The Arvidsson Bore 

The construction of historical recorders is most likely the result of a long series more or less successful experiments, and trial and error.  Some instruments turned out to be quite good and have served as prototypes for the historic makers.  Most of today’s makers begin with the same successful historical models, often with an adjustment in the pitch and perhaps other small changes. 
It is quite simple to correct a lone intonation problem – for example, an octave that is too narrow in a certain tone – through changing the diameter of the bore in an appropriate place.  However it is impossible, without really advanced calculations, to find out how one such change affects all the other tones on the instruments, especially if the higher harmonics are also considered. One can imagine that the bore of a historical recorder is the result of a number of such minor changes, and minor corrections of minor changes!

 It is therefore not a surprise that a computer-based analysis of the harmonic relationships that are created by the bores of historical instruments reveal an observed disorder among the higher resonance frequencies of the different tone holes.  Through the placement and size of the tone holes, the first and second resonance frequencies are always in accord with a perfect octave, but the third and fourth resonance frequencies are sometimes, and unrelated to each other, higher or lower than the corresponding harmonic overtones.  Instruments made by different historical makers (Stanesby, Bressan, Steenbergen, Denner) show, from tone to tone, a completely different pattern in this disorder. What effect does this phenomenon have?

From a theoretical point of view it can be stated that the higher harmonics will be individually influenced in amplitude and phase from tone to tone.  This in turn will have an influence on the tone timbre and probably also on the response to tonguing.  
My conclusion is that to achieve good equality in timbre and tonguing over the entire range, the higher resonance frequencies for all tones must be uniformly tuned.
Based on some mathematical relations, familiar to me from my engineering work, I have succeeded in designing a new baroque recorder bore which perfectly fulfils that requirement.

This bore is the result of a straightforward design process and can be completely described by a mathematical equation. The instruments I build with this new bore have a very stable and full tone in the low end of the range and a fast attack and good equality over the whole range.