The Greater and Lesser Perfect Systems
The study of Greek Esoteric Music is a lifelong pursuit, due to the quantity of surviving theory (much of it collected in Barker, its subtlety and complexity, and its connection with other Esoteric Disciplines (e.g. numerology, astrology, theurgy and alchemy). To this must be added two millenia of later esoteric investigations of Greek music.
The present work is primarily a set of annotated and cross-linked charts to serve as an introduction to the theory and practice of Greek Esoteric Music. The focus is on the esoteric aspects, including practical exercises, as opposed to the theory and practice of mundane music (interesting and worthwhile though that be).
The Greater and Lesser Perfect Systems
The Greater Perfect System (Systêma Teleion Meizon) comprises the Tetrachords Hypatôn, Mesôn, Diezeugmenôn and Hyperbolaiôn.
The Lesser Perfect System (Systêma Teleion Elasson) comprises the Tetrachords Hypatôn, Mesôn and Synêmenôn.
The complete system above, comprising the Greater and Lesser Perfect Systems, is called the Unmodulating or Immutable System (Systêma Ametabolon).
Asterisks represent Fixed Notes in the systems. See the four string lyre of Hermes and The planetary Heptachord for more on the Fixed Notes.
A Tetrachord includes both of the Fixed Notes (*) that bound it; see also The five tetrachords.
The Greek Note names are normally modified by the Tetrachord in which they occur (Nêtê Hyperbolaiôn, Nêtê Diezeugmenôn, etc.).
The complete Greek Note names can be read off the chart: Proslambanomenos, Hypatê Hypatôn, …, Likhanos Hypatôn, Hypatê Mesôn, …, Likhanos Mesôn, Mesê, Tritê Synêmenôn, …, Paranêtê Hyperbolaiôn, Nêtê.
See Meanings of the greek names of the Notes and Tetrachords for an explanation.
The absolute pitch of the Greek scales is uncertain, and was probably never fixed as definitely as modern pitch. Therefore, I have identified the modern A with the Roman A, from which it was derived, and hence with Proslambanomenos, which is equivalent to Roman A (Pole 99-100). In working with the Roman Notes, it is convenient to start each octave with A (ABCDEFG, abcdefg etc.), rather than with C as is conventional now (CDEFGAB, cdefgab, etc.).
The correspondences with the Vowels, Planets and Zodiacal Trigons are given by Aristides Quintilianus (I.13, 14, III.21).
There is a chart of the Zodiacal Trigons.
The Vowels follow a cycle Alpha-Eta-Omega (AÊÔ), except at the foundation points Proslambanomenos (A) and Mesê (a), both corresponding to Epsilon, and in the Tetrachord Synêmenôn, which corresponds to the Fixed Stars.
Aristides Quintilianus is not explicit about the order of the Planets in the Upper Octave (K-P = c-aa). Barker (II.523n179) thinks it is most likely that they occur in the same order as in the Lower Octave, as shown here. However, Aristides says,
But the Planets have Two-fold Powers, since They exercise one kind of power by night, another by day. Again, then, we shall assign to each of Them one of the remaining Notes, on the principle of opposition to Their daytime powers…
This suggests the possibility that the upper Planetary Spheres are a mirror image of the lower, with Moon to Saturn corresponding to the decreasing pitches P-K = aa-c. The Diazeuxis or whole-tone Gap of Disjunction (between Mesôn and Diezeugmenôn) separates the Lower Planets from the Upper.
The Double Octave of the Greater Perfect System is the primary harmonic structure of the Pythagoreans (Barker II.11).
The basic meaning of Harmonia is a fitting-together. The Pythagorean Philolaus (fr. 10) says, “Harmonia comes to be in all respects out of opposites: for Harmonia is a unification of things mutually mixed, and an agreement of things that disagree.”
The 15 notes of the Greater Perfect System correspond to the 15 days of the waxing Moon and again the 15 days of its waning (P = aa representing the full moon and A the new moon).
Alternately, Ptolemy (III.ch 13) allots the Four Tetrachords of the Greater Perfect System to the four phases of the Moon and of the other Planets: Hypatôn is First Sighting (after conjunction) to First Quarter, Mesôn is First Quarter to Full; Diezeugmenôn is from after Full to Third Quarter, and Hyperbolaiôn is Third Quarter to New. Phases on opposite sides of the circle of phases are an octave apart and thus form a complementary whole. For example the First Quarter is Hypatê Mesôn (E) and the Third Quarter is Nêtê Diezeugmenôn (e). The Full Moon is Mesê (a) and the New Moon is simultaneously Proslambanomenos (A) and Nêtê Hyperbolaiôn (aa); it is called Old-and-New in Greek. The identification of these two notes is the rule whenever the GPS is treated cyclically (Barker II.19, 21).
Ptolemy’s correspondences for the Greater Perfect System can be used to pick a Tetrachord to work with during each week of the Lunar Month:
In working with the Greater Perfect System it is preferable sometimes to raise the Vowels and Planets one tone in the lower octave (i.e., B = Alpha = Moon, C = Eta = Mercury, etc. to a = Omega = Saturn). In this case Proslambanomenos is identified with the Earth. Such a system appears in a Greek manuscript (Jan, Mus. Scr. Gr. 30), as well as in A. Kircher’s Musurgia Universalis (1650). However, the more correct system has Proslambanomenos = Moon, since (as the early Pythagorean Philolaus explains) the Moon represents the entire Sublunar or Mundane realm, which includes the Earth.
The Roman Notes may be continued for another octave (QRSTVXZ = bb-aaa), which completes the 22 letters of the classical Roman alphabet.
The alphabetic correspondences may be used for translating words and phrases into melodies. It is reasonable, although not necessary, to reduce them to a single octave to avoid large leaps. Replace post-classical Roman letters (J, U, W, Y) by their classical equivalents; that is, I = J (note b) and U = V = W = Y (note ff). Here is a summary chart for convenience:
The 22 Roman Notes invite Tarot correspondences.
Likewise, the Ancient Greek musical notation, which was preserved by Alypius (and perhaps dates to the 5th cent. BCE), extends over three octaves and an additional whole tone, which is to say 22 notes (Anderson 203-4).
In its central octave the Alypian notation assigns one of the 24 Greek letters to each of the Eight Notes in the Three Genera.
The Four-String Lyre of Hermes
Henricus Glareanus (1547) says that the original Lyre of Hermes had three strings, corresponding the three original Seasons of ancient Greece (Summer, Spring, Winter, from high to low). He says that Orpheus added the fourth string, corresponding to Autumn, when that Season was adopted from the East. Most sources, however, attribute the Four-String Lyre to Hermes. (Godwin HS 198)
It is generally believed that the Homeric Phorminx (Lyre) had three or four strings. Some believe that they were tuned to the Musical Tetractys E-a-b-e as given here; others believe they were tuned to A-B-C-E or to the Elemental Tetrachord A-B-C-D (Anderson 47, 63, 199; Godwin HS 194, 451n16). This chart accepts the Tetractys tuning (6:8:9:12), because of its esoteric importance.
Thus the Four Strings of the Musical Tetractys define the Fixed Notes of the Greater perfect system of tuning. They are the stable harmonic structure (Eabe) that defines the Disjoint Tetrachords of the Planetary Heptachord (E[FG]ab[cd]e).
All the most ancient Greek musical instruments seem to be based on Four Notes.
Plato’s Phaedrus (108d4) alludes to the Art of Glaucus (Glaukou Tekhnê): The Pythagorean Hippasus made four metal disks whose thicknesses were the Musical Tetractys and Glaucus discovered how to play them. (Barker I.30-1)
The Aulos (a reed instrument) often has four finger holes (Barker I.15; Anderson 141). Normally the Greeks played Double Auloi, each having four holes, perhaps corresponding to the two disjoint Tetrachords of the octave. Likewise some early Lyres have eight strings in two groups of four. See The Planetary Heptachord on the two Tetrachords in the Octave.
The Musical Tetractys defines the ratios of the fundamental intervals of Pythagorean Harmony: 6:12 = the Octave (1:2), 6:9 = 8:12 = the Fifth (2:3), 6:8 = 9:12 = the Fourth (3:4), and 8:9 = the whole tone. The structure is two interlocking Fifths (6:9, 8:12), which are equivalent to two Fourths (6:8, 9:12) and the Tone of Disjunction (8:9) between them (as in the Greater perfect system and the Planetary Heptachord). (Increasing numbers correspond to lower pitches because the numbers represent lengths.)
According to the Ikhwan al-Safa’ (Brethren of Purity, 9th or 10th c. CE) and Athanasius Kircher (c.1601-1680), the ratios of Earthly Harmony are embodied in the Cube, the Platonic Solid corresponding to the Element Earth, because the Cube has:
24 right angles
8 solid angles
Thus, 24:12 gives the Octave, 12:8 the Fifth, and 8:6 the Fourth. (Godwin HS 115, 269,439)
The correspondences between the Strings, Elements, Humors and Qualities are given by Hunayn (c.803-873 CE), the Ikhwan al-Safa’ (Brethren of Purity) and Isaac ben Haim (c.1467-after 1518). (Godwin HS 97, 113-4, 154)
The two interlocking Fifths correspond to the Opposed Elements: Fire/Water and Air/Earth.
According to Hunayn and Isaac ben Haim, some feelings and character traits associated with the Humors are:
Notice how opposing Humors (Yellow Bile vs. Phlegm, Blood vs. Black Bile, corresponding to opposed Elements) are associated with opposing feelings and traits.
The correspondences between the Qualities and the Seasons and Moon Phases are the usual ones in the Greek Tradition (e.g. Ptolemy Tetrabib. I.5, 8).
See The element tetrachord and the Ancient Greek Esoteric Doctrine of the Elements for additional Elemental correspondences to their explanation.
See The element tetrachord for the use and significance of the Plektrum (Pick).
(TO BE CONTINUED)
by John Opsopaus