In the Introduction to this book, I briefly discussed the place of the science of music in the disciplinary classifications of the medieval Islamic world, whereby music was classified as a subdiscipline of mathematics, itself one of the branches of philosophical knowledge. Furthermore, I also noted how this classification enabled the science of music to cover an expansive range of topics from the characteristics of “audible” music to more abstract discussions on the mathematical underpinnings of the ratios and intervals of musical notes, inter alia. In this chapter, I will expand on these themes by situating mathematics and music within the cosmology of the medieval Islamic world and explaining the role the two played as branches of knowledge within the existing scientific and philosophical paradigm of that era, namely, the Aristotelian/Ptolemaic paradigm.Footnote ¹ While examining this cosmology in detail lies well beyond the scope of this book, a general familiarity with some of its more fundamental tenets is necessary to appreciate the place of mathematics and music within the knowledge systems of the medieval Islamic world.Footnote ² In what follows, I will first provide a brief overview of the Aristotelian/Ptolemaic cosmology as it underwent modifications at the hands of Islamic philosophers and scholars alike to fit it into the larger cosmological and theological debates particular to Islam. I will then take up the classification of the sciences introduced by Islamic philosophers through which they aimed to study the world. In doing so, I will attempt to delineate the subject matter of mathematics and its subdiscipline, the science of music.

The Aristotelian/Ptolemaic Cosmology of the Late Antiquity

Before discussing the Aristotelian cosmology within the context of the medieval Islamic world, a point of ambiguity should be clarified. As A. I. Sabra and George Saliba (separately) point out, the term “Aristotelian Cosmology/Astronomy” refers to two distinct versions of the same cosmology.Footnote ³ First, there is the more direct “Aristotelian” cosmology, whose characteristics were defined in some of Aristotle’s own works, particularly his De Caelo and Meteorologica.Footnote ⁴ While Sabra considers this cosmology to be a “stronger or stricter program” on account of its more regulated structure, Saliba considers it to be ultimately weaker on account of its many internal inconsistencies.Footnote ⁵ Second, there is the broader Aristotelian cosmology that was based on some of Aristotle’s own cosmological principles but developed by later Neoplatonic philosophers, chief among them Claudius Ptolemy (d. first century ce). The main difference between the two versions was the use of homocentric circles in Aristotle’s own cosmology and their replacement with epicycles and eccentric circles in the later Neoplatonic Aristotelian cosmology.Footnote ⁶ In both versions, however, Aristotelian cosmology represented the universe as consisting of two parts, as I will elaborate here.

In a nutshell, the cosmology divided the universe to two main parts (or spheres, as Sabra calls them): one above the moon – the supralunar realm – and one below the moon – the sublunar realm. The entire system, consisting of the two realms, presupposed a gravitational point that was located at the center of the universe.Footnote ⁷ The placing of the Earth at the center of the cosmos gave birth to what we now identify as the geocentric model of the universe. This placing also meant that the Earth was located in the sublunar realm, a realm that Aristotle called the realm of generation and decay (kawn wa fasād in Arabic and Persian of the later Islamic adaptations). As the realm was the realm of generation and decay, everything in this realm was subject to motion and change (in the Aristotelian sense of the words).Footnote ⁸

This was contrasted with the supralunar realm, where nothing changed (in the Aristotelian sense of the word) and everything was in a state of stability and in uniform circular motion. What existed in this realm were the heavenly bodies, including the Moon, the Sun, the five planets, and all the stars. The heavenly bodies were arranged according to the following order: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn. Encircling all the other spheres was the sphere of the fixed stars, on which the stars and constellations were located. Ptolemy also introduced a ninth sphere, the sphere of spheres (falak al-aflāk in Arabic and Persian of the later Islamic adaptations), that encircled the sphere of the fixed stars and accounted for another type of heavenly movement, precession.Footnote ⁹ Such was the cosmology of the classical Greek period up to the late antiquity. As Sabra puts it, “all Islamic astronomers from Thabit ibn Qurra in the ninth century to Ibn al-Shatir in the fourteenth, and all natural philosophers from al-Kindi to Averroes and later, are known to have accepted” the Aristotelian/Ptolemaic cosmology.Footnote ¹⁰ It was through this cosmology that Islamic philosophers and even some non-philosopher intellectuals came to conceptualize the universe.

Aristotelian/Ptolemaic Cosmology in the Islamic World

The introduction of the classical Greek heritage into the Islamic world is a subject that has received ample attention by scholars of the history of Islamic sciences, with many of its aspects and characteristics having been analyzed and studied obsessively almost to a fault.Footnote ¹¹ While some scholars such as Dimitri Gutas tie the rise of interest in the classical Greek heritage to the rise of the Abbasid dynasty as a means to emulate previous imperial cultures to gain legitimacy for the newly born dynasty, others like Saliba trace this interest as far back as the mid-Umayyad period (the late first/seventh century).Footnote ¹² Regardless of when this interest started, however, scholarship agrees that by the mid-third/ninth century, study of the classical Greek heritage had gotten enough wind in its sails to make it one of the most significant sociocultural forces of the medieval Islamic world. This interest in the classical Greek heritage resulted in wholesale translation of almost the entirety of the known Greek corpus on philosophy and sciences into Arabic, the lingua franca of the early medieval Islamic world.Footnote ¹³

Of course, not everything in the Aristotelian/Ptolemaic cosmology was acceptable by scholars like al-Kindi and even al-Farabi, who operated in a decidedly Islamic environment and changed certain aspects of the cosmology to accord them with Islam. Among these changes, for instance, was al-Farabi‘s identification of the intellect of the heavenly bodies with angels as opposed to the Greek notion of the “divine” – by way of Alexander of Aphrodisias.Footnote ¹⁴ Another issue that followers of a monotheistic religion such as Islam found fault with, was the identification of the heavenly bodies with Aristotle’s unmoved mover.Footnote ¹⁵ In Aristotelian cosmology, each and every one of the heavenly bodies was equal to Aristotle’s unmoved mover, meaning, they did not move in the Aristotelian sense of motion, and they were capable of putting affairs in motion in the sublunary realm. This also meant that they were all equal to each other in terms of their powers and there was no hierarchy among them. This was obviously very problematic for Muslim scholars (and indeed followers of any other monotheistic religion), since they believed in an omnipotent God that was clearly on a higher plane of existence compared to these heavenly bodies (which were not considered to be divine anymore).Footnote ¹⁶ Al-Kindi’s solution to the problem is a rather ingenious reworking of Aristotelian arguments, wherein God is identified as the efficient cause or first agent that brings into existence the cosmos. This act of “being-ification,” as Twetten calls it – or creation – is considered a form of motion by al-Kindi. At the same time, the heavenly bodies are considered to be unmoved proximate efficient movers.Footnote ¹⁷ As such, al-Kindi “has the resources to distinguish between two kinds of ‘prime mover’ corresponding to two kinds of ‘motion’: God versus the unmoved proximate efficient mover that is the soul of the heavenly spheres in the Aristotelian cosmos.”Footnote ¹⁸

Later philosophers of the Islamic world such as al-Farabi and Ibn Sina further elaborated on the cosmology and introduced arguments to address what they considered to be some of the most problematic shortcomings of the cosmology.Footnote ¹⁹ Their elaborations were not radical departures from the mixture of Greek and Islamic foundations of the cosmology, but rather, efforts to further reconcile the two sides of the cosmology and as such, they remained faithful to this unique Islamic interpretation of the Aristotelian/Ptolemiac cosmology. In fact, even some medieval scholars who are seen by contemporary scholarship as opponents of the falsafa tradition, adhered to this Islamic Aristotelian/Ptolemaic conception of the universe. An example of such scholars is al-Ghazali (d. 505/1111), the famous theologian, Sufi, and jurist of the fifth/eleventh century, who is commonly identified as one of the staunchest opponents of the falsafa tradition. In a number of his treatises, al-Ghazali criticizes philosophers such as Ibn Sina and al-Farabi, which has led some scholars to argue that he favored an occasionalist cosmology over the Aristotelian one discussed in this chapter.Footnote ²⁰ Yet, as Frank Griffel has demonstrated, his objections to philosophers are on very particular issues and not to philosophy as a whole.Footnote ²¹ In fact, when it came to cosmological issues, al-Ghazali utilized some elements of the Aristotelian/Ptolemaic cosmology whose principles were laid out by the same philosophers that he supposedly opposed.Footnote ²² Far from just al-Ghazali, the Aristotelian/Ptolemaic cosmology was the dominant way of conceiving the universe for majority of Muslims who adhered to vastly different interpretations of Islam, from Jurists to Sufis, to kings and rulers, to ordinary Muslims up until the introduction of the modern scientific paradigm in the late eighteenth and early nineteenth centuries.Footnote ²³ It was within the scopes of this cosmology that medieval Islamic philosophers and scholars studied the universe and classified the sciences that pertained to this study.

The Place of Music and Mathematics in the Classification of the Sciences

Given the division of the universe into the two realms of the sublunar and supralunar, it should not be surprising to find that the classification of the sciences that studied the universe was influenced by this schema. In this part, I will examine this classification within the context of the Aristotelian/Ptolemaic cosmology as it was appropriated by Islamic scholars. I will begin this section by looking at the classification of the sciences presented by Ibn Sina at the beginning of his philosophical encyclopedia, al-Shifaʾ. While many scholars before Ibn Sina had introduced classifications that accorded with this cosmology, arguably the best formulated and most influential of these classifications was the one presented by Ibn Sina.Footnote ²⁴ I will then analyze some later classifications that were under the influence of Ibn Sina’s but became the dominant classifications within the Persianate and Arabic worlds of the late medieval period, namely, those of al-Tusi and Ibn al-Akfani.

Ibn Sina’s writings regarding the classification of the sciences do not have any sections exclusively dedicated to the subject. Instead, he discusses the matter at the beginning of the first book of his encyclopedia, the Book of Logic, which Marmura has identified as the Isagoge of al-Shifaʾ.Footnote ²⁵ First of all, in this section we learn that speculative philosophy is the branch of philosophy that deals with theoretical questions regarding the nature of things and as such it belongs to the world of contemplation, which elevates its status above that of practical philosophy.Footnote ²⁶ Second, there are three main criteria that delimit the divisions of speculative philosophy: motion (ḥaraka), substance/matter/subsistence (qiwām and mādda), and estimation/conceptualization (wahm and taṣawwur).Footnote ²⁷ Ibn Sina explains how these three criteria are mixed with each other to create three distinct groups of the speculative philosophy.Footnote ²⁸ The first group, the natural sciences (al-ʿilm al-ṭabīʿī), is rather easy to demarcate: It studies whatever belongs to the realm of motion and requires both a material dimension and a conceptual dimension, meaning, they can be grasped by the human estimation. This science clearly studies the world of the sublunary realm, as this world consists of things subject to motion in the Aristotelian sense and possessing a material presence. The third group is also easy to demarcate: It studies whatever transcends motion, substance, and estimation. Ibn Sina identifies this group as the theological sciences or the science of the divine (al-ʿilm al-ilāhī).

It is the second group that poses the most difficulty, as it floats between the other two groups. We know that Ibn Sina calls this group the mathematical sciences and that they share some of the characteristics of the other two groups. For instance, they require substance and motion for their existence, just as the beings of the sublunar realm. At the same time however, humans have the ability to conceive of them without reference to their substance. Ibn Sina’s examples in this regard are illuminating:Footnote ²⁹ If we intend to study human affairs we should turn to the natural sciences, since the subject of this discipline pertains to motion, substance, and conception. We cannot study human form – what makes a human look like a human – without recourse to how the human form changes and undergoes Aristotelian motion. In other words, we cannot abstract the form of a horse or a human from the physical being that is the horse or the human. We can, however, abstract the shape of a square from square-like objects. A square does not require a specific substance to be square. It can be made of wood or gold – as opposed to a human that must be made of flesh and bone to be human. Regardless of the substance involved, we can abstract the shape of the square from its objects. The key difference is the act of abstraction (tajarrud) that enables the form in question to exist outside of the sublunar realm of generation and decay. Ibn Sina reiterates this point later in his Isagoge where he points out that mathematical operations such as addition and subtraction can be estimated or conceived independently of matter and motion despite their existential contingency on matter and motion. Numbers also belong to this category and as such are subjects of mathematics.Footnote ³⁰ To recap, mathematics is the branch of speculative philosophy that deals with existents whose existence depends on substance and motion but can be conceived of independent of substance and motion. With that in mind, let us examine how this conceptualization of mathematics shaped the medieval understanding of music as a mathematical science.

A significant part of the science of music involved numerical operations to measure musical ratios.Footnote ³¹ These aspects of the science would still be considered mathematical by modern standards.Footnote ³² At the same time, there are other parts in the medieval study of music that do not fit a modern understanding of mathematical sciences. Some of these include discussions of the various melodic and rhythmic modes, as well as acoustical discussions regarding the mechanics of sound production.Footnote ³³ Inclusion of such discussions within a mathematical discipline might seem out of place for a modern audience. But once we reconsider the question in light of Ibn Sina’s definition of mathematics, the existence of such topics in a mathematical discipline becomes the only viable option. Melodic and rhythmic modes are among the existents that can be abstracted from their matter. We do not need actual sound to be present to conceptualize certain melodies or melodic modes. As such, musical discussions regarding melodic modes need not restrict themselves to the practice of music, although the practice of music must be represented in such discussions. In other words, although the practice of music must be reflected in musical writings, there are other potential melodies and melodic modes that can be conceptualized without having any material presence in the practice of music since the science is supposed to study everything that can be conceptualized without a substantive presence. This approach, which was already present in Ibn Sina’s predecessor, al-Farabi, explains the latter’s appropriation of, and addition to, Ptolemy’s tables of possible tetrachordal genera.Footnote ³⁴ Al-Farabi confirms this approach himself as much, when he divides music into two categories: “Those melodies whose construction was completed while being perceptible by the ear, and those that are constructed and composed while not being perceptible by the senses.”Footnote ³⁵ One can compose music without having any sounds attached to it. In other words, one can conceptualize sound without making any physical sound. What Ibn Sina and al-Farabi are proposing here, is beyond simple mathematical gamesmanship for its own sake. Rather, the very notion of mathematics stipulates conceptualizing everything that can be conceived regardless of actual substantive existence, hence the expansion of the Ptolemaic tables by al-Farabi, Ibn Sina, and even the later so-called systematists, such as al-Urmawi.Footnote ³⁶

Furthermore, since defining these melodic modes depends on ratios and ratios are also objects of mathematical study, it is reasonable to categorize all of them under the rubric of music, which, as Ibn Sina tells us, is the science of composing melodies according to the consonance and dissonance of notes and the durations intervening therebetween.Footnote ³⁷ Hence, numbers, geometrical forms, and numerical operations are only one side of mathematics. At the same time, Ibn Sina warns us that the study of the nature of numbers is different from the study of their mathematical properties, meaning, ontological questions about what numbers are and what their inherent properties are, cannot be answered through mathematics proper.Footnote ³⁸ On an epistemological level it is understandable why Ibn Sina (and in fact Aristotle of Metaphysics, from whom Ibn Sina is drawing his arguments) would opt for these theoretical categorizations of knowledge.Footnote ³⁹ If all the existent beings in the world were to be joined in an interconnected web of infinite cosmic relations, then any effort to produce knowledge would be inevitably futile, as it would lead to a process of infinite regress. Nothing could be explained without recourse to another connected existent which itself would be unexplainable without recourse to its own connected existents ad infinitum. This would require clear theoretical demarcations that would isolate subjects from one another to enable their study. Hence, Ibn Sina’s insistence that the study of the properties and nature of numbers cannot be carried out under the rubric of mathematics.

As sophisticated as they may be, Ibn Sina’s arguments are not without their shortcomings. Besides the somewhat convoluted nature of his discussions, there are two more major problems to which I would like to attention here: First, there is the matter of the practicality of his solution to isolate certain topics from others; as theoretically genius as it is, it is not clear to what extent this is viable. For instance, as I will demonstrate in Chapter 7, despite Ibn Sina’s insistence that the natural properties of numbers cannot be studied under the rubric of mathematics, they do play a prominent role in Ibn Sina’s own discussions on musical consonance, a distinctly mathematical discipline according to his own classification. But there is a second problem with his arguments as well, one that later philosophers, scholars, and categorizers of knowledge attempted to remedy: namely, the redundant use of motion as a necessary condition in demarcating the boundaries of knowledge. Take Nasir al-Din al-Tusi, for instance, in his discussion of the classification of the sciences at the beginning of his Persian-language work on ethics, Akhlaq-i Nasiri (Nasirean Ethics):Footnote ⁴⁰

From the outset, it is clear that al-Tusi’s arguments on the question have been very much influenced by Avicennian discourse. Two major differences that can be identified are first and foremost terminological. First, there is the matter of what he calls philosophy. While for Ibn Sina the term used is falsafa, the Arabized form of philosophy, al-Tusi opts in favor of an entirely different term, ḥikmat (wisdom).Footnote ⁴² One consequence of this shift is that al-Tusi can equate ḥikmat qua philosophy with ḥikmat qua wisdom as it is presented in the above-quoted Qur’anic verse. This conflation endows a garb of Qur’anic authority on philosophy, as it implies that al-Tusi’s philosophy is the same wisdom that God has bestowed upon some men as He has seen fit.

The second terminological shift is of more relevance to our discussion regarding the classification of the sciences. While for Ibn Sina motion is one of the main criteria in delimiting the various sciences, the term is completely absent in al-Tusi’s classification, with the only concepts of salience being matter and the ability to conceptualize beings. It is not difficult to see why al-Tusi would omit motion as a criterion for classification of the sciences. Aristotelian motion, as mentioned earlier, is exclusively a characteristic of matter in the sublunary realm. Meanwhile, matter and the ability to conceptualize beings are enough to differentiate between different types of beings in both the sub- and supra-lunary realms, which makes motion redundant. Furthermore, with the criteria of classification now simplified, we can better understand how the mathematical sciences are distinguished from the physical and metaphysical sciences: they do not belong to the divine realm of supernatural beings as they require matter to exist. The supernatural realm, al-Tusi tells us, belongs to immaterial beings such as “God [ilāh], may He be exalted, and those close to Him on whose command have become the premises [mabādī] and causes [asbāb] of other beings.”Footnote ⁴³ At the same time, even though the beings pertaining to the study of mathematics require matter to exist, we can still think of them and conceive them without recourse to their material existence. In other words, even though they belong to the seen cosmos, they do not belong to the realm of generation and decay, which means the study of the visible beings of the supralunar realm belongs to this category as well (i.e., astronomy). Nevertheless, not everything that belongs to mathematics belongs to the supralunar realm. Numbers are one example of beings that do not belong to the supralunar realm, yet their study belongs to mathematics to some extent. As such, the criteria introduced by these Neoplatonic philosophers significantly broadens the scope of mathematics well beyond that of modern mathematics. Anything that can be conceived of without requiring matter falls under the domain of this discipline. Al-Tusi, following Ibn Sina, identifies the sub-subjects of this discipline as arithmetic, geometry, astronomy, and music.Footnote ⁴⁴

Ibn al-Akfani is yet another scholar who makes a similar attempt at remedying the redundancy of motion. In his Guide for Those Pursuing the Most Radiant Destinations (Irshad al-Qasid ila asna l-maqasid), a short tract on the classification of the sciences,Footnote ⁴⁵ he reiterates the rationale provided by Ibn Sina albeit without mentioning motion:

The terminology used by Ibn al-Akfani is a mixture of terms unique to him as well as some found in Ibn Sina and al-Tusi. On the one hand, and just as with al-Tusi, Ibn al-Akfani replaces falsafa with a variation of ḥikma. At the same time, and just as with Ibn Sina, he refers to the higher sciences as the theological (ilāhī) sciences. On the other hand, he replaces some of the terms used by other scholars, such as “human soul” and “conceptualization/estimation with “rational soul” and “mind.” The reason behind these terminological preferences is not immediately clear. Ibn al-Akfani, however, very much like al-Tusi and unlike Ibn Sina, decides to forgo motion as a necessary component of delimiting the sciences. What all three scholars have in common though is the tripartite division of the sciences and the medial nature of mathematics as a science that is situated between the superior realm of the divine and metaphysical knowledge on the one hand, and the inferior realm of the natural sciences on the other. This medial positionality of the mathematical sciences coupled with the practical difficulties of applying the theoretical division of the sciences resulted in interesting consequences that I will examine here. The opinions of the three scholars examined here give us a reliable overview of the classification of the sciences in the eastern Islamic world during the medieval period that held prominence even in the early modern period and under Ottoman rule.Footnote ⁴⁷

Music and the Interconnected Web of Cosmic Relations

One interesting feature of the mathematical sciences is their ability to act as a medium in connecting the affairs of the sublunar realm to the beings of the supralunar realm. Take the disciplines of astronomy and astrology for instance: as per George Saliba, the two disciplines were separated from one another for the first time in their history during the Islamic early medieval period. Saliba argues that the separation of the two disciplines was effected to preserve astronomy from the attacks of religious authorities against astrology’s suspicious claims and disrepute in the Islamic world as a dubious scientific discipline.Footnote ⁴⁸ At the same time, one cannot ignore the epistemological benefits that such a separation would have brought to the study of astronomy. As I have argued here, such theoretical demarcations of the boundaries of different scientific disciplines would have prevented the knowledge system from devolving into a process of infinite regress. This is particularly the case with a science like astrology. On the one hand, the cosmology to which Ibn Sina adhered necessitated a belief in the theoretical legitimacy of astrology. On the other hand, the impossibility of isolating the effects of different stars and planets on humans would have made the study of the discipline impractical for all intents and purposes. As an opponent of the discipline of astrology Ibn Sina must have been aware of this problem. In fact, by refuting the validity of the discipline he confirms this position, stating “the science which is infinite cannot be apprehended.”Footnote ⁴⁹ The interconnectedness of astrology – a discipline that was deemed impossible to study by the likes of Ibn Sina, Ibn Rushd (d. 595/1198), and Maimonides (d. 601/1204) – to astronomy would have made the study of the latter impossible as well, at least in theory, hence the separation of the disciplines. In practice, however, and with the public more interested in astrology than in astronomy, the interconnectedness was bound to bring the two disciplines together.Footnote ⁵⁰ This meant that a mathematical discipline (i.e., astronomy) connected the supralunar realm to humans in the sublunar realm through its association with astrology, however unwanted – by philosophers such as Ibn Sina – this association was.

This interconnectedness held for all other scientific disciplines as well. For instance, geography was considered an independent discipline by most scholars of the medieval Islamic world. At the same time, astronomy had a significant impact on the study of geography, since the map of the sky and the position of the heavenly bodies vis-à-vis the constellations was an extremely useful tool to calculate the distance of different geographical locations from one another.Footnote ⁵¹ But the involvement of the heavenly bodies came with a catch, as they channeled the divine will onto the realm of generation and decay. This resulted in many scholars producing tracts about different physiological, physiognomical, and personal characteristics of the peoples of different geographical locales in accordance with the astrological properties of these locales.Footnote ⁵² Geography itself impacted the admixture of different humors in the human body, which in turn impacted humans’ medical conditions. As Olsson remarks, “In the medieval Islamic worldview humoral pathology and the theory of the climes proved to be particularly well-suited bedfellows.”Footnote ⁵³ Different people reacted differently to different medications since their humoral mixture differed according to their place of origin. Knowing when and under what astrological conditions someone was born was important for determining the kind of treatment they should receive for certain ailments.Footnote ⁵⁴ This was all possible through the infinitely connected cosmos that medieval Islamic intellectuals had constructed.Footnote ⁵⁵

It should be noted, however, that the acceptance of the cosmology’s theoretical framework did not mean that scholars accepted the validity of every discipline that was permitted therein. The opposition to the validity of some disciplines such as astrology and alchemy manifested itself in different forms. As I have already mentioned, some philosophers such as Ibn Sina, Ibn Rushd, and Maimonides objected to the validity of astrology on the grounds of the impossibility of producing reliable knowledge about the subject. Even al-Ghazali’s objections to astrology followed the same pattern, with him characterizing the science as “pure guessing.”Footnote ⁵⁶ But al-Ghazali also believed that astrology, much like medicine, had the capacity to uncover God’s manner of intervention in the world.Footnote ⁵⁷ This was in fact, not a position unique to al-Ghazali since other scholars found benefit in astrology insofar as it helped reveal natural laws that were set by God, as they enabled humans to appreciate God’s power and creation.Footnote ⁵⁸ The same issue, however, caused some Muslim scholars, such as Ibn Qayyim al-Jawziyya (d. 751/1350), to condemn the pursuit of astrology and alchemy, as Livingston argues, for the hubris that al-Jawziyya saw in some people’s claims to have uncovered the secrets of the cosmos – secrets that he believed belonged to God and God alone.Footnote ⁵⁹ Interestingly, this position was also held by Ibn Sina as well, who according to some modern scholars was not a true Muslim, having been too much steeped in the Hellenistic worldview.Footnote ⁶⁰ In his refutation of astrology, the philosopher informs his readers that humans are incapable of possessing the kind of knowledge that is reserved only for God by invoking a verse from the Qur’an (Q 27:65 “Say: None in the Heavens and Earth knows the unseen except for God”).Footnote ⁶¹ In either case, what was being objected to was not the theoretical validity of the disciplines, but the charlatanry and hubris of those who claimed to practice them: astrologers and alchemists.

As a mathematical discipline, music was no different from all the other sub-branches. Numbers and numerical operations were crucial in determining the nature of ratios. But the soul and its various faculties were key to understanding how consonance and dissonance were perceived by humans.Footnote ⁶² For the so-called Pythagorean philosophers such as al-Kindi and Ikhwan al-Safa (probably active in the third/ninth century), the soul had a significant impact on how different people were influenced by different kinds of music. Many of these philosophers composed treatises explaining how different types of music affect people according to their physiological predispositions. Al-Kindi went as far as mapping certain strings of the musical instrument ʿūd to different humors, seasons, parts of the day, constellations, etc.Footnote ⁶³ But even for al-Farabi and Ibn Sina, the cosmological connections comprised a part of the discourse on the science of music as well. Thus al-Farabi argues that natural perception of consonance and dissonance closely follows geography: peoples who reside between fifteen and forty-five degrees in latitude (e.g., Arabs, Persians, the Greek, and Romans) have the most natural of tastes in life, drinks, foods, and presumably music. Others living outside this zone (e.g., Nomadic Turks and Slavs) do not benefit from such natural tastes.Footnote ⁶⁴ Although al-Farabi does not provide the rationale behind the more “natural” inclinations of the peoples of his ideal zone, the impact of the Aristotelian/Ptolemaic cosmology, to which he himself was an adherent, is undeniable.

One is bound to ask why the question of the effects of music on humans, a subject that can hardly be abstracted from the realm of generation and decay, is being discussed under the rubric of music, a decidedly mathematical discipline. This question can be answered through the interconnected nature of the medieval conceptualizations of the cosmos and the subsequent categorization of the sciences according to this cosmology. Different people’s souls were created under different circumstances, which meant that they possessed different compositions of humors. This also meant that they responded to melodies and melodic modes in different ways. At the same time, the interconnected nature of the medieval body of knowledge meant that all these discussions would be relevant to the science of music. As demarcated and delimited as the science of music was, it was still a part of an intricate system of knowledge that connected the entirety of the cosmos (both macro and micro) to each other through an infinite web of cosmic relations.

One last note should be raised about al-Farabi’s critiques against Pythagoreans and their cosmological doctrines regarding the music of the heavenly bodies. On the one hand, al-Farabi in no uncertain terms refutes the idea of the heavenly bodies producing any sound.Footnote ⁶⁵ On the other hand, as a philosopher of the medieval Islamic world, he believed in the same cosmology that enabled such “Pythagorean” arguments. Furthermore, as I pointed out, he relied on Neoplatonic cosmological doctrines that are linked to the heavenly bodies to justify his selection of the peoples of the temperate regions of the world as those with the most “natural” tastes. How do we reconcile al-Farabi’s adherence to the Aristotelian/Ptolemaic cosmology with his objections to the music of the cosmos in light of the medieval understanding of mathematics and music?

Let us take a closer look at his statement regarding the music of the cosmos. As Yaron Klein points out, al-Farabi’s objections to this notion are on two grounds. First, there are physical principles according to which heavenly bodies cannot emit sound. Second, most of what is considered music is a human phenomenon and thus, even if heavenly bodies did emit sound, they would not be subject to the science of music.Footnote ⁶⁶ As for the first point, Klein is correct in asserting that al-Farabi does not believe in the heavenly bodies emitting sound: According to al-Farabi, “the heavens and the spheres and the planets cannot produce sound with their movement.”Footnote ⁶⁷ But the key term here is sound and the key issue is its production. That the heavenly bodies cannot produce sound does not mean there will not be any music coming from them. For as al-Farabi himself points out, there need not be sound for there to be music. In other words, al-Farabi’s objection is to the notion of the heavenly bodies having audible music. As for inaudible and imperceptible music of the heavenly bodies, al-Farabi says nothing. If anything, according to his own arguments, one should be able to conceive of the music of the spheres without hearing it. Al-Farabi’s objection is more directed toward those who claim they can hear the music of the cosmos. In other words, much like Ibn Sina and his objections to the practitioners of astrology, al-Farabi’s objection here is to the charlatanry of those who make claims about hearing the music of the cosmos (i.e., Pythagoreans) and not to the music of the cosmos per se.

As for the second point, Klein is correct in identifying al-Farabi’s inclination toward a humanistic approach to music. Al-Farabi invokes the role of conceptualization (taṣawwur) and imagination (takhayyul) that arise from the human soul in composing melodies.Footnote ⁶⁸ But where does the human soul receive its own inspiration? Other than a few scarce references to fiṭra (natural disposition) and ghariza (instinct), al-Farabi is mostly silent on this issue in his Kitab al-Musiqi al-Kabir.Footnote ⁶⁹ After all, the book is about music and not the relationship between humanity and the cosmos. He does, however, discuss this issue in his other works, including his Virtuous City. There, he discusses human soul and its different faculties, one of which is the imaginative faculty whose task is to retain sensible impressions that are no longer (physically) present. At the outset, it is clear that this faculty would have much to do with mathematical existents, as they encompass things that need to have matter but can be conceived of without the presence of the said matter. The faculty is also responsible for combining and separating sensible experiences to and from each other to form new compositions, some of which will be true and others false.Footnote ⁷⁰ In fact, al-Farabi directly mentions these true and false impressions in the Kitab al-Musiqi al-Kabir confirming that in the case of music he indeed has the imaginative faculty in mind as the responsible faculty.Footnote ⁷¹ But this faculty is the same faculty that can receive divine revelations and other forms of inspiration for people with more perfect imaginative faculties through the intermediary role of the active intellect. Obviously, the most perfect imaginative faculties belong to the prophets. But other individuals also can have access to less perfect imaginative faculties through which they can receive suprahuman inspirations. The active intellect itself is responsible for governing the sublunar world together with the second intellects, which are one and the same as the celestial bodies.Footnote ⁷² In other words, despite his insistence that the celestial bodies do not produce sound, his cosmology necessitates their involvement in the production of music through their relationship with the active intellect and its role in providing humans with inspiration.

Taken out of context, al-Farabi’s critiques of Pythagoreans seem to suggest he is against any kind of involvement of the heavenly bodies in music production. But when we put his arguments in the larger context of his cosmological system, we can see that, in fact, he could not have denied the impact of the heavenly bodies in musical (or in fact any other human) affairs. It is this same context that enables music to be a part of the mathematical sciences; the same context that allows post-Farabian philosophers such as Ibn Sina to consider mathematics itself as one of the classes of the speculative philosophy that deals with the existents whose conceptualization can be independent of their material existence. Far from our modern understanding of it, this is the science of music whose production and education will be examined in the following chapters of this book.