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In page Recorder (musical instrument):

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The primary function of the thumbhole is to serve as an octaving vent. When it is leaked, the first mode of vibration of the air column becomes unstable: i.e., the register changes. In most recorders, this is required for the playing of every note higher than a ninth above the lowest note. The player must adjust the position of the thumb for these notes to sound stable and in tune.[citation needed]