Comparative Analysis of Robab’s intervals with the Zarlinian Scale

Document Type : Research Paper

Authors

1 Faculty Member of Music Department, Faculty of Art and Architecture, Tehran Central Branch, Islamic Azad University, Tehran, Iran.

2  Faculty Member of Music Department, Faculty of Art and Architecture, Tehran Central Branch, Islamic Azad University, Tehran, Iran.

3 Faculty Member of Music Department, Faculty of Music, Tehran University of Art, Tehran, Iran.

4 Master of Playing International Instruments, Department of Music, Faculty of Art and Architecture, Tehran Central Branch, Islamic Azad University, Tehran, Iran.

Abstract

The current research contains a comparative analysis of intervals for the instrument, Robab, as recorded in Al-Farabi’s book, titled Al-Mousighi Al-Kabir.  This research brings together the analysis of this instrument in regards to the Zarlinian scale, in order to find the relation between Robab’s intervals and those of the Zarlinian scale. First, the ratios of the frequencies of the Robab’s intervals have been analyzed. With a brief explanation of the Zarlinian scale, these unique intervals have been compared against the intervals of the Zarlinian scale by means of multiplying and dividing the corresponding mathematical proportionalities. In a reevaluation of the Zarlinian scale, notwithstanding its commonly-known problems which include a perfect fourth with a frequency ratio greater than that of 4:3 and the perfect fifth with a frequency ratio less than that of 3:2, we found another problem regarding the formation of the Zarlinian scale. While researchers currently believe that this scale consists of two kinds of a chromatic semitones, and one kind of a diatonic semitone, this article will prove that this scale is comprised of two kinds of a diatonic scale, and only one kind of a chromatic semitone. Conclusion: Findings we achieved in this article could be divided into these divisions as given below:

Interval frequency ratios of the Robab instrument, according to Farabi’s aforementioned book, fully conform to that of the diatonic major scale based on the Aristoxen-Zarlinian system of intonation.
Lack of conformity of the frequencies of the interval ratios, within the Robab with that of the chromatic Aristoxen-Zarlinian
Stating a problem pertaining to the Aristoxen-Zarlinian theory of intonation system based on the arrangement of chromatic intervals therein: In former theories, the Aristoxen-Zarlinian scale was believed to contain a kind of diatonic semitone with a proportion of 16:15, equal to 28.02 Savarts, and equal to 111.72 Cents. Also two kinds of a chromatic semitone with proportions of: A. A major tone equal to 135:128, equal to 23.12 Savarts, and equal to 92.17 Cents
The chromatic semitone in a minor tone, with a proportion of 25:24 equal to 17.72 Savarts, and equal to 70.66 Cents

Given a major scale from the upper chromatic semitone based on these proportions, the placement of major and minor intervals would become interchanged.
 
Suggesting a reformative theory: According to findings in this article, the mentioned scale consists of two kinds of a diatonic semitone, and only one kind of a chromatic semitone as explained below: Diatonic semitone in major tone: proportion equal to 16:15 equal to 28.02 Savarts, equal to 111.72 Cents. diatonic semitone in minor tone: proportion equal to 256:243 equal to 22.63 Savarts, equal to 90.21 Cents. And the chromatic semitone: proportion equal to 135:128, equal to 23.12 Savarts, equal to
 92.17 Cents. Given the mentioned frequency ratios above, intervals of the Robab will fully conform to the ratios of the chromatic Aristoxen-Zarlinian scale. Also if a major scale would be formed based on these ratios on the upper chromatic semitone, the minor and major semitones won’t get switched anymore.


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References

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Journal of Fine Arts: Performing Arts & Music
Volume 27, Issue 3
September 2022
Pages 27-36

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