The Abjad Notation and the Presentation of Cycles
Ferhat ÇaylıThis article examines the Abjad notation that was used to describe maqamic structures between the 13th-15th centuries starting with Safiyuddin Urmawi’s Book of Cycles. The article highlights the potential issues that may arise from considering the Abjad notation as a representation of the pitches in the Pythagorean 17-tone tuning system. The proposed solution is to view this notation as a contextual system that represents the lahnı [melodic] intervals. Accordingly, the notation implies the limma for consecutive notes, the mujannab for skipping one note, and the tone for skipping two notes. Therefore, the intention appears to be to indicate the intervallic relationships between notes rather than the notes themselves.
The article demonstrates that associating the Abjad notation with a fixed tuning would lead to problems in interpreting the music theory of that period. The text discusses the possible authentic interpretation of the notation based on historical sources and also illustrates how the adwar [cycles] are formed by combining only these three intervals. In conclusion, the Abjad notation is interpreted as a practical notation system that facilitates the recognition of these lahniyyat [melodic intervals] that constitute the cycles, and the argument is made that this notation system should not be identified with a fixed pitch sequence.
Ebced Notası ve Devirlerin Gösterimi
Ferhat ÇaylıBu makale, Safiyüddin Urmevî’nin Devirler Kitabı’ndan itibaren 13.-15. yüzyıllar arasında makamsal yapıları tarif etmek için kullanılmış olan ebced notasını konu edinmektedir. Makalede öncelikle, ebced notasını “17-eşit-olmayan-aralıklı ses sistemindeki perdeleri temsil eden bir gösterim” olarak değerlendirmenin yol açabileceği sorunlara işaret edilmektedir. Çözüm için, söz konusu notasyon sisteminin “ezgisel (lahnî) aralıkların” sıralanışını gösteren bağlamsal bir gösterim biçimi olarak değerlendirilmesi gerektiği savunulmaktadır. Buna uygun olarak, sabit bir perde taksimatına karşılık gelmeyen ebced notasında bütün ardışık notalar arasında “B” (bakiye), bir atlayan notalar arasında “C” (mücenneb), iki atlayan notalar arasında ise “T” (tanini) aralığının bulunduğu vurgulanmaktadır. Dolayısıyla ebced notasının, seslerin kendisinden ziyade aralarındaki aralıksal ilişkileri belirtmek maksadıyla tasarlanmış esnek bir notasyon sistemi olduğu savunulmaktadır.
Makale, ebced notasındaki sembollerin sabit bir perde taksimatıyla özdeşleştirilmesinin, söz konusu dönemdeki müzik teorisinin yorumlanması aşamasında birtakım sorunlara yol açacağına örneklerle işaret etmektedir. Ardından, dönem kaynaklarından alıntılarla ebced notasının aslına uygun şekilde nasıl yorumlanabileceği tartışılmaktadır. Makalenin son bölümünde, Urmevî tarafından ortaya koyulan “devir” yapılarının tamamen T, C ve B aralıklarının kombinasyonundan oluştuğu örneklenmektedir.
Sonuç olarak lahniyyat kavramı üzerinden ele alınan ebced notası, devirleri oluşturan bu üç aralık tipinin kolayca anlaşılabilmesini sağlayan pratik bir notasyon sistemi olarak değerlendirilmekte ve söz konusu notasyon sisteminin sabit bir perde dizgesi ile eşleştirilmemesi gerektiği savunulmaktadır.
Written by Safiyuddin Abdulmumin Urmawi in the first half of the 13th century, Kitab al-Adwar [The Book of Cycles] is considered one of the earliest works of music theory to systematically employ maqam names similar to those in use today. Urmawi’s work laid the foundation for a unique system of music theory known as the ilm al-adwar [Theory of Cycles] that remained in use until the end of the 15th century. This system is characterized by its use of special structures called adwar [cycles, singular dawr] and unique Abjad notation technique. Within the tradition of the Theory of Cycles, Urmawi and subsequent theorists provided mathematically detailed explanations of pitch ratios. Until recently, the Abjad notation was generally considered a notational system for representing the pitches of the Pythagorean 17-tone tuning system that had been calculated in the works of these theorists. However, interpreting Abjad notation in this manner presents certain challenges when trying to understand certain aspects of the music theory system of that era. Based on a comparative analysis of the writings of Urmawi and his successors, this article aims to propose a solution for how the Abjad notation should be interpreted in its authentic form.
The theorists of the Theory of Cycles tradition wrote their treatises at a time when music theory was still considered a branch of mathematics and studied interval ratios through various arithmetical calculations based on the proportions of an imaginary string (monochord), a practice that had continued uninterruptedly from Ancient Greece until their time. Starting with Urmawi’s Book of Cycles, they especially focused on the Pythagorean 17-tone tuning. In their writings, they used the Hisab al-Jummal [Abjad numerals that assign numerical values to the Arabic alphabet’s 28 letters] to number the pitches resulting from the division of the monochord in accordance with the Pythagorean 17-tone tuning. However, they also used the same numeral symbols as the so-called Abjad notation while explaining the maqamic structures in the rest of their works. Therefore, modern literature generally considers the abjad notation as a system that represents the pitches demonstrated by the ratios of the monochord. However, upon close examination of Urmawi’s and his followers’ treatises, this assumption appears to be questionable.
The article discusses the issues that arise in interpreting certain aspects of the Theory of Cycles when using Abjad notation as a fixed pitch sequence and questions the validity of this modern understanding. As a solution, the article suggests that the Abjad notation should be interpreted in terms of lahniyyat [melodic intervals]. In support of this argument, the article provides many quotations from historical treatises.
In the Theory of Cycles system, the cycles (i.e., scales) are formed by sequencing the melodic intervals (i.e., T [tone], C [mujannab], and B [limma]) in various orders. Therefore, the primary function of Abjad notation is to display the order of these three melodic intervals. Since this notational system is written in Hisab al-Jummal, these melodic intervals can be easily understood through the interval between the notational symbols, which are basically numbers. In this system, B intervals are represented by consecutive notes (i.e., numbers; e.g., 1-2, 2-3, 3-4). C intervals are represented by the skipping of one note (e.g., 1-3, 2-4, 3-5), and T intervals are represented by skipping two notes (e.g., 1-4, 2-5, 3-6). Therefore, unlike modern notational systems, this system seems to have been designed to represent intervallic relationships between notes rather than the notes themselves.
In conclusion, the argument is made that the Abjad notation, rather than being intended to represent the pitches of the Pythagorean 17-tone tuning system, was instead a flexible system that indicated the arrangement of melodic intervals (T, C, B). These intervals were not treated as specific intervallic units with absolute values but rather as a spectrum of approximate values, each of which could vary according to the melodic sequence. Furthermore, many theorists from the Theory of Cycles tradition, including Urmawi, stated that the differences within the spectrums do not make a significant aural difference regarding the melodic composition.
Abjad notation has played an important role in the narratives of maqamic music theory for nearly two centuries as a reader-friendly system that facilitates the recognition of the ‘melodic intervals’ that constitute the ‘Cycles’, without the need for complex mathematical operations. As discussed in the article, the interrelation between the Abjad notation and the concept of lahniyyat supports previous studies that have suggested this notational system should not be considered as a fixed division of pitches.
