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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 possibilty
of the playing of (^{4}C_{1}=4) separate notes, (^{4}C_{2}=6) harmonic intervals,
(^{4}C_{3}=4) melodic chords of three notes and (^{4}C_{4}=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 **15**th 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 **31**st odd integer, showing how EL prescribes the Greater Perfect System.

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