The Greater and Lesser Perfect Systems

1. The Greater Perfect System (Systêma Teleion Meizon) comprises the Tetrachords Hypatôn, Mesôn, Diezeugmenôn and Hyperbolaiôn.

2. The Lesser Perfect System (Systêma Teleion Elasson) comprises the Tetrachords Hypatôn, Mesôn and Synêmenôn.

3. The complete system above, comprising the Greater and Lesser Perfect Systems, is called the Unmodulating or Immutable System (Systêma Ametabolon).

4. Asterisks represent Fixed Notes in the systems. See The Four-String Lyre of Hermes and The Planetary Heptachord for more on the Fixed Notes.

5. A Tetrachord includes both of the Fixed Notes (*) that bound it; see also The Five Tetrachords.

6. The Greek Note names are normally modified by the Tetrachord in which they occur (Nêtê Hyperbolaiôn, Nêtê Diezeugmenôn, etc.).

7. 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.

8. See Meanings of the Greek Names of the Notes and Tetrachords for an explanation.

9. 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.).

10. The correspondences with the Vowels, Planets and Zodiacal Trigons are given by Aristides Quintilianus (I.13, 14, III.21).

11. There is a chart of the Zodiacal Trigons.

12. 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.

13. 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.

14. The Double Octave of the Greater Perfect System is the primary harmonic structure of the Pythagoreans (Barker II.11).

15. 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."

16. 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).

17. 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).

18. 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:

    Week	Phase	Tetrachord
    	New	A
    1	First Sighting to First Q.	B, C, D, E
    2	First Q. to Full	E, F, G, a
    3	After Full to Third Q.	b, c, d, e
    4	Third Q. to New	e, f, g, aa

19. 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.

20. The Roman Notes may be continued for another octave (QRSTVXZ = bb-aaa), which completes the 22 letters of the classical Roman alphabet.

    Extended Roman Note:	Q	R	S	T	V	X	Z
    Modern Note:	bb	cc	dd	ee	ff	gg	aaa

    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:

    A	B	C	D	E	F	G
    H	IJ	K	L	M	N	O
    P	Q	R	S	T	UVWY	X
    Z

21. The 22 Roman Notes invite Tarot correspondences.

22. 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).

23. In its central octave the Alypian notation assigns one of the 24 Greek letters to each of the Eight Notes in the Three Genera.

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Last updated: Sun May 9 22:53:06 EDT 1999