This research point is about different tuning systems used throughout history and in different parts of the world. The task is to write about 400 words on the topic, but as I have once again delved quite deeply into the subject, I decided to do a much longer four-part series of posts. I will talk about ancient tuning systems in the first two, while the third will cover the period between Gothic music and Romanticism in order to reach the modern systems in the final post.
Out of an infinite continuum of pitch, the idea of tuning systems developed in music as an organizational tool that serves to define particular pitches that will be used in performance in relation to one another, providing neutral models of interval size for the hierarchical distribution of tones in scales. The early tuning systems had no fixed pitch reference, and as such, represent relative-pitched quantifications or calculations of mathematic ratios. Tuning systems around the world and in different historical periods emerged for the musical needs of their culture, as well as to meet the special requirement of specific instruments, which comparing to the voice, necessitate the determination of precise pitches in order to be played. (Britanica) In this way, the earliest pitch-related concepts formed in relation to the construction of instruments and their tuning processes, preserved not only orally and in notation, but also in the traditional practice of building instruments to the certain traditional specifications. (music and memory)
Recorded through the cuneiform texts, the Ancient Near East was the seat of one of the oldest developed music systems in the world, where the comprehensive pitch palette was formed on the idea of dichords, referring to string pairs of the ancient lyre, which classify a series of seven descending pentads and seven ascending triads. (Fig. 1) According to Dumbrill, the tonal space was organised into the fundamental descending linnear enneatonic system consisting of two conjoined pentachords in relation to a central pitch, construed on the archetypal lyre fitted with nine strings. Unlike the Western ascending order of the pitches, the order corresponds to the palindromic numbering 1-2-3-4-5-4b-3b-2b-1b of the lyre, where the “tonic note was the axis of symmetry of the system. Supertonic and subtonic were, respectively, one step above and one step below the tonic; mediant and submediant were each a third above and below the tonic, and dominant and subdominant were a fifth above and below the tonic.” (Fig. 2) There were nine enneatonic sets and the ambitus of the Greater Babylonian System could expand to 11, 13, 15 and 17 pitches, always arranged in symmetry from the central common pitch. In terms of quantifying the pitches, Crickmore asserts that the theoricians used sexagesimal arithmetics from their standard tablets of reciptocals, which represented an early type of just tuning, in which the pitches resulted from the ratios of small whole numbers. While initially diatonic in the theoretical construction, certain inflixes were present in the practical music-making to express the mood of music. Interestingly, in the first millennium BC, the system became cyclical, whereby the linear system was bent into a hexagram, based on the alternation of fifths and fourths, with the two extreme/opposite pitches now overlapping each other, creating a heptatonic model. However, this is only in the sense of heptatonicism being a ‘subsystem of enneatonism’, since the concept of the octave was ‘hitherto unknown in the Near East’, being unstable as expressed in the sexagesimal ratios. In this setting, the pitches beyond the original range don’t necessarily stand precisely an octave apart from the already established note, and so, an extended pitch set may not merely repeat the exact pitches at an octave.
Not only was the tuning system of the Ancient Near East embryonic of the Maqam theory and modality established in the Golden age of Islam, with the earliest scales being formed of pentadic and triadic ajnas not dissimilar to the triads and pentads that formed the enneachic sets, but its scholarship also spread to the Ancient Greece from the late eighth century BC, during the Orientalizing Period. Here, the imported principles of diatony were encrypted in the tradition as Terpander’s legendary invention of the seven-stringed lyre that challenged the old Greek music-making, which might have actually been the re(-invention) of the Near Eastern diatonic tuning system for the new heptatonic Greek instrument. The seven-string lyre, whose two outermost strings were tuned octave apart, introduced the concept of octave as a fundamental unit of division for tuning, which has the unique property that its two notes are felt in some indefinable way to be ‘the same, but different’, having twice the frequency of the other, under the ratio of 2:1. Especially important in this regard are Eratocles and his pupils, who demonstrated how the intervals can be transferred from one end of the octave to the other. Although the idea had little practical importance at the time, it became the central concept of the Western music theory, where the notes that have frequencies which are successive doublings of the same fundamental are referred to be of the same pitch class. The lyre also produced the idea of tetrachord units, internally structured by a tone that separates a lower fourth from the upper within the heptatonic setup. With the strings that were added to produce modulating tones, there was a development of the chromatic tonal division. On the other hand, aulos pipe was another common instrument in Greece that allowed for the use of microtones, which were codified into the enharmonic tonal division. Both the chromatic and enharmonic tonal divisions were unique to Greece and could have represented the continuation of roots much older than any musical importations from the Near East. In any case, as the instruments grew more versatile, there was a conception of a model arrangement of pitches, the linear Perfect system, with the ambitus of two octaves. It is conceived in the tetrachordal framework, whose two inner moving notes can be tuned in various ways, being able to build any of the three divisions or genera – imported diatonic and possibly indigenous chromatic and enharmonic. These were systematized into a comprehensive description of the modulating tonal space by Aristoxenus, which consisted of the cycle of fifths in thirteen keys and an infinite number of possible microtonal shades. However, while Aristoxenus drew together the strands of practice-oriented theory, advocating for empiricism and the judgement of the ear in regard to specific intervals as superior to mathematic ratios, there was a more speculative branch of music theory associated with Pythagoras, which came to be separated from the practical music-making.
Emancipating itself from the banalities of the actual practice of music in order to contemplate hypothetical cosmic harmonies, the tuning system as defined by the Pythagoreans came to abstract pitch relations on the monochord and similar experimental instruments designed for the specific purpose of studying intervals through numerical descriptions of ratios. Using mathematical calculations, by alternating mathematically pure fifths and fourths up to the point of no gap being larger than a tone, the resulting diatonic scale consists of the arrangement of ideal whole tones that are 204 cents, and lammas, small semitones that are 90 cents. In this setting of pure fifths and fourths, there is a compromise on the resonance of the third and the sixth, which much of Western music theory will be concerned with from the Rainassance on, especiqlly with the development of the choral harmony. The tension between the abstracted Pythagorean music theory, which priviledged the ideal diatonic scale constructed through mathematical means, and the empirical Aristoxenian system, which established the three genera on equal par with infinite possible microtonal shades from the practical perspective, was somewhat resolved by Ptolemy. Formulating his tuning system on the idea that the ear and the ratios should be in agreement, he applied the mathematical layout to create a set of seven keys in all genera and several shades using superparticular ratios, but only bridging the Pythagorean mathematics and the Arisroxenian system on the lyre. While Quintilianus also used a similar combination of Pythagorean and Aristoxenian ideas, with Boethius, who transmitted the Greek theory into the Middle Ages in Latin, the Pythagorean diatonic approach became dominant in the West, despite being heavily influenced by Aristoxenian concepts, which suited not only the unisonal Gregorian chant, but also the early attempts of polyphony in the parallel fifths and fourths of the organum. However, when the third and the sixth became imperfect consonants, the Pythagorian tuning was increasingly considered too rough, sharp or flat and so the process of its softening or tempering began, with Zarlino interestingly turning to Ptolemy’s syntonic diatonic tuning, which coincides with the modern just intonation, although Pythagorean tuning still remained influential. (More on this subject, see my next post)
Contrasting the West and its neglect of the Ancient Greek tunings in the chromatic and enharmonic genera with microtonal shades, such as the ones described by Aristoxenus, Ptolemy and similar theorists, the Medieval Near East came to inherit them with the fading memory of its own musical past when the cuneiform sources became obsolete. In this curious twist of fate, the scholars also lost knowledge of any Ancient Near East antecedence in the Greek tuning systems, since the Greeks themselves were not willing to give any credit for the borrowed diatonic heptatony that helped formulate the theoretical blueprint for its other two genera and the tonal space in general. With occidentalisation, the octavial concept was adopted at the expense of ennaetonicism, and the tetrads, inspired by tetrachords, were added to pentads and triads in the construction of heptatonic scales. However, the enneatonic framework wasnt completely discontinued, being mentioned, discussed or illustrated since the first millennium in the works of Plato, Boethius, Kircher and in the Byzantine musicology.
Leaving aside the entangled web of influences between the Near East and Greece, the next post will focus on the discussion of the Far Eastern ancient tuning systems in India and China.