Scientific pitch
| Note | Frequency (Hz) | Audible |
|---|---|---|
| C−4 | 1 | |
| C−3 | 2 | |
| C−2 | 4 | |
| C−1 | 8 | |
| C0 | 16 | ✓ |
| C1 | 32 | ✓ |
| C2 | 64 | ✓ |
| C3 | 128 | ✓ |
| C4 | 256 | ✓ |
| C5 | 512 | ✓ |
| C6 | 1,024 | ✓ |
| C7 | 2,048 | ✓ |
| C8 | 4,096 | ✓ |
| C9 | 8,192 | ✓ |
| C10 | 16,384 | ✓ |
| C11 | 32,768 | |
| C12 | 65,536 |
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 261.62 Hz, making it approximately 37.594 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.
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. Even though Verdi tuning uses 432 Hz for A4 and not 430.54, it is said by the Schiller Institute to be derived from the same mathematical basis: 256 Hz for middle C..
Note that 256 being a power of 2, only octaves (factor 2) 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 432 = 2*2*2*2*3*3*3, 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 ca. 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.
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