Calculating scale tunings of Polynesian nose flutes

Abstract

The Polynesian nose flute is found in two versions that are blown in a similar manner but fingered and tuned differently. The Eastern Polynesian flute, known in Hawai'i as 'ohe hano ihu, but is found also to Tahiti and Niue. The tube is closed by a segment node at one end but with a hole for blowing and open at the other end. It typically has two or three finger holes along the tube and three or four playable notes. Being similar to other flutes, the scale tunings can be calculated from hole and tube dimensions by analytic expressions. In Fiji, New Zealand, Samoa, and Tonga, where it is known as fangufangu, both ends of the Western Polynesian flute are closed by segment nodes. There are five holes are placed along the top, usually evenly spaced from one end to the other, with a sixth hole in the middle underneath, giving a variety of fingering options with four to six notes and two registers. The scale tunings are determined by first calculating the frequency response using a lumped-element method.