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I recently obtained an inexpensive plastic recorder and am amazed that it’s possible to play a chromatic scale on it across two octaves. Many of the fingerings seem magical to me - as in, how did anyone figure out that combination X leads to note Y?

That got me wondering more generally how the size and position of recorder holes were determined. There has to be some physics at play here to figure out how the hole positions change the frequency of the notes. But it’s not as simple as “uncovering the next hole moves up a half step or whole step,” since many of the note fingerings involve closing previously opened holes.

What was the process by which the modern recorder finger hole positions and associated fingerings were invented?

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    I would bet on trial and error. It’s a very old instrument.
    – Todd Wilcox
    Apr 18 at 23:36
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    As Todd says, initially trial and error, later (much later) the frequencies given by an oscillating column of air of a particular length were worked out and the placement of the holes could be discerned to fit any particular tuning system. A primer on the maths is here ; physicsclassroom.com/class/sound/Lesson-5/Open-End-Air-Columns. Fingerings that leave one 'upper' hole open to get a different note likely reley on some cancellation of specific harmonics, but I'll leave that to more knowledgeable folks!
    – OwenM
    Apr 18 at 23:51
  • You might as well ask how any wind instrument got its hole placement. As OwenM points out ,by the 19th century enough physics was known to all folks like Adolphe Sax to design specific bores and place holes/pads appropriately.
    – Carl Witthoft
    Apr 19 at 0:19
  • @CarlWitthoft I agree this question could be more general, and that would itself be something I’d be very interested in hearing the answer to!
    – templatetypedef
    Apr 19 at 0:56
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    @CarlWitthoft I don't see any indication that Sax knew much about physics nor that he calculated bores and hole placement. It seems rather more likely that he tweaked the details of his instrument designs through experimentation just as instrument designers had been doing for centuries.
    – phoog
    Apr 19 at 10:09

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Okay, first thing to keep in mind: The pitch depends on both position and size of the tone holes (as well as on the bore). So if you want a simple diatonic instrument you can simply place the holes at whatever positions feels good and control the pitch by size. Then if you want to play chromatically you’ll start adding lower holes to flatten the pitch. Eventually people will experiment and try to find holes that make this doable by simple fingerings, offer good response and remain more or less in tune when overblowing.

So I’d say there is a clear path.

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I found a couple of articles about the subject.

Leah Fader "Development of the Flute From Pre-history to Modern Days"

http://centerprode.com/conferences/2IeCSHSS/coas.e-conf.02.01001f.pdf

Most discussions go from about 42000 BC to current times. The scale is considered to be the same as today's diatonic scales. I am not sure I agree with the identification. Mostly this article talks about later developments.

Theobald Böhm (the guy who invented the modern woodwind mechanisms)

https://play.google.com/store/books/details?id=mt8PAAAAYAAJ&rdid=book-mt8PAAAAYAAJ&rdot=1&pli=1

This is a Google Book from 1882 (the book, not Google's copy).

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  • Neither of those references are about the recorder.
    – PiedPiper
    Apr 19 at 20:37

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