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euler

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Journal Article
Journal of Music Theory (1 October 2013) 57 (2): 245–286.
Published: 01 October 2013
...Roger Mathew Grant The music-theoretical formulations of the early modern mathematician Leonhard Euler (1707-83) are customarily remembered—and often dismissed—for their unconventional rankings of the consonances. A closer examination of Euler’s writings, however, reveals that he intended his...
Journal Article
Journal of Music Theory (1 October 2009) 53 (2): 163–190.
Published: 01 October 2009
... he described in patents of 1829 and 1844. Like the later tonal spaces of the German dualist theorists, the concertina's button layouts were inspired by the work of eighteenth-century mathematician Leonhard Euler, who used a lattice to show relationships among pitches in just intonation. Wheatstone...
Journal Article
Journal of Music Theory (1 October 2002) 46 (1-2): 127–151.
Published: 01 October 2002
... acoustically pure intervals (as in Euler, etc or to intervals in pitch-space, then the struc- ture implicitly projects into an infinite plane. The realizations [of the ton- netz] that will hold our focus are generated by equally tempered intervals in some modular system, where the modular congruence...
Journal Article
Journal of Music Theory (1 October 2014) 58 (2): 179–233.
Published: 01 October 2014
... . 1891 . Das mathematisch reine Tonsystem . Leipzig : Breitkopf und Härtel . Euler Leonhard . 1774 . “ De harmoniae veris principiis per speculum musicum repraesentatis .” In Novi Commentarii academiae scientiarum Petropolitanae , vol. 18 , 330 – 53 . St. Petersburg : Teubner...
Journal Article
Journal of Music Theory (1 April 2012) 56 (1): 1–52.
Published: 01 April 2012
... is primary: Leonhard Euler originally designed the structure so that maxi- mally consonant intervals—the perfect fifth and major third—corresponded to the graph’s edges. The Tonnetz’s second role, as a representation of single- step voice-leading relationships...
Journal Article
Journal of Music Theory (1 October 2007) 51 (2): 277–332.
Published: 01 October 2007
Journal Article
Journal of Music Theory (1 October 2002) 46 (1-2): 57–126.
Published: 01 October 2002