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The intonation of a flute is also governed by the strength of the airstream, and by the amount the lips cover the embouchure hole. The mathematics of flute tubes, embouchure holes, and tone holes does not necessarily produce an accurate sounding instrument.
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From a mathematical perspective, these two approaches are distinctly different and require separate discussions.Īs all experienced flute players know, the intonation of a transverse flute - with either a very simple or a very complex embouchure hole - depends not only on the precision of instrument construction, but also on the performer. On the other hand, we may realize a given tuning by making a flute according to another sequence of equations. This method provides convenient solutions when a flute is extremely fragile and cannot be played, or is simply not available for playing.
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We may predict the tuning of an existing instrument by first measuring various flute bore, embouchure hole, and tone hole dimensions, and then substituting these data into a sequence of equations. It is possible to approach the subject of flute tunings from two different perspectives. In a work entitled The Greek Aulos, Kathleen Schlesinger (1862–1953) attempted to reconstruct Greek music theory by analyzing the remains of ancient reed flutes. Wind instruments are unique, however, because they alone embody the physical dimensions of scales and tunings. Part I: Equations for the Placement of Tone Holes on Concert Flutes and Simple Flutesįlutes, harps, and drums are the oldest musical instruments created by man. ON THE ART AND SCIENCE OF ACOUSTIC INSTRUMENTS