Editing Parity (mathematics) (section)

==Additional applications==
In [[information theory]], a [[parity bit]] appended to a binary number provides the simplest form of [[error detecting code]]. If a single bit in the resulting value is changed, then it will no longer have the correct parity: changing a bit in the original number gives it a different parity than the recorded one, and changing the parity bit while not changing the number it was derived from again produces an incorrect result. In this way, all single-bit transmission errors may be reliably detected.<ref>{{citation|title=A Student's Guide to Coding and Information Theory|first1=Stefan M.|last1=Moser|first2=Po-Ning|last2=Chen|publisher=Cambridge University Press|year=2012|isbn=9781107015838|pages=19–20|url=https://books.google.com/books?id=gFhJXsGXNj8C&pg=PA19}}.</ref> Some more sophisticated error detecting codes are also based on the use of multiple parity bits for subsets of the bits of the original encoded value.<ref>{{citation|title=Codes and turbo codes|first=Claude|last=Berrou|publisher=Springer|year=2011|isbn=9782817800394|page=4|url=https://books.google.com/books?id=ZLPWNq8JN9QC&pg=PA4}}.</ref>

In [[wind instrument]]s with a cylindrical bore and in effect closed at one end, such as the [[clarinet]] at the mouthpiece, the [[harmonic]]s produced are odd multiples of the [[fundamental frequency]]. (With cylindrical pipes open at both ends, used for example in some [[organ stop]]s such as the [[Flue pipe#Diapasons|open diapason]], the harmonics are even multiples of the same frequency for the given bore length, but this has the effect of the fundamental frequency being doubled and all multiples of this fundamental frequency being produced.) See [[harmonic series (music)]].<ref>{{citation|title=An Introduction to Acoustics|first=Robert H.|last=Randall|publisher=Dover|year=2005|isbn=9780486442518|page=181|url=https://books.google.com/books?id=l9pO7vAvLpUC&pg=PA181}}.</ref>

In some countries, [[house numbering]]s are chosen so that the houses on one side of a street have even numbers and the houses on the other side have odd numbers.<ref>{{citation|title=GIS and Public Health|edition=2nd|first1=Ellen K.|last1=Cromley|first2=Sara L.|last2=McLafferty|publisher=Guilford Press|year=2011|isbn=9781462500628|page=100|url=https://books.google.com/books?id=LeaEPg9vCrsC&pg=PA100}}.</ref> Similarly, among [[United States numbered highways]], even numbers primarily indicate east–west highways while odd numbers primarily indicate north–south highways.<ref>{{citation|title=The Big Roads: The Untold Story of the Engineers, Visionaries, and Trailblazers Who Created the American Superhighways|first=Earl|last=Swift|publisher=Houghton Mifflin Harcourt|year=2011|isbn=9780547549132|page=95|url=https://books.google.com/books?id=59dQ_rwoh3UC&pg=PA95}}.</ref> Among airline [[flight number]]s, even numbers typically identify eastbound or northbound flights, and odd numbers typically identify westbound or southbound flights.<ref>{{citation|title=Southwest Airlines|series=Corporations that changed the world|first=Chris|last=Lauer|publisher=ABC-CLIO|year=2010|isbn=9780313378638|page=90|url=https://books.google.com/books?id=NpZbEihL0ZgC&pg=PA90}}.</ref>