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...essbooks.pub/openmusictheory/chapter/intervals-in-integer-notation/ |title=Intervals in Integer Notation |website=viva.pressbooks.pub |access-date=2024-02-08}}< == Pitch Intervals == ...

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

|examples = C-F{{music|#}}-c-f{{music|#}}-c'-f&nbsp;'{{music|#}}<br>B-F-b-f-b'-f' ...r-tuning, one major-third interval is interjected amid four perfect-fourth intervals.]] ...

...uction |page={{mvar|xviii}} |title="Maximum Clarity" and Other Writings on Music |editor-first=Bob |editor-last=Gilmore |place=Urbana, IL |publisher=Univers ...you further in the same direction. Lattices in just intonation (limited to intervals comprising primes, their powers, and their products) are theoretically infi ...

...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}} ...

...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 == ...

[[File:Harmonic entropy Farey sequence.png|300px|thumb|The space around intervals is shown above for the Farey sequence, order 50.]] '''Paul Erlich''' (born 1972) is a [[guitarist]] and [[music theorist]] living near [[Boston]], Massachusetts. He is known for his semin ...

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

...be derived from using [[neutral seventh|11:6]] (B{{music|11}}{{music|b}}{{music|minus}}, 1049.36 cents, {{audio|Neutral seventh on C.mid|Play}}) to approxi ...f> {{audio|Harmonic seventh on C.mid|Play}} though both have nice [[triad (music)|triads]]<ref name="Milano"/> ({{audio|Beta scale major triad on C.mid|Play ...

...y ratio]] equal to either one third of an [[octave]] (1200/3 = 400 [[Cent (music)|cent]]s: [[major third]]) or one tenth of a [[Decade (log scale)|decade]] [[Category:Intervals (music)]] ...

...of golden ratio intervals in Hz.png|thumb|400px|Stack of golden ratio (φ) intervals, measured in Hz ((11.09 + 6.854) ÷ 11.09 = 11.09 ÷ 6.854 = 1.618).]] ...ts scale the way notes 1200 cents apart are in traditional tunings). Other music theorists such as [[Walter O'Connell]], in his 1993 "The Tonality of the Go ...

...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|)}}. ...

...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 ...tunings are constructed entirely from stacking of three basic purely-tuned intervals (octaves, thirds and fifths). Since the perception of consonance seems rela ...

|other_names = Uniform tunings<br />All-[[interval (music)|interval]] tunings |disadvantages = Makes it difficult to play music written for standard tuning. ...

{{short description|Mathematical model used in music theory}} ...2007 | publisher = Springer | book-title = Mathematics and Computation in Music, First International Conference, MCM 2007 Berlin, Germany, May 18–20, 2007 ...

...sion''' is an audio processing technique used to effectively encode silent intervals, reducing the amount of storage or bandwidth needed to transmit audio recor ...detection of the silent intervals and the subsequent compression of those intervals. Applications of silence compression include [[telecommunications]], audio ...

===Music theory=== ...rational multiple of <math>2\pi</math>, and similarly other common musical intervals other than the octave do not correspond to rational angles.{{r|barcal}} ...

...ee review by [[Cyril Domb]]<ref>[[Cyril Domb]] (1989) ''Covering by random intervals and one-dimensional continuum percolation'', J. Stat. Phys. 55, 441-460.</r ...ian Empire]] and is a historian of [[Alpine folk music|Danube-Swabian folk music]].<ref>{{cite book|last=Rohr|first=Robert|date=1994|title=Unser Klingendes ...

...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 ...r Piano''''' and finished between 1949 and 1950. It was published in ''New Music Edition'', a quarterly of modern composition, in Los Angeles in October 195 ...

{{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> ...