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• W57600658 abstract "Many properties of the mechanical word s = (b(n+1)gcb ngc)n=0,1,2,... play a strikingly illuminating role in music theory when g = log2(3/2). This number represents the pitch height ratio between the musical intervals fifth and octave. The word s exemplifies the discrete rendering of the kernel of the linear pitch height form p : Z 2 ! R with p(m,n) = gm + n on the Pythagorean tone lattice, which is the free Z-module of all linear combinations of these two intervals. Although this kernel as such should be musically it turns out that the Christoel-prefix es of its discrete rendering correspond to prominent musical tone systems ? as a side eect of the discretisation of a single pitch height level. More than that: Christoel-dualit y and its extension to conjugates of Christoel words provides deep insights into the constitution of musical modes. Sturmian morphisms provide a transformational meta- language to this study. It is particularly challenging to music-theoretically interpret the role of special standard morphisms within the monoid St0 of all special Sturmian morphisms. For example, the authentically divided Ionian mode (aaba,aab) is the image of the pair (a,b) under the special standard morphism GGD, sending a to aaba and b to aab. The associated fifth up / fourth down - folding (yx,yxyxy) from Fa to Fa) is the image of the reversed special standard morphism DGG, sending x to yx and y to yxyxy. The theory of Sturmian sequences and morphisms is a rich treasure of mathematical facts of ideas with cross-connections to combinatorics, number theory, braid groups, symbolic dynamics and other domains, and all of which may potentially constribute to the music-theoretical interpretation of the apparently redundant pitch height kernel and its translates." @default.
• W57600658 created "2016-06-24" @default.
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• W57600658 date "2008-01-01" @default.
• W57600658 modified "2023-09-27" @default.
• W57600658 title "STURMIAN SEQUENCES AND MORPHISMS A MUSIC-THEORETICAL APPLICATION" @default.
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