Given the number of flute manufacturers who advertise their adoption of "The Cooper Scale" (in some cases to the degree of engraving the fact on the flutes themselves), one may be forgiven for thinking - assuming - that there is somewhere a single fixed specification that Cooper defined, so to speak as the final word on the matter. Cooper himself saw things differently.
"Cooper's Scale? What's that? There isn't 'a' scale. There is a constant revision taking place so that, at any one time, there is a set of figures which you can use to design your flute, but these will change in the light of experience. I altered the scale a little as the years went by, mostly according to certain criticisms levelled at it. I now feel that I have more or less reached the end of the road scale-wise".
(Quoted by Trevor Wye in the Wye-Bennett-Spell paper "Cooper's Scale Revisited")
At a fundamental level this amounted to the need to overcome and replace the old scale based on A=435, which presented the defining problem of "sharp at the top, flat at the bottom". As Cooper discusses extensively in the little privately printed booklet The Flute he published in 1980 (see below), presenting a copy to flute players as and when, there was always more to creating a flute scale than deciding on tone hole positions. Tone hole sizes and heights also mattered (with the modern style using several different sizes on the body joint alone), and the perforated keys ("open holes") of the French style add further complications.
It is clear from Cooper's booklet that he took a somewhat dim view of open holes on a flute; one original idea he introduced was what is now often referred to as the "orchestral" pattern, with closed holes in the left hand and open in the right hand.
(Side note: Cooper happened to mention this to me one day in my workshop in Clerkenwell, London, some time around 1978, and the thought stayed with me right through to making my first flutes after moving to Bath in 1979. My very first attempt "Number 1", which I still use, was a conventional open-hole instrument, but for two commissions (one silver, one 9ct gold) I followed the orchestral pattern. These may have been the first flutes made in that form, after Cooper himself. They should still be out there, somewhere.)
Significant input into this process came from flute players with an interest in the theory and mathematics involved. The goal of course was to incorporate all these issues as closely as possible into a formula – a new Schema in effect – which could be used reliably as a framework by which to set the scale for any root pitch (A=442 increasingly becoming the new default), whatever tone hole sizes the maker might choose.
In the UK, Elmer Cole (principal, English National Opera) was all of professional player, mathematician and experimental maker of headjoints; in the US, Eldred Spell contributed significant work especially on rationalising tone hole displacements according to size and style of key (open/closed-hole), increasingly bringing computing tools to bear.
Also in the UK, Trevor Wye (for many years a regular co-principal partner to Wibb) tuned flutes for various players (including the middle-period plated Louis Lot I acquired around 1974), in between collecting and curating obscure 19th Century flute repertoire broadly classified as "Victoriana"; and of course establishing a pre-eminent reputation as a teacher. He also invented an "automatic" pneumatic machine for testing flute scales independently of a player.
After Wibb's death in 2022, Michie Bennett very kindly passed on a few things to me; one of these was the copy of "The Flute" which Cooper had presented to Wibb. This is the first edition (blue cover). I never knew until that moment that the book existed. There is a second edition (yellow cover) which I have yet to find. In the meantime, I have scanned most of the book for download here. The text is not as dark and crisp to read as one would like, for which I apologise. It covers, as one would expect, both tuning and making, with some photos (monochrome and some none too clear even in the original) which beyond their intrinsic interest give some evidence of the personality of the man, always generous, and often light-hearted as to become playful.
I have split the scans into three parts, covering the 15 compact chapters.