How were tetrachords used in ancient Greek music theory?

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scale The universality and innate nature of music, and the pentatonic scale, as demonstrated by singer Bobby McFerrin.

In ancient Greek music, the tetrachord—a series of four notes spanning a perfect fourth—served as the fundamental unit of analysis. Unlike modern Western usage, these were typically conceived as descending sequences.1

Scale systems, known as the Greater and Lesser Perfect Systems, were constructed by linking these tetrachords together. While the outer notes of a tetrachord remained fixed, the internal pitches were flexible, defining the specific genus of the scale:1

Diatonic: The basic form, characterized by a sequence such as a–g–f–e.1
Chromatic: A modification featuring pitches such as a–f♯–f–e.1
Enharmonic: A specialized form involving microtonal intervals, such as a–f–e+–e♮, where e+ represents a pitch between e♮ and f.1

The theorist Cleonides provided significant documentation regarding these structures and their genera during the 2nd century CE.1