“The long necked lute called the tanbur has many frets on the neck to determine the notes to be played. The diagram shows a tanbur with the fret at H the full length L of the string from the bridge at B.  If we take the note played from the open string, length L, as 600 cycles per second = (c/sec).  Then the note played at the fret position M, which is ½ L from the bridge i.e. B to M, would be 1,200 c/sec (octave). Pythagoras experimented with an instrument like the tanbur to show that these intervals produced notes which were all musical or pleasing to the human ear.  If the string on the tanbur is now played at fret K, length B to K which is 2/3 L, the vibrations can be determined by the multi-plication of 600 x 3/2 = 900 c/sec.(perfect 5th).  So we see that the ratio of the two lengths is inverted in order to calculate the vibrations. Therefore, the note played at fret J would be 600 x 4/3 = 800 c/sec. (perfect 4th) These last two ratios, 3:2 and 4:3, are the next in the natural harmonic series and are the beginning of the fundamental division of the octave ratio 2:1 as we shall see later.”

(Dr. Prosser, The Music of Rumi - preview)