The study of scale in Persian music according to notes spectrums

In this paper we have extracted the notes of Iranian scale from the traditional music played by the great musician Shahnazi on the TAR. Then, by analyzing the spectrum of the notes and by using our special averaging we have found the pitch attributed to the components’ frequency and found the interval between the notes. The results are in comple agreement with Pythagorean scale. Pitch is a subjective quantity that attribute auditory sensation in terms of which sounds maybe ordered on a scale extending from low to high. For a pure tone pitch depends mainly on the frequency of the sound stimulus, but for complex tones or musical sounds pitch depends on partials of the complex tone and when the partials of a complex tone are not harmonic however the determination of pitch is more subtle. Indeed the vibrations of string instruments give rise to overtones which are not exactly multiples of fundamental, so the pitch of musical sound that we perceive is a subjective quantity related to frequencies of the overtones. In this paper we study the effect of partials in pitch of musical notes and by averaging between partials we introduce a subjective quantity which represents the pitch of musical note which is in quite agreement with experiments. As we know there are two famous scales for music, Aristoxenuss and Pythagoraean scale. The intervals in Aristoxenuss scale are and in Pythagorean scale are Farabi, the well-known philosopher, based Iranian traditional music on Pythagorean scale and our measurements of pitch and intervals of the notes show this scale has remained unchanged for a thousand years.