id: 05829733
dt: a
an: 05829733
au: Carey, Norman
ti: A diatonic chord with unusual voice-leading capabilities.
so: Klouche, Timour (ed.) et al., Mathematics and computation in music. First
    international conference, MCM 2007, Berlin, Germany, May 18‒20, 2007.
    Revised Selected Papers. Berlin: Springer (ISBN 978-3-642-04578-3/pbk).
    Communications in Computer and Information Science 37, 449-463 (2009).
py: 2009
pu: Berlin: Springer
la: EN
cc: 
ut: 
ci: 
li: doi:10.1007/978-3-642-04579-0_45
ab: Summary: Diatonic set theory, as established by John Clough and others,
    applies the tools of standard set theory of 12-tone ET to the
    heptatonic set of seven tones of the diatonic scale. The two universes
    differ from each other in a number of ways other than simple
    cardinality. Although 12 is nearly twice as big as 7, the fact that 7
    is prime and 12 composite contributes to a number of subtle differences
    between them. Every positive integer less than 7 is a unit mod 7, thus
    every diatonic interval generates the entire set. In the set of 12
    tones, there are only four units, 1, 5, 7, and 11. Further, because of
    tuning, the geographies, if you will, of the sets also differ. In the
    equal-tempered 12-tone landscape, every place looks like everyplace
    else. In the diatonic scale, each generic span is inhabited by several
    different specific intervals. Because of this, the terrain is
    everywhere distinct, contributing to the phenomenon of gravitational
    asymmetry and of tonality.
rv: