Contrary to modern practice, ancient Greek musical theorists conceived of the pitch of scales as descending, not ascending. They regarded the octave as being built from two tetrachords and a whole tone. Ancient Greek music always seems to have used two identical tetrachords to build the octave. The single tone could be placed between the two tetrachords (between perfect fourth and perfect fifth) (termed disjunctive), or it could be placed at either end of the scale (termed conjunctive). The Greater Perfect System (Systêma Teleion Meizon) was composed of four stacked tetrachords called the Hypatôn, Mesôn, Diezeugmenôn and Hyperbolaiôn tetrachords. They span the 15 notes of two descending octaves.

A harmonic interval is two notes played together. A harmonic chord is three or more notes played together. A tetrachord allows the possibility of the playing of (⁴C₁=4) separate notes, (⁴C₂=6) harmonic intervals, (⁴C₃=4) melodic chords of three notes and (⁴C₄=1) chord of four notes, i.e., 15 "sounds"). They include (6+4+1=11) harmonic intervals/chords. If we consider two octaves A-A′-A′′ built from conjoint and disjoint tetrachords, the number of sounds playable with the tetrachord BCDE is 15 (14 other than the single note E). Therefore, the number of sounds playable with the two conjoint tetrachords B-C-D-E & E-F-G-A′ = 2×14 + 1 = 29 (the 15th odd integer). Including the single note A and the harmonic interval playable with A & B, the number of sounds playable in the octave A-A′ = 29 + 1 + 1 = 31, the number value of EL, Godname of Chesed. Similarly, the number of sounds playable in the two conjoint tetrachords B′C′D′E′ & E′F′G′A′′ = 29, so that, including the harmonic interval playable with A′ & B′, the number of sounds playable in the octave A′-A′′ = 30. The total number of sounds playable in the two octaves A′-A′′ of the Greater Perfect System = 31 + 30 = 61. This is the 31st odd integer, showing how EL prescribes the Greater Perfect System.

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