I'd like to understand how recorder fingerings work, e.g. for a Baroque alto recorder. Let's say you know which holes are open, which ones are partially open and which ones are closed. How can you guess the tone that will sound if you blow softly, the tone that you will hear if you blow harder, etc., other than trying it out and listening to what happens? Or the other way around: let's say you have a note. How can you derive all the possible fingerings?
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1Acoustics ;^) ?– TomCommented Apr 20 at 17:48
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1 Answer
The acoustics of woodwind instruments are well studied and it's theoretically possible to calculate the notes and their harmonics for any combination of fingerings. There's a web page that calculates notes for any combination of keys on a concert flute: the Virtual Flute. Unfortunately I don't know of a site that does the same for the recorder.
On the other hand the recorder is fairly simple: a modern recorder has ten holes, one of which (the thumb) can also be partially closed. This gives a total of 1536 fingerings (3*2^9) and they were presumably all tested long before acoustics was studied and computers invented. The vast majority are useless and the rest found their way into fingering charts.
For an experienced woodwind player faced with a new instrument there's a good strategy for finding useful fingerings for. Mostly putting all the fingers down and pulling them off one by one produces a scale (usually major). If these notes are not in tune or chromatic notes between them are needed then one tries different combinations of fingers below the highest open hole to bring them down to pitch. A good example is the low register four-finger B-flat on the alto recorder which is far too sharp, fingers six and seven are needed to bring it down to pitch. Just finger six is not quite enough. For the B-natural the only way to play it to add fingers to the C below the open hole. There are three holes (ignoring the double holes) so eight combinations. Adding fingers five and six is the only combination that's in tune. And so on... Then you get to the octave using the where the acoustics are more complicated. For the octave B-flat just the sixth finger is enough. Then from E-flat you're using the next harmonic and things get even more complicated, the open third finger hole functions as a vent and has asimilar function to the thumb hole.
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Thank you for the virtual flute link. What I've found most interesting is that most combinations I've tried don't result in a single pitch but have e.g. five playable notes, some of them unusually sharp or flat, and twelve multiphonics. Commented Apr 21 at 8:43
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About the simplicity of the recorder: i don't think it's the whole story. Technically, the thumbhole is not the only hole that can be partially covered. I've never seen a chart that suggests partially covering e.g. the fourth hole, but even if it isn't useful it would be great to know why. Also, like on a flute, one combination can lead to different pitches, and there are multiphonics, too (see Sarah Jeffery, youtube.com/watch?v=oKF7GFfYn0A). Commented Apr 21 at 8:51
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1@zabolekar Physical models like the the virtual flute predict the different pitches and the multiphonics for a fingering. Partially covering holes other than the thumb is not usual on the recorder, but as with any woodwind instrument partially covering the lowest open hole lowers the pitch of the note and enables glissandi between those notes. That would be useful for microtonal music and presumably fingering charts for microtonal music use partially covered holes. Commented Apr 21 at 10:06
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1@zabolekar Here's an example of a microtonal fingering chart using half-hoies: siementerpstra.com/recorder Commented Apr 21 at 10:55
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1As a recorder maker, I'd just like to add- there's no perfect solution here. Even if we agree on, say, 12Tet, there's no way to perfectly implement it, without shading. Such is life. Commented Apr 23 at 12:57