Standard definitions of meter, such as those in New Grove, categorize rhythmic structures strictly as “duple or triple” and “simple or compound.” Under this taxonomy, a 6/8 measure is rigidly defined as “compound duple,” ontologically distinct from the “simple triple” of 3/4. This paper challenges these boundaries by proposing a distinct, objective rhythmic category: Sextuple Meter. Rather than a derivative of duple or triple time, Sextuple Meter is an autonomous temporal architecture built on senary modules—cycles of six primary time units (chronoi/azmina)—that act as a fixed container for duple or triple subdivisions without disrupting the fundamental flow.

This theoretical foundation is traced through a lineage of five key figures: Aristoxenus, Aristides Quintilianus, St. Augustine, Al-Fārābī, and Francisco de Salinas. Operating within a Mediterranean and Near Eastern tradition that prioritized the fixed temporal period, Aristoxenus provided the initial mathematical proof, identifying senary feet as the only magnitude capable of equal (1:1) and double (2:1) divisions.

This senary logic survived through St. Augustine, who justified alternating duple and triple divisions within the six-unit period, and reached its sophisticated peak with Al-Fārābī (10th c. CE). By defining rhythm through the physical strike of a plectrum, Al-Fārābī established a system where meters act as flexible containers, provided the total duration of the cycle remains constant.

Finally, Francisco de Salinas (16th c.) bridges this ancient quantitative theory with the early modern world by applying classical senary feet to the Spanish romance. Building on David Wulstan’s research into the Ionic-Anacreontic meters, this paper demonstrates the survival of these senary structures—a 12-unit cycle naturally oscillating between BBLL BBLL and BBLB LBLL—in both medieval monody and contemporary practice.

By establishing the “container before the content,” this model views metrical alternation as an inherent, generative feature of a unified senary system that has survived in continuous practice since ancient times. Ultimately, we must return to these expansive historical frameworks to transcend current metric constraints and reclaim a richer understanding of the longue durée of musical time.

This paper presents a taxonomy of phrase endings in traditional qin music through a pioneering corpus study of four of the earliest surviving qin anthologies from the Ming Dynasty (1368–1644 CE): Shenqi Mipu 神奇秘譜 (1425), Wusheng Qinpu 五聲琴譜 (1457), Xilutang Qintong 西麓堂琴統 (1525), and Songxianguan Qinpu 松弦館琴譜 (1614).

A seven-string plucked melodic chordophone, the qin boasts a vast traditional repertoire preserved in jianzipu 減字譜, a tablature notation using elements of Chinese characters (Yung 1984). Hu 2024 has argued that “harmony in diversity,” or the sounding of pitches related by interval class (ic) 0 that are articulated differently, is the primary way a traditional qin phrase ends. Seeking empirical evidence for Hu’s theory, I examine all marked phrases in the corpus by realizing them on the instrument while consulting treatises on historical qin fingerings (Guan 2020 [1967]), theories of punctuation marks in ancient Chinese literature (Guan 2002), historical theories by Chen Zhuo (c. 9^th century) and Zequan the Monk (?–1045), and contemporary interpretations of these anthologies (Wu 2008; Zhu 2011). The resultant data is consistent with Hu’s theory while revealing an additional type of “harmonious” ending by ic 5 and “non-harmonious” endings by ics 4, 3, 2, and 1: Among the 13623 examined phrases, 12633, or 92.7%, are “harmonious,” while 990, or 7.3%, are “non-harmonious.” I also discuss two emergent subcorpora, or notable data subsets discoverable only through a large-scale survey, related to the seemingly heterogeneous endings by ic 0.

The strikingly uniform distribution of phrase ending types across the corpus suggests that Ming Dynasty qin practitioners shared a common understanding of phrasing. More importantly, these “harmonious” intervallic options enable multiple contrasting interpretations of the same jianzipu score—a higher-level “harmony in diversity” in line with qin music’s aesthetic of favoring personalized interpretations (Zhu 1425). By offering a taxonomy of qin phrase endings, this paper contributes to the interpretation of historical qin manuscripts and the theorization of large-scale musical forms in traditional qin music.

This paper argues that the duality between the Guidonian gamut and the Ancient Greek Greater Perfect System constitutes a unified theoretical framework in Marin Mersenne's Harmonie Universelle (1636). Through this framework, Mersenne dramatically expands the traditionaltreatment of octave species by integrating genera, interval species, modes, tuning systems, and permutations within a single theoretical structure. Given the interpretative challenges posed by Mersenne's seventeenth-century French, his characteristically enigmatic style, and the lack of terminological distinction between different species-sets, this paper clarifies his treatment of the ordinary species of the fourth and fifth and demonstrates how these function as generative components for constructing three distinct categories: ordinary, complementary, and extraordinary octave species.

The analysis begins from Mersenne's most expansive claim: the theoretical possibility of 5,040 octave species generated through all permutations of intervals within the octave, a radical expansion from the seven species of ancient Greek theory. I demonstrate that this figure is mathematically correct, deriving directly from factorial permutation, and make its underlying formula explicit. I further confirm the accuracy of Mersenne's reduction to 210 distinct speciesonce the actual intervallic content of the diatonic octave is applied, establishing the corresponding mathematical formulation.

I then clarify Mersenne's intermediate sets of 24 and 22 species, whose conceptual and mathematical foundations he leaves largely implicit. A reconstructed Combinational Hexachordal Octave Species System reveals the structural interaction between ordinary and complementary species, showing how the latter fill gaps left by the former. My analysis of the extraordinary species, however, uncovers a previously unnoticed inconsistency: Mersenne's claim of 22 possible configurations in fact yields only 21 distinct arrangements, pointing to an unrecognized redundancy that necessitates revising the extraordinary species count to six. While Ellie (1979) and van der Miesen (2025) have partially investigated Mersenne's theoretical writings, the third book of Harmonie Universelle remains largely understudied.

Following Redwood (2023), I argue that this exhaustive enumeration serves not a practical compositional aim but a theological one: by mapping every possible configuration within a finite musical system, Mersenne seeks to manifest the rational perfection of creation and demonstrate the existence of God through number, order, and combinatorial completeness.