The Effects of Hall Capacity in the City-Theater Complex of Tehran on the Changes of Their Income From 2009 to 2017, Based on William Baumol’s Theories

Rengs, as a renowned type of Dastgah rhythmic music in Iran, are often performed to finish a musical performance or to accompany a dance. These pieces have been usually recorded in written sources of music based on the normal 6/8 time signature. In the theory of western classic music, 6/8 time signature is a part of the combined rhythm with two pulses, where each pulse can be divided into three parts. The equality of duration of both main pulses in every bar is one of the essential features of this western classical rhythm which has been accepted in notation in Iranian contemporary theoretical music; however, examples of the recorded performances of this musical type from the past hundred years until the present, show a flexible and unequal nature of the performance of Rengs in Dastgah music of Iran. By analyzing audio samples recorded from Rengs, it is possible to obtain this precise numerical ratio that can change during the performance of a piece and sometimes returns to equilibrium. Since fifty years ago, some musicians have expressed this difference in the notation and performance of 6/8 time signature and some  have ffered a number of suggestions for the unequal notation of the main pulses. Most researchers who have carefully studied this rhythm or cited the results of earlier research believe that the rhythm of Rengs is a different rhythm with two unequal pulses and have tried to find the differences between these two pulses. The highest concentration of votes is also on the (4 + 3) ratio. This study, in addition to providing a review of different ideas of classical musicians and contemporary musical theoreticians, by computational analysis of voice samples, has extracted the exact temporal difference between the duration of the first and the second pulses. During the time period chosen for this research, which spans about seventy years (from the first period of Iranian music records in 1906 up to the samples in 1970s), there are many records of Reng performances with various media such as gramophone discs, magnetic reel and cassette tapes. In the selection of samples used to measure the difference in pulses, it has been attempted to avoid selecting samples with equal pulses. After examining more than 300 Reng samples from different recording periods, a selection has been chosen for the research samples in this study, which show unequal pulses and also express the maximum amount of flexibility in the rhythm. This study also shows that this flexible rhythm has the capability of performance of two equal pulses with a 50% ratio up to unequal pulses with 62.5% and 37.5% ratios. There is always a duration increase in the first pulse and a decrease in the second pulse in this rhythm. Also it is noteworthy that in many old records of Rengs, the length ratio of the two major pulses can be equal, or be considerably taller and shorter and return to equality again in the same piece. In other words, the most flexible rhythm in Dastgah music is Reng that can exit from its original pulses and subsequently return to equilibrium after a while.