I recall as a beginning flutist (coming from background in saxophone) finding the third-octave fingerings to be a confusing, illogical jumble, but they do actually make some sense. There is an incorrect explanation for these fingerings that I hear every so often, and have seen published on a couple of flute-related blogs recently. It goes something like this: the flute’s third-octave fingerings are some kind of combination of two different first/second-octave fingerings. For example:
+ | = | ? | |||
Or…
+ | = | ? | |||
If I squint my eyes just right I can sort of see how this almost makes sense fingerings-wise and overtones-wise, but ultimately this system is unnecessarily confusing and also doesn’t reflect acoustical realities.
Here’s a better way to look at third-octave flute fingerings: they are the same as the first/second octave fingerings, with a vent opened. This is very similar to how upper registers are achieved on the reed instruments: by adding an octave or register key or releasing a whisper key to open a vent. Since the flute doesn’t have dedicated vent holes, toneholes are used.
For some of the third octave notes, additional keys must be added or subtracted to improve pitch, tone, or response; again this is analogous to the systems used for the reed instruments. But here are the simplest examples of opening single vents for the third octave:
→ | open vent | → | ||
→ | open vent | → | ||
→ | open vent | → | ||
→ | open vent | → | ||
It is probably worth pointing out that having any “system” for remembering fingerings is just a crutch; for a performing musician, the only practical “system” is to thoroughly habituate them to the point that no conscious thought is required. Practice carefully and be on the alert for dubious pedagogy.
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