The F 11, 5, Construct #1, Lydian Mode - Scale. This one poses an interesting "enharmonic" spelling issue. The frequency ratio of 55/32 is an interval 937.63 cents wide. In theory one could choose to notate it as a major 6 +37.63 cents. Yet I choose to call it an augmented sixth -62.37 cents. The reason for that is that the 55/32 is the sum of 11/8 and 5/4 (when "adding" frequency ratios one multiplies the fractions). The 11/8 is an augmented fourth, the 5/4 is a major third. When spelled correctly, the augmented fourth plus a major third form an augmented sixth.
If standard notation wasn't so readily understood by a wide range of performers I would be tempted to abandon it altogether because spelling/conceptual issues such as this expose the mounting compromises and inadequacies for representing extended harmony. I am currently wrestling with numerous notation issues that arise when one employs tuning systems that contain no octaves. I'll have more to say about that when I'm ready to post details about my fourth string quartet (now in progress).
1 comment:
Notation is politics by other means: one of my big frustrations with European common practice notation was not being able to express certain (not at all complex) rhythms without having to resort to funny ‘tuplets’ which would just make obtuse what were simple ideas. It was much, much easier just tapping out the rhythms for the performers….
tig
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