The Planetary Heptachord

1. As discussed in The Greater and Lesser Perfect Systems, relative pitch is more significant than absolute pitch; the Modern Notes are conventional and chosen for convenience; their relation with the Greek and Roman notes is also discussed in The Greater and Lesser Perfect Systems.

2. The Planetary Spheres correspond to the Notes in several different ways depending on the purpose that is to be accomplished. This chart shows the most basic arrangement, in which higher notes correspond to higher spheres.

3. The Fixed Notes (Hestôtes), marked with "*", determine the basic harmonic structure of the system by determining the boundaries of the Tetrachords.

4. The fundamental structure of Greek harmony is the Elemental Tetrachord. Two Tetrachords are combined to construct a Planetary System.

5. The earliest Lyre had four strings and the earliest Aulos (reed flute) had four holes. The four notes may have comprised a Tetrachord or the Fixed Notes of an octave (see The Four-String Lyre of Hermes). Later both the lyre and aulos were expanded. The seven-string lyre was standard until Pythagoras (or Terpander) added an eighth string.

6. In the oldest harmonic system the two Tetrachords are conjoined into a Heptachord by identifying the upper tone of one with the lower tone of the other, as the Tetrachords Mesôn and Synêmenôn in the Lesser Perfect System. This yields an (ascending) interval structure STT STT (S = semitone, T = tone), with the Sun as Mesê, the Middle Note (in accord with Pythagorean Doctrine). The pitches can be written EFGAB^bCD or BCDEFGA. Some vase paintings show lyres with seven strings in groups of four and three, the latter higher pitched, suggesting conjunct Tetrachords (Anderson 63n11).

7. Pythagoras is credited with revising the Planetary System into an Octochord comprising two disjoined Tetrachords with a whole tone (the Tonos Diazeutikos) between them (as in the Tetrachords Mesôn and Diezeugmenôn in the Greater Perfect System and as shown in this chart). In this Octochord the (ascending) interval structure is STT T STT (e.g. EFGABCDE). Likewise some Middle Minoan lyres have two divergent sets of four strings (Anderson 6), suggesting disjoint Tetrachords. The result is an Ogdoad or Double Tetrad comprising the Seven Planets and the Eighth Sphere of Fixed Stars. (See The Elemental Tetrachord for the Double Tetractys of the Elements and their Qualities.)

8. The Planetary Heptachord may be extended by allotting the four lowest notes (Tetrachord Hypatôn and Proslambanomenos) to the four Elemental Spheres, as shown here. This "Elemental extension" can be found in Robert Fludd (Godwin HHE, 114-5).

9. Instead of representing all the Fixed Stars by a single pitch (e), we may make the "Astral extension" and allot the Tetrachord Hyperbolaiôn (e, f, g, aa) to the Four Trigons, in a manner similar to Aristides Quintilianus (see The Greater and Lesser Perfect Systems). When both the Elementary and Astral extensions are made, the system comprises two full octaves (A - aa).

10. The Movable Notes (Pheromenoi), with no "*", determine the Genus of the harmony. As shown in the chart, they are in the Diatonic Genus (a semitone and two tones, e.g. EFGA). If the upper Movable Note in a Tetrachord is flatted a semitone (e.g. G to Gb), then the Tetrachord is Chromatic. If the lower Movable Note is flatted a quarter tone (e.g. F to E+) and the upper Movable Note is flatted a full tone (e.g. G to F), then the Tetrachord is Enharmonic.

11. It is worth keeping in mind that the ancient Tone and Hemitone are not equivalent to the modern, equal-tempered Tone and Semitone. (The Semitone is a little larger than a Hemitone, but the equally-tempered Tone is a little smaller than a Pythagorean Tone.) The ancient scale may be approximated on a harp by tuning in Fifths and Fourths (as given in The Four-String Lyre of Hermes) until all the notes of the Diatonic scale have been determined. Discussion on these pages has been expressed in terms of the modern scale, but the Pythagorean tuning is truer to esoteric principles.

12. See The Planetary Heptagram for a diagram of the relation between the Notes, Planets and Days of the Week.

13. According to Ptolemy (Harm. III.16, Tetr. I.5), each of the Planets belong to a Dominion or Sect (hairesis, secta, conditio). The Sect of the Sun comprises the Sun, Jupiter and Saturn; the Sect of the Moon comprises the Moon, Venus and Mars; Mercury (the ambassador and boundary-crosser) belongs to both. In each Sect, the individual Planets have Offices; the nearest Planet is the Imperator (Master), the next is Beneficus (Bringer of Good), and the most remote is Maleficus (Bringer of Evil). The Dominion of the Sun is the realm of Day, which is predominantly Male, Warm and more Active; the Dominion of the Moon is the realm of Night, which is predominantly Female, Moist and more Passive. (See The Ancient Greek Esoteric Doctrine of the Elements for the meanings of these terms.) In each Sect, the Maleficus has an opposing character (Cool Saturn in the Sun's Sect, Dry Mars in the Moon's), which mitigates their malevolent character, according to Ptolemy. In playing or chanting the tones of the Planets, their characters should be considered.

14. Pairs of Planets that combine opposing properties (Warm + Cool, Moist + Dry) are considered especially beneficial, for example, Saturn + Jupiter, Mars + Venus. Combinations that combine the Cool and Moist (Saturn + Moon or Venus) are considered evil; those that are Warm and Dry (Mars + Sun or Jupiter) are considered treacherous (Barker II.391). These relationships should be considered in constructing melodies.

15. Obviously the Seven Vowels of the Greek alphabet correspond to the Planets and the Heptachord. This may be done in two ways (Alpha-high or Omega-high) to different effect. (See Godwin MSV for more information.) This chart uses the Omega-high system for several reasons. One is that the correspondence is more consistent with that given by Aristides Quintilianus in The Greater and Lesser Perfect Systems, especially with regard to the male and female characteristics of the Planets and Vowels (see The Elemental Tetrachord on the Vowels).

16. However, there are several purposes for which the Alpha-high arrangement is preferable. The later vowels (O, U, Ô) are deeper than the earlier (A, E, Ê) and are more like the denser elements and the lower chakra centers. Interestingly, ancient Greek musical notation used the alphabet for notes from higher to lower pitch, and the Seven Vowels come very near to defining a diatonic scale.

17. The Fixed Notes are defined by the fundamental numbers of Pythagorean Harmony, 12-9-8-6. The ratio 12:6 gives the Octave (E:e). The ratios 12:9 and 8:6 are the Fourths (E:a, b:e). The ratios 12:8 and 9:6 are the Fifths (E:b, a:e). See The Four-String Lyre of Hermes.

18. There is a relation of a Fifth (3:2) between corresponding notes of the upper and lower Tetrachords.

19. The Movable Notes in the Pythagorean Diatonic are defined by 9:8 for each of the two whole tones and by the "remainder" 256:243 for the semitone. The ratio of the Tone of Disjunction is also 9:8.

20. The entire Scale may be constructed by Fourths and Fifths (i.e., in terms of the Tetrachords), much as a musician would tune a lyre, harp or cithara.

21. According to Plato (Rep. 400a), the Scale may be constructed from the ratios 2:1, 3:2, 4:3 and 9:8.

22. Pythagorean Doctrine teaches that many Cosmic Relationships are revealed by the numerical ratios of the Notes. With the exception of the "Remainder," they are all Epimeric Ratios (i.e., N+1 : N), a bisexual pair of numbers (odd = male, even = female).

23. According to Ptolemy, the Pythagorean Archytas gave a different division of the Tetrachord: 9:8, 8:7, 28:27 from high to low. In some repects it is preferable, because of the smaller whole-number ratios (see also Pole, ch. XI).

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Last updated: Sun May 9 23:03:17 EDT 1999