of 430.54 Hz.

Since 256 is a power of 2, only octaves (factor 2:1) and, in just tuning, higher-pitched perfect fifths (factor 3:2) of the scientific pitch standard will have a frequency of a convenient integer value. With a Verdi pitch standard of A₄ = 432 Hz = 2⁴ × 3³, in just tuning all octaves (factor 2), perfect fourths (factor 4:3) and fifths (factor 3:2) will have pitch frequencies of integer numbers, but not the major thirds (factor 5:4) nor major sixths (factor 5:3) which have a prime factor 5 in their ratios. However scientific tuning implies an equal temperament tuning where the frequency ratio between each half tone in the scale is the same, being the 12th root of 2 (a factor of approximately 1.059463), which is not a rational number: therefore in scientific pitch only the octaves of C have a frequency of a whole number in hertz.