Generator sequence: Difference between revisions
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Defining *uniform* refinements. |
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To exclude the case when the generator is a 1-step or a (len(scale) − 1)-step, the modifier ''non-step'' can be used. | To exclude the case when the generator is a 1-step or a (len(scale) − 1)-step, the modifier ''non-step'' can be used. | ||
Given a choice of equave ''E'' and a WFGS ''S'' = GS(''x''<sub>1</sub>, ..., ''x''<sub>r</sub>), a ''refinement'' of ''S'' is a WFGS GS(w<sub>1</sub>, ..., w<sub>r</sub>) where each w<sub>i</sub> is a sequence of ''k'' | Given a choice of equave ''E'' and a WFGS ''S'' = GS(''x''<sub>1</sub>, ..., ''x''<sub>r</sub>), a ''refinement'' of ''S'' is a WFGS GS(w<sub>1</sub>, ..., w<sub>r</sub>) where each w<sub>i</sub> is a sequence of ''k'' = ''k''(''i'') intervals, ''y''<sub>i1</sub>, ..., ''y''<sub>ik</sub>, where ''y''<sub>i1</sub> + ... + ''y''<sub>ik</sub> ≡ ''x''<sub>i</sub> modulo ''E''. If ''k'' does not depend on ''i'', call the refinement ''uniform''. For instance, the GS for Zil, GS(8/7, 7/6, 8/7, 7/6, 8/7, 7/6, 8/7, 189/160, 8/7, 7/6) is a uniform refinement of GS(4/3, 4/3, 4/3, 27/20, 4/3), which generates Zarlino. | ||
== Series arising from well-formed generator sequences == | == Series arising from well-formed generator sequences == | ||