Tone-hole opening must preserve modal frequency ratios for correct tuning

Evidence

Woodwind reed instruments have resonators whose modal behavior is crucial to the operation of these instruments and provides the sound modifier function. Woodwind instruments incorporate finger holes to enable chromatic scales to be played from the first mode to the second mode when the fingering can be used again as the reed excites the second mode. These mode changes continue up the chromatic scale to cover the full playing range of the instrument (see Figure 4.3). Clearly it is essential that the modes of the resonator retain their frequency ratios relative to each other as the tone holes are opened, or else the instrument’s tuning will be adversely affected as higher modes are reached. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1211

Categorization

• QUESTION: How do real fingering systems preserve these ratios across the whole chromatic range—what exactly does the Benade constraint describe in practice?
• XREF: connects to: Only bores keeping fixed mode ratios as holes open are musically useful — David Howard, Jamie Angus, coustics and Psychoacoustics, 1240; Shifting resonance ratios as holes open would wreck woodwind tuning — David Howard, Jamie Angus, coustics and Psychoacoustics, 1239; Instrument makers shape bore profiles to tune woodwind modes around tone holes — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1225