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...out of use in modern pure mathematics, but continues to be used in [[music theory]] and in the [[history of mathematics|historical study of mathematics]]. *Partch, Harry (1979). ''[[Genesis of a Music]]'', p.68. {{ISBN|978-0-306-80106-8}}. ...

...were emphasised,<ref>Kubovy, Michael: Concurrent-Pitch Segregation and the Theory of Indispensable Attributes. In: Kubovy, Michael/Pomeranz, James R. (Eds.): ...d is stressed.<ref>Kubovy, Michael/Valkenburg, D. Van: ''In defense of the theory of indispensable attributes.'' Cognition 87, 2003, pp. 225–233, here: p. 22 ...

...and there are 34.1895 per octave.<ref name="Benson">Benson, Dave (2006). ''Music: A Mathematical Offering'', p.232-233. {{ISBN|0-521-85387-7}}. "Carlos has {{Microtonal music}} ...

...val {{Frac|3:2|[[major third|5:4]]}}, which equals [[minor third|6:5]] (E{{music|b}}, 315.64 cents, {{audio|Just minor third on C.mid|Play}}). Thus the step ...ce]] delta scale is based on the [[tritave]] and the 7:5:3 "wide" [[triad (music)|triad]] ({{audio|BP chord 357 just.mid|Play}}) and the 9:7:5 "narrow" tria ...

...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== ...

...appeared in the ''Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science'', Banff, Alberta, Canada, July 31–August 3, 2005, pp. 47–56.</ == Other uses of Euclid's algorithm in music == ...

{{Short description|Concept in musical set theory}} In [[Set theory (music)|musical set theory]], there are four kinds of interval:<ref name="VivaIntervalNotation">{{cite ...

...their vibrating length. This has the net effect of increasing the [[pitch (music)|pitch]] of a note (or notes as the case may be). String-bending allows exp ...c where it was most notably popularized by [[B.B. King]], and later [[rock music]]ians adopted the string-bending technique in the 1960s.<ref name=campbell2 ...

...oston]], Massachusetts. He is known for his seminal role in developing the theory of [[regular temperament]]s, including being the first to define '''pajara ...ath>{105:120:140:168}</math>. Components of dissonance not modeled by this theory include [[critical band]] roughness as well as tonal context (e.g. an [[aug ...

==Music== * ∪, a symbol used to represent [[Union (set theory)|union in set theory]] ...

...g multiples of a single interval, but without requiring (as [[temperament (music)|temperament]]s normally do) an [[octave]] (2:1). It may be approximated by ...[[perfect fifth|3:2]] | [[major third|5:4]] }} {{=}} 6:5 }} }} {{big|(}}E{{music|b}}, 315.64&nbsp;cents, {{audio|Just minor third on C.mid|Play}} {{big|)}}. ...

In music, '''96 equal temperament''', called 96-TET, 96-EDO ("Equal Division of the ...erament.aspx#edo-table |website=Tonalsoft Encyclopedia of Microtonal Music Theory |publisher=Joe Monzo |access-date=26 February 2019 |date=2005}}</ref> ...

* [[Divisor function]] in number theory σ * [[Sigma-algebra]] (σ-algebra, σ-field) in set theory ...

{{short description|Mathematical model used in music theory}} .../9781461494744 |title=Mathematical and Computational Modeling of Tonality: Theory and Applications |publisher = Springer |isbn=978-1-4614-9474-4 |series=Inte ...

...f>Halter-Koch, Franz and Tichy, Robert F.; eds. (2000). ''Algebraic Number Theory and Diophantine Analysis'', p.478. W. de Gruyter. {{ISBN|9783110163049}}.</ ...uration <math>1/8</math> the length of a single measure in [[common time|{{music|time|4|4}}]] (eighth-notes) is, [[divisive rhythm|divisively]] (<math>2/2^1 ...

The development and practical realization of digital antenna arrays theory started in 1962 under the guidance of [[Vladimir Varyukhin]] ([[USSR]]). ...ua/Slyusar_ICATT_2017_m.pdf]</ref> In the 1940s this theory evolved to the theory of three-channel antenna analyzers.<ref name=slyusardaa/> ...

...nsion between diverse musical influences and styles. Between [[Renaissance music]] and jazz; between [[musique concrète]] and post-[[Anton Webern|Webernian] ...or New Music at the [[Hochschule für Musik Freiburg|Freiburg University of Music]]. Since 1996, he is a member of the [[Academy of Arts, Berlin]]. In 2012 h ...

book-title=Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture| [[Category:Homotopy theory]] ...

...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 ...rvals can be imagined to extend indefinitely in a 3-dimensional [[Lattice (music)|lattice]] (one dimension, or one direction, for each prime). If octaves ar ...

...alker's early mathematical research, in the 1960s and 1970s, concerned the theory of [[abelian group]]s. In the 1990s, her interests shifted to [[fuzzy logic ...versity of Colorado Boulder]], with a year off to work as a primary-school music teacher in Colorado, and graduated in 1957. Next, she went to the [[Univers ...