register is near a 12th above the fundamental in cylindrical tubes, but can approach an octave jump (8th) if a decreasing taper is used. According to the Fundamental Principle for pan flutes, the frequency and the length of the tube are inversely proportional. Every time the pitch goes up one octave, the frequency doubles. Because there are 12 notes in a chromatic scale or a full octave, every half-step in a chromatic scale is multiplied by the 12th root of 2 to get the note next to it. By this, it is possible to calculate the length of any pipe, given that one knows the length of any one pipe. The formula for calculating the length of a pan flute pipe is L = (c / f) / 4 (the "theoretical length" L equals the speed of sound c = 343 m/s, divided by the desired frequency in hertz f, that quantity divided by 4; this simplifies and rearranges to: Length of pipe (in centimeters) × Frequency (in hertz) = 8575). Because of a property of compression within the tube, the length must be a little shorter to correct flat pitch. The extra length is helpful for a maker, who can use a cork or plug at the bottom to adjust the pitch. Some instruments use wax or pellets to tune the fundamental pitch of each tube. A tube that has a diameter 1/10 of its length yields a typical tone colour (see Timbre). An inner diameter range between 1/7 and 1/14 of the length L is acceptable. A narrow tube will sound "reedy", while a wide one will sound "flutey". A more exact method is to multiply the bore diameter by 0.82 and subtract this value from the tube length. This compensates for internal compression slowing frequency and the lips partially covering the voicing. Only tiny adjustments will be needed then to adjust fundamental pitch for air density and temperature. Playing The pan flute is played by blowing horizontally across an open end against the sharp inner edge of the pipes. Each pipe is tuned to a keynote, called the fundamental frequency. By overblowing, that is, increasing the pressure of breath and tension of lips, odd harmonics (notes whose frequencies are odd-number multiples of the fundamental), near a 12th in cylindrical tubes, may also be produced. The Romanian pan flute has the pipes arranged in a curved array, solidly