| Note | Approximate 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 | 1024 | ||
| C7 | 2048 | ||
| C8 | 4096 | ||
| C9 | 8192 | ||
| C10 | 16384 | ||
| C11 | 32768 | ||
| C12 | 65536 |
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.
See main article: Concert pitch. Concert tuning pitches tended to vary from group to group, and by the 17th century the pitches had been generally creeping upward (i.e., becoming "sharper"). The French acoustic physicist Joseph Sauveur, a non-musician, researched musical pitches and determined their frequencies. He found several frequency values for A4 as presented to him by musicians and their instruments, with A4 ranging from 405 to 421 Hz. (Other contemporary researchers such as Christiaan Huygens, Vittorio Francesco Stancari and Brook Taylor were finding similar and lower values for A4, as low as 383 Hz.) In 1701, Sauveur proposed that all musical pitches should be based on a son fixe (fixed sound), that is, one unspecified note set to 100 Hz, from which all others would be derived. In 1713, Sauveur changed his proposal to one based on C4 set to 256 Hz; this was later called "philosophical pitch" or "Sauveur pitch". Sauveur's push to standardize a concert pitch was strongly resisted by the musicians with whom he was working, and the proposed standard was not adopted.[7] The notion was revived periodically, including by mathematician Sir John Herschel and composer John Pyke Hullah in the mid-19th century, but never established as a standard.[8]
In the 19th century, Italian composer Giuseppe Verdi tried to stop the increase in the pitch to which orchestras were tuned. In 1874 he wrote his Requiem using the official French standard diapason normal pitch of A4 tuned to 435 Hz. Later, he indicated that 432 Hz would be slightly better for orchestras.[9] One solution he proposed was scientific pitch, but he had little success.[9] [10]
In 1988, Lyndon LaRouche's Schiller Institute initiated a campaign to establish scientific pitch as the classical music concert pitch standard. The Institute called this pitch "Verdi tuning" because of the connection to the famous composer.[11] 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.[12] The Institute's arguments for the notation included points about historical accuracy and references to Johannes Kepler's treatise on the movement of planetary masses.[13] The Schiller Institute initiative was opposed by opera singer Stefan Zucker. According to Zucker, the Institute offered a bill in Italy to impose scientific notation on state-sponsored musicians that included provisions for fines and confiscation of all other tuning forks. Zucker has written that he believes the Schiller Institute claims about Verdi tuning are historically inaccurate. Institute followers are reported by Tim Page of Newsday to have stood outside concert halls with petitions to ban the music of Antonio Vivaldi and even to have disrupted a concert conducted by Leonard Slatkin in order to pass out pamphlets titled "Leonard Slatkin Serves Satan".[14]
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