Tone-hole fingering requires modes to keep constant frequency ratios as holes open
Evidence
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. Benade (1976) summarizes this effect and indicates the resulting constraint as follows: “Preserving a constant frequency ratio between the vibrational modes as the holes are opened — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1211
Categorization
Category: Factual Claims
- XREF: Shows a physical constraint analogous to place-dependence in geography/cartography — the same ratio must hold at every scale, like an invariant across a map.
Related
- Tone-hole opening must preserve modal frequency ratios for correct tuning (similarity 0.94)
- Shifting resonance ratios as holes open would wreck woodwind tuning (similarity 0.89)
- Woodwind tone holes must preserve mode frequency ratios to stay in tune (similarity 0.82)