(BEING CONTINUED FROM 30/03/11)
The primary diatonic tetrachord is semitone-tone-tone (ascending), that is, Water-Air-Fire-Earth, BCDE or EFGa. In the table the Elements are listed in their usual order, Earth-Water-Air-Fire, for the Greater and Lesser Perfect Systems are based on Earth.
The Elements and Qualities together constitute the Double Tetraktys, an Ogdoad (group of eight) comprising a complete octave (ABCDEFGa).(Werner 240-5) The Planetary Octachord is based on a Double Tetraktys.
In the Greek Tradition, the Directions (East, South, West, North) are correlated with the Qualities (Moist, Warm, Dry, Cool), the Seasons (Spring, Summer, Autumn, Winter), the Phases of the Moon (see The Four-String Lyre of Hermes) and all the Cycles of Nature. The Vowels may be intoned on their Pitches to the corresponding Directions.
The Vowel correspondences are given in Aristides Quintilianus (II.13), but date back at least as far as the sixth century BCE (Barker II.479n120). The correspondences between these and the Elements are given by Aristides (III.25).
The Vowels may be intoned on their pitches either with or without a preceding T- corresponding to Aithêr, the Fifth Element (see The Five Tetrachords). Aristides Quintilianus observes that the Fifth Element brings life to the four Mundane Elements. The T should be pronounced without any aspiration (puff of air), like an Italian T. The tones will sound like plucked strings, for the T is shaped like thePlektrum (Pick) and represents the Plektrum of Apollo’s Lyre, the Holy Ray of the Sun, which brings life to Earth. (Ar. Quint. III.25, Barker II.531n220)
In ancient Greek practice, the Plektrum was stroked toward the body, which is toward the lower-pitched, but higher-positioned strings (in the ancient manner of holding the lyre). In this way the Power of Apollo is drawn down into greater manifestation (Fire, Air, Water, Earth), which is the Sunwise motion from East to West. (Anderson 176) However, in earliest times no Plektrum was used (Anderson 36)
Aristides (II.13) says this of the long Vowels: Eta, which extends the mouth horizontally, is primarily female, fluent, emotional and passive; Omega, which extends it vertically, is predominantly male, dry, rigid and active. The short vowels Alpha and Epsilon are of mixed character, but Alpha is more male and Epsilon more female. The short vowel Omicron is also characterized as somewhat male; Iota and Upsilon are not mentioned. The primary Opposed Elements, Water and Fire, correspond to Alpha and Omega. (See also A Brief Guide to Ancient Greek Pronunciation for additional suggestions.)
Aristides Quintilianus’ (III.25) assigment of Genders does not agree with the usual Ancient Greek Esoteric Doctrine of the Elements (female Earth & Water, male Air & Fire), as reflected in theDeities. He explains that Water is male because it fertilizes the (female) Earth, and that Air is female because it is malleable and passive. Thus his gender assignments to the Vowels and Elements are mutually consistent.
To establish a correspondence between any Diatonic Tetrachord (comprising a semitone and two tones) and the Elements and Vowels, place the semitone between Water and Air, and assign the rest in order, as in the chart. Thus in D-major we can establish E-F#-G-A = Earth-Water-Air-Fire = Epsilon-Alpha-Eta-Omega.
Godwin (MSW 31) observes that the Vowels Upsilon and Omega were added to the alphabet after 403 BCE, so the earlier vowels were Alpha, Epsilon, Eta, Iota and Omicron. As noted above, the character of Omicron is similar to that of Omega. This suggests that the original Elemental Vowels might have been Epsilon (Earth), Alpha (Water), Eta (Air) and Omicron (Fire), with Iota left for Aithêr, the Fifth Element.
Harmoniai, Modes, intervals and melodies derive their character from the characters of the Notes in them (A.Q. II.14). The character of a melodic interval is a combination of the characters of its two bounding Notes.
When music is used for therapeutic purposes, one may pick music contrary to the undesirable condition in order to counteract it and restore balance; this is the Principle of Antipathy recommended by the Pythagoreans. Alternately, one may begin with music of similar character and then transform it in the desired direction; this is the Principle of Sympathy. If the nature of the condition is unknown, then experimentation may be necessary in order to find a Resonance between the music and the patient’s condition. See Aristides Quintilianus (II.14).
The Seven Harmoniai
The chart uses the Ancient Greek names of the Harmoniai (roughly, “modes”). Here we use the Greek forms of the names to distinguish them from the more familiar Eight Modes of the Middle Ages, which use the same names but in different ways. For example, medieval Dorian = ancient Phrygisti (Phrygian). (See The Eight Modes for the correspondence.) The Greek names are pronounced with the accent on the final “i.”
A Harmonia is a scale structure (a structure of harmonic ratios): an ordering of tones and semitones (or “remainders”); its absolute pitch is not significant. However the structure of any particular (diatonic) Harmonia may be described by the octave founded on a corresponding pitch in a modern major scale.
Each of the Dôristi, Phrygisti and Lydisti Harmoniai comprises a lower Fourth (two tones and a semitone) and an upper Fifth (three tones and a semitone). In the corresponding Hypodôristi, Hypophrygisti and Hypolydisti Harmoniai, the Fourth and Fifth are reversed. For example, STT+TSTT (EFGabcd) in Dôristi becomes TSTT+STT in Hypodôristi (abcdefg).
C-Major Degree gives the lowest pitch or Foundation Note of the Harmonia in the modern C-major scale. Thus the Dôristi Harmonia has the structure EFGabcd. The interval structure (STT T STT for Dôristi) is all that matters; the absolute pitch is irrelevant.
The Day for a “Hypo” Harmonia precedes the Day of the basic Harmonia; thus Hypodôristi on Monday precedes Dôristi on Tuesday. For the “Hypo” Harmoniai, the Planets are three away (i.e. a musical Fourth) from the corresponding basic Harmoniai (e.g. Saturn for Hypophrygisti is three above the Sun for Phrygisti). Likewise their Foundation Note is a fourth higher.
The correspondence between the Harmoniai, scale Degrees and Planets are given by Aristides Quintilianus (I.8, III.22), and are based on the Planet corresponding to the Foundation Note of the Harmonia as given in the Greater Perfect System. For example, Mars is associated with E, which is the Foundation Note of the Dôristi Harmonia.
The practice of singing of hymn in a different mode on each day can be traced back to Sumerian and Babylonian times (Werner 223-4, 244-5; Wellesz 152).
Therefore, on each Day of the week play or improvise a melody in the Harmonia corresponding to that day. Notice that the Foundation Notes of the Harmoniai of successive Days (Monday to Monday) proceed by the Circle of Fifths (AEBFCGDA). (See also the Planetary Heptagram.)
There are many undertainties about ancient Greek melodic structure, but the following may suffice for esoteric purposes. (For a discussion see Barker II.316nn3, 20; 336n78; Pole 122; Winnington-Ingram 4-9, 34-40, 46.)
The melody should emphasize or focus on the Dynamic Middle (which functions somewhat like the tonic of tonal music or the dominant of modal music). The Dynamic Middle always corresponds to the note A (think “Apollo”) when a Harmonia is transposed to a step of the C-major scale. Thus it is “a” within the E-d range of Dôristi, and within the D-c of Phrygisti; it is the lowest note (Foundation Note) of Hypodôristi (a-g). For instruments whose primary major scale is not C, the Dynamic Middle is the sixth degree of its primary major scale (e.g. B on a D-instrument).
The melody often begins on the Dynamic Middle, which is therefore called Beginning (Arkhê) or Leader (Hêgemôn). It typically ends on the lowest note of the Harmonia (the Foundation Note), which is therefore called the End (Teleutê) or Final Note (similar to a modal final cadence). Thus it will end on E for Dôristi, D for Phrygisti.
The Dynamic Middle occupies the same position within the scale structure of each Harmonia: below the Tone of Disjunction between the Tetrachords Mesôn and Diezeugmenôn (see The Greater Perfect System). This is the Sphere of the Sun, as we can see in the Planetary Heptachord, and represents the power of Apollo.
Each Harmonia rotates the Planetary Heptachord so that a different Planetary Pitch becomes the Foundation Note. This becomes the End (Teleutê) at which the melody is directed. The initial sounding of the Dynamic Middle, and every repetition of it, invokes the Power of Apollo and directs it to the End, for example, at the Moon in the Hypodôristi Harmonia, and at the Sun itself in the Phrygisti. The melody creates a pattern of invocation of the Planetary Powers as it visits their notes.
Finally, observe that the Dynamic Middle occupies successively higher degrees in each of the Harmoniai: it is the Foundation in the Hypodôristi, II in Hypophrygisti, and so on up to VII in Mixolydisti. These seven positions correspond approximately to the Planetary Heptachord (sometimes they are off by a semitone). Thus the Dynamic Middle on I in the Hypodôristi activates the Moon, on IV in Dôristi activates the Sun, on V in Phrygisti activates Mars, and on VII in Mixolydisti activates Saturn. Therefore, especially in these Harmoniai, there is a complex interaction between the Dynamical Middle, the End, and the other Planetary Pitches. Each Harmonia has an individual character that must be discovered through exploration.
Ptolemy (III.12) associates the Harmoniai with the Seven Parallels defined by the Zodiac. The northernmost reach of the Zodiac defines the Tropic of Cancer and the southernmost the Tropic of Capricorn. Two Signs lie on each of the other five Parallels. Libra and Aries, marking the Equinoxes, lie on the Celestial Equater, which corresponds to the Dôristi Harmonia. Each of a pair of Signs are called Observers (Videntia) of each other.
We have placed Hypodoristi at the bottom of the chart because it corresponds to the southernmost Sign. However, since absolute pitch is irrelevant, it may put also at the top of the chart, which preserves the order of the Planets and their Pitches (A-G).
Cancer and Capricorn are called the Gates of the Sun; Cancer is the Northern Gate, Capricorn the Southern. More specifically, Cancer is the Gate of the Moon (and Cancer is its House), the path of moist generation, through which souls descend into incarnation, just as Capricorn is the Gate of the Sun by which they ascend to bright Olympus. When a soul is born into earthly life, it descends through the Signs Cancer, Leo, …, Capricorn; on death it ascends through Capricorn, Aquarius, …, Cancer. Thus the soul visits the Signs in the same sequence as the Sun; in each case it passes through the Seven Planetary Spheres. (See Porphyry On the Cave of the Nymphs, ch. 10-13, and Macrobius’ Commentary on the Dream of Scipio, ch. 12.)
Each Harmonia has an Ethos (Character). The Greeks considered the Dôristi Harmonia to be primary because of its nobility and courageousness. The Phrygisti was commonly associated with the ecstasies of Dionysus and Cybele. The Lydisti was considered sad, but it and the Hypolydisti were also associated with laxity and indulgence. (See Jeans, Science & Music 180; compare also the Humors and Effects associated with the Eight Modes.)
The Guardians (Tutores) of the Zodiacal Signs are given, for example, in Manilius’ Astronomica (2.433-52). They are different from the Planetary Houses, which can be found in any astrology text.
The Eight Modes
Henricus Glareanus (1547) is generally credited with rearranging the names of the Seven Harmoniai of ancient Greece to name the medieval Modes defined by Pope Gregory (c.540-604). In this chart the medieval names and numbering are used because they better reflect the relation of the Modes to the Elements and Humors: Phlegmatic (Phlegm), Choloric (Yellow Bile), Sanguine (Blood) and Melancholic (Black Bile). For the same reason the (non-classical, Gregorian) Eighth Mode, the Hypermixolydian has been included. The C-major Foundation Note and ancient Greek name (Harmonia) have been included to facilitate correlation with the Seven Harmoniai.
The odd-numbered Modes are Authentic and increase the corresponding Humor (as indicated under Change); the even-numbered are Plagal and decrease it. (Odd and Even Numbers are respectively Male and Female, according to the Pythagoreans. Compare also the Planets with the Numbers of their Modes.)
The compass of a Plagal Mode is a fourth lower than the corresponding Authentic Mode. The exception in this chart is the Hypermixolydian, whose pitch duplicates that of the Moon but in a higher octave, as specified by Ramis and others. The more familiar Eighth Mode is the Hypomixolydian, whose Foundation Note D is indeed a fourth lower than the Mixolydian’s.
Except for the VIII Mode, the Foundation Notes follow a Circle of Fifths. (If VIII is taken to be Hypomixolydian then there is no exception.)
In medieval usage of the Modes, the focus is the Dominant (at step V) for Authentic Modes, and degree VI for Plagal Modes. The melody ends on the Final, which is the Foundation Note for an Authentic Mode, and the Final of the corresponding Authentic for a Plagal Mode. (See Oxf. Comp. Music s.v. Modes.)
(TO BE CONTINUED)
by John Opsopaus