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A log-log plot of word frequency in Wikipedia (November 27, 2006). 'Most popular words are "the", "of" and "and", as expected. Zipf's law corresponds to the middle linear portion of the curve, roughly following the green (1/ x ) line, while the early part is closer to the magenta (1/ x 0.5 ) line while the later part is closer to the cyan (1 ...
Various scales: lin–lin, lin–log, log–lin, and log–log. Plotted graphs are: y = 10 x (red), y = x (green), y = log e (x) (blue). The top left graph is linear in the X and Y axes, and the Y-axis ranges from 0 to 10. A base-10 log scale is used for the Y axis of the bottom left graph, and the Y axis ranges from 0.1 to 1,000.
For example, an audio amplifier will usually have a frequency band ranging from 20 Hz to 20 kHz and representing the entire band using a decade log scale is very convenient. Typically the graph for such a representation would begin at 1 Hz (10 0 ) and go up to perhaps 100 kHz (10 5 ), to comfortably include the full audio band in a standard ...
Because log(x) is the sum of the terms of the form log(1 + 2 −k) corresponding to those k for which the factor 1 + 2 −k was included in the product P, log(x) may be computed by simple addition, using a table of log(1 + 2 −k) for all k. Any base may be used for the logarithm table.
The California Job Case was a compartmentalized box for printing in the 19th century, sizes corresponding to the commonality of letters. The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Arab mathematician al-Kindi (c. 801–873 AD), who formally developed the method (the ciphers breakable by this technique go ...
Logarithmic plot of frequency in hertz versus pitch of a chromatic scale starting on middle C. Each subsequent note has a pitch equal to the frequency of the prior note's pitch multiplied by 12 √ 2. The base-2 logarithm of the above frequency–pitch relation conveniently results in a linear relationship with or :
Acoustic – G 10, the highest pitch sung by Georgia Brown, who has a vocal range of 8 octaves. 44.1 kHz: Common audio sampling frequency: 10 5: 100 kHz: 740 kHz: The clock speed of the world's first commercial microprocessor, the Intel 4004 (1971) 10 6: 1 megahertz (MHz) 530 kHz to 1.710 MHz: Electromagnetic – AM radio broadcasts 1 MHz to 8 MHz
Frequency analysis, the study of the frequency of letters or groups of letters; Letter frequencies; Oxford English Corpus; Swadesh list, a compilation of basic concepts for the purpose of historical-comparative linguistics; Zipf's law, a theory stating that the frequency of any word is inversely proportional to its rank in a frequency table