Scientific pitch

Not to be confused with scientific pitch notation.
256 Hz
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Note Approximate
frequency
(Hz)		 Audible?
C−4 1
C−3 2
C−2 4
C−1 8 checkY
C0 16 checkY
C1 32 checkY
C2 64 checkY
C3 128 checkY
C4 256 checkY
C5 512 checkY
C6 1024 checkY
C7 2048 checkY
C8 4096 checkY
C9 8192 checkY
C10 16384 checkY
C11 32768
C12 65536

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,[1] 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 power of 2 when expressed in hertz (symbol Hz).[2][3] The octaves of C remain a whole number in Hz all the way down to 1 Hz in both binary and decimal counting systems.[4][5] 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.[6]

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.

  1. ^
  2. ^ Marshall Long, Architectural acoustics, p.81, Elsevier, 2006 ISBN 0-12-455551-9.
  3. ^ Clarence Grant Hamilton, Sound and Its Relation to Music, p.56, Read Books, 2009 ISBN 1-4446-7429-3.
  4. ^ Eli Maor, Trigonometric delights, p.210, Princeton University Press, 2002 ISBN 0-691-09541-8. "Scientific pitch...has the advantage that all octaves of C correspond to powers of two."
  5. ^ Herbert Stanley Allen, Harry Moore, A text-book of practical physics, p.202, Macmillan, 1916. "The reason for the choice of 256 as middle C in scientific work is in order that the number of vibrations corresponding with any C shall be a whole number."
  6. ^ Turtur, Claus Wilhelm (2011). Prüfungstrainer Physik: Klausur- und Übungsaufgaben mit vollständigen Musterlösungen (in German) (3 ed.). Springer. p. 151. ISBN 978-3834809407.