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Zipf's law can be visuallized by plotting the item frequency data on a log-log graph, with the axes being the logarithm of rank order, and logarithm of frequency. The data conform to Zipf's law with exponent s to the extent that the plot approximates a linear (more precisely, affine) function with slope − s.
Lowers the pitch of a note to a pitch matching the indicated number in the harmonic series of the root (bottom) of the chord. The diagram shows a specific example, the septimal flat, in the context of a septimal minor third, in which the E ♭ is tuned exactly to a 7:6 frequency ratio with the root (C).
The Railsback curve contrasts a theoretically correct equal-tempered piano tuning against one that compensates for a piano's inharmonicity. The Railsback curve, first measured by O.L. Railsback, expresses the difference between inharmonicity-aware stretched piano tuning, and theoretically correct equal-tempered tuning in which the frequencies of successive notes are related by a constant ratio ...
This is an accepted version of this page This is the latest accepted revision, reviewed on 27 September 2024. Observation that in many real-life datasets, the leading digit is likely to be small Not to be confused with the unrelated adage Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the ...
Harmonics of a string showing the periods of the pure-tone harmonics (period = 1/frequency) The harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency. Pitched musical instruments are often based on an acoustic resonator such as a string ...
Letter frequency is the number of times letters of the alphabet appear on average in written language. Letter frequency analysis dates back to the Arab mathematician Al-Kindi (c.801 –873 AD), who formally developed the method to break ciphers. Letter frequency analysis gained importance in Europe with the development of movable type in 1450 ...
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency.The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals.
The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...