On the flute, there are several notes that have identical fingerings: each note from bottom-line E through third-space C-sharp has exactly the same fingering as the note an octave higher. Obviously, some factor other than fingerings must account for the octaves, but flutists as a group seem to be unclear on what it is.
I got curious and dug through some pedagogical sources to see what flutists have published about it. I have compiled my findings into a chart:
To achieve the upper octaves on the flute
I have started from the baseline of the lowest octave’s tone production methods, and framed the authors’ ideas in terms of what has to be done to move into higher octaves. And I’ve grouped the answers together as best I can, hopefully with reasonable accuracy as to the authors’ intended meanings. For example, “move jaw” and “move jaw forward” obviously overlap, but I separated them to try to maintain the authors’ original levels of specificity. And “jaw” and “chin” may really be the same thing for most flute-playing purposes, but I’ve separated in them in a case where the author seemed to see them as distinct.
Some of the authors address the issue specifically and in detail, while others just mention something in passing, so the chart does not necessarily represent their complete and definitive views. I have provided a bibliography with page numbers so you can read the authors’ words in context, and I highly recommend doing this if you’re interested in the topic. I’ve color-coded things so you can see at a glance which ideas are most popular, though I don’t think this is an issue to be settled by popular vote.
There are some surprising outliers. Most authors who mentioned the size of the aperture indicated that it should get smaller in the upper octaves, but a couple insisted that it should not change. Several authors indicated that the distance from the aperture to the blowing edge decreases for upper registers, but one said it actually increases. There’s significant disagreement on whether blowing harder is part of achieving the higher octaves.
I think some of the differences of opinion shown in the chart may be due to flutists actually doing the same things but describing them differently. It’s also possible that the techniques listed can be combined in different ways to create different tone production “recipes” that produce similar results.
I’m interested in continuing to expand this in the future. If you can point me toward a published source, then send it along (I’m not really interested in anecdotes or private opinions), or let me know if you think I have misread or misinterpreted someone’s views (especially if you’re the author!).