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[[Image:Triadic harmonic entropy.png|thumb|Harmonic entropy for triads with lower interval and upper interval each ranging from [[File:Harmonic entropy Farey sequence.png|300px|thumb|The space around intervals is shown ...

...n function]] (WDF) are famous time–frequency methods, useful for analyzing music signals such as notes played on a piano, a flute or a guitar. ==Knowledge about music signal== ...

...:First members of harmonic sequence.svg|thumb|The first ten members of the harmonic sequence <math>a_n = \tfrac{1}{n}</math>.]] In [[mathematics]], a '''harmonic progression''' (or '''harmonic sequence''') is a [[sequence|progression]] formed by taking the [[multiplic ...

...uction |page={{mvar|xviii}} |title="Maximum Clarity" and Other Writings on Music |editor-first=Bob |editor-last=Gilmore |place=Urbana, IL |publisher=Univers ...onal higher-limit tunings have been mapped by [[Erv Wilson]]. The [[limit (music)|limit]] is the highest prime number used in the ratios that define the int ...

...tuning''', or '''5-prime-limit tuning''' (not to be confused with [[limit (music)#Odd-limit and prime-limit|5-odd-limit tuning]]), is any system for [[music ...the perception of consonance seems related to low numbers in the harmonic series, and 5-limit tuning relies on the three lowest primes, 5-limit tuning shoul ...

...r=[[American Mathematical Society]], The [[London Mathematical Society]] | series=History of Mathematics | volume=34 | year = 2009 }} Biography on p.128-130 ...nvergence and divergence of the [[Harmonic series (mathematics)#P-series|p-series]] ...

...ads to a new and broad theoretical framework that will be essential to his music thereafter. ...same moment, the twelve-tone compositional technique of the [[Avant-garde music|avant-garde]] in the [[interwar period]] defended by Schoenberg was replace ...

...peed of rotation. It is hard to excite the fundamental and even the second harmonic, but the higher harmonics are easily excited." {{ISBN|9780299215804}}.</ref ...of suitable length and diameters, the range extends well up the [harmonic] series, where the available tones are close together and you can, with practice, p ...

===Music theory=== In [[music theory]], a [[musical interval]] describes the ratio in [[frequency]] betwe ...

The '''''Studies for Player Piano''''' is a series of 49 [[étude]]s for [[player piano]] by American composer [[Conlon Nancarr ...e=Dated and annotated list of the works, premieres and arrangements of the music of Conlon Nancarrow|url=http://fuerst-heidtmann.de/html/nancarrow_works.htm ...

...p. 79-88">Matthews, M. (1999). Introduction to timbre. In P.R. Cook (Ed.), Music, cognition, and computerized sound: An introduction to psychoacoustic (pp. ...chive.org/details/musicphysicsengi0000olso |url-access=registration |title=Music, Physics and Engineering |publisher=Dover Publications |isbn=9780486217697 ...

{{short description|Collection of keyboard music by J.S. Bach}} .... |title=J. S. Bach, The Well-Tempered Clavier, Volume I |publisher=Alfred Music publishing |isbn=}}</ref> ...

...- Springer Verlag 2006 - {{ISBN|3-540-34027-0}}</ref><ref>[http://www.crm-music.it/ CRM - Centro Ricerche Musicali]</ref> and at the Istituto Gramma in L'A ...ptive Instrument Feed-Drum | title=Computer Music Modeling and Retrieval | series=Lecture Notes in Computer Science | date=2006 | last1=Lupone | first1=Miche ...

...d by this scheme are similar, but are the [[dual impedance]] forms whereby series elements become parallel, capacitors become inductors, and so on.<ref>{{har ===Harmonic telegraph=== ...

...le:Completeness in Hilbert space.png|thumb|right|Completeness means that a series of vectors (in blue) results in a [[Well defined|well-defined]] net displac ...ia for concluding that limits exist. A [[Series (mathematics)|mathematical series]] ...

...network]], [[maximum likelihood]] and [[Multiple signal classification]] (MUSIC). ...2015|url=https://www.microflown.com/resources/scientific-papers/real-life-harmonic-source-localization-using-a-network-of-acoustic-vector-sensors}}</ref> and ...

...ations are the separation of an audio signal before application to [[bass (music)|bass]], [[mid-range speaker|mid-range]], and [[tweeter]] [[loudspeaker]]s; ..., as well as filters to separate out the signals at the receiving end. The harmonic telegraph achieved this with electromagnetically driven tuned reeds at the ...

...ation|first=Thomas|last=Christensen|title=The Cambridge History of Western Music Theory|year=2002|page=[https://archive.org/details/cambridgehistory0000unse ...Limiting]] difference between the [[Harmonic series (mathematics)|harmonic series]] and the [[natural logarithm]]. ...

{{defn|A signal represented as a time series of samples taken at regular intervals.}} {{defn|A digital algorithm to analyze a time series of sampled data into a set of sine and cosine frequency components.}} ...

...er than 1 by the [[Absolute convergence|absolutely convergent]] [[infinite series]] [[Leonhard Euler]] considered this series in the 1730s for real values of s, in conjunction with his solution to the ...