Principles of consonances of the modes of the Saba Radif

In this article, in order to find the principles of consonance of the modes of the Saba Radif, common features in the arrangement of intervals of tetrachords, pentachords and modes in it have been studied so that they can be considered as an example of the current rules in Iranian classical music. The results of this research show that the Saba Radif consists of 72 modes, which are formed by combining 9 tetrachords and 9 pentachords in 22 different types. Each of the modes in the Dastgah and Avaz of the Saba Radif is considered in the range of one octave, which is formed by combining one tetrachord and one pentachord. The Shahed tone is also considered in the common tone between the connected tetrachords and pentachords. The mentioned tetrachords and pentachords are divided into three parts: 1. Zalzali 2. Tanini and 3. Mostazad, each part includes three subgroups. The tetrachords and pentachords of the Zalzali include: 1. Tork, 2. Shur, and 3. Segah. The tetrachords and pentachords of the Tanini include: 1. Mahur, 2. Nava, and 3. Dashti. The tetrachords and pentachords of the Mostazad include: 1. Chahargah, 2. Mokhalef, and 3. Zabol. By combining these tetrachords and pentachords, a total of 162 modes can be formed, of which 22 combinations have been used and 140 other combinations remain as potential. Of these 140 potential combinations, 63 do not comply with the criteria for minimum consonances in the modes in this Radif, which is the presence of at least 5 consonant ratios and a maximum of three single tones in a mode, and will be considered dissonant. However, there are 77 other potential combinations that are in accordance the aforementioned criteria, and their acceptance in modulations or as new modes seems likely to the contemporary listener. Because that the role of the Shahed tone, which has the most important role among the tones of a mode, is clear in these potential modes, there will be a great potential for implementing these modes and applying the results of this article. In addition, just as 72 modes are formed from 22 combinations of tetrachords and pentachords in this Radif, it is possible to create more than one mode from one type of combination by changing other important tones, such as the Ist tone. Apart from the criterion of having at least 5 consonant ratios and a maximum of 3 single tones in consonant or semi-consonant modes, there are 4 other criteria in tetrachords, pentachords, and consonant and semi-consonant modes, which are: 1. No succession of two Baghiyeh intervals, 2. No succession of more than two Mojannab intervals, 3. No succession of more than two Tanini intervals, and 4. Succession of the Mostazad and Baghiyeh intervals. These principles existed in Iranian music in the 7th century AH as well, and Safi al-Din Ormavi mentioned some of them in his book Advar. In general, it can be said that the principles and criteria of consonances in Iranian music have not changed significantly from the 7th century to the present.