Greek esoteric music theory charts

09-02-11 11:04 ne ome ee Greek Esoteric Music Theory ' Charts | John Opsopaus ©1999 A collection of annotated and cross-linked charts to aid the use of Ancient Greek Music for esoteric purposes. 1. Introduction. 2. The Greater and Lesser Perfect Systems. An overview of all tne harmonic relationships. 3. The Four-String Lyre of Hermes. The Musical Tetractys, which is the basis of Pythagorean Harmonics. The Elemental Tetrachord. The fundamental structure from which Ancient Greek Harmony is constructed. Correspondences with the Elements, Qualities, Deities, etc. Elemental Sequences. All possible sequences of the Elemental Tetrachord categorized according to effect. The Zodiacal Trigons. The Zodiacal Trigons (Triplicities) correspond to the notes of the Tetrachord as part of the Immutable System. . The Five Tetrachords. The Five Tetrachords of the Immutable System correspond to the Five Elements, Senses, etc. The Planetary Heptachord. The Heptachord and the Octave are constructed from two Tetrachords. Includes correspondences with Planets, Vowels, Days, etc. The Planetary Heptagram. Shows the relationships between the Planets, Days of the Week and Notes, as explained in The Planetary Heptachord.

09-02-11 11:05 Charts John Opsopaus ©1999 A collection of annotated and cross-linked charts to aid the use of Ancient Greek Music for esoteric purposes. 1. Introduction. 2. The Greater and Lesser Perfect Systems. An overview of all the harmonic relationships. 3. The Four-String Lyre of Hermes. The Musical Tetractys, which is the basis of Pythagorean Harmonics. 4. The Elemental Tetrachord. The fundamental structure from which Ancient Greek Harmony is constructed. Correspondences with the Elements, Qualities, Deities, etc. 5. Elemental Sequences. All possible sequences of the Elemental Tetrachord categorized according to effect. 6. The Zodiacal Trigons. The Zodiacal Trigons (Triplicities) correspond to the notes of the Tetrachord as part of the Immutable System. 7. The Five Tetrachords. The Five Tetrachords of the Immutable System correspond to the Five Elements, Senses, etc. 8. The Planetary Heptachord. The Heptachord and the Octave are constructed from two Tetrachords. Includes correspondences with Planets, Vowels, Days, etc. 9. The Planetary Heptagram. Shows the relationships between the Planets, Days of the Week and Notes, as explained in The Planetary Heptachord.

09-02-11 11:05 10. The Seven Harmoniai. Shows correspondences with the Seven Harmoniai (ancient modes) of Greek music, including Planets, Signs and Guardian Deities. 11. The Eight Modes. Shows correspondences with the Eight Medieval Modes, including, Planets, Elements, Humors and their Effects. 12. Meanings of Greek Names of Notes and Tetrachords. 13. Sources. Note: These pages make extensive use of tables, and won't make sense when viewed with browsers that don't support tables. Return to Biblioteca Arcana page Send comments about this page

09-02-11 11:06 Introduction 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 (see Godwin HS and MMM for a selection). 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). Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page

The Greater and Lesser Perfect Systems 09-02-11 11:06 The Greater and Lesser Perfect Systems Greater Perfect System Tetrachord * * Hyperbolaiôn * Diezeugmenôn * Rom. Mod. Note Note Greek Note Vowel Planet P aa Nêtê A Saturn O g Paranêtê Ô Jupiter N f Tritê Ê Mars M e Nêtê A Sun L d Paranêtê Ô Venus K c Tritê Ê Mercury I b Paramesê A Moon Lesser Perfect System TetraMod. * chord Note * Synêmenôn Greek Note H a Mesê G G Likhanos Ô Saturn F F Parhypatê Ê Jupiter E E Hypatê A Mars D D Likhanos Ô Sun C C Parhypatê Ê Venus * B B Hypatê A Mercury * A A Proslambanomenos E Moon Mesôn * Hypatôn * Zodiac d Nêtê A Trigon IV c Paranêtê Ô Trigon III Ê Trigon II E Trigon I b flat Tritê * Vowel a Mesê 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.

The Greater and Lesser Perfect Systems 09-02-11 11:06 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.

The Greater and Lesser Perfect Systems 09-02-11 11:06 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. Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page

The Four-String Lyre of Hermes 09-02-11 11:06 The Four-String Lyre of Hermes Musical Tetractys Fixed Note Element Humor Quality Season Moon Phase 6 e Nêtê Fire Yellow Bile (Choler.) Warm Summer to Full 8 b Paramesê Air Blood (Sang.) Moist Spring to 1st Q 9 a Mesê Water Phlegm (Phleg.) Cool Winter to New 12 E Hypatê Earth Black Bile (Melan.) Dry Autumn to 3rd Q 1. 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 FourString Lyre to Hermes. (Godwin HS 198) 2. 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. 3. 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). 4. All the most ancient Greek musical instruments seem to be based on Four Notes. 5. 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) 6. 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. 7. 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.) 8. 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 12 edges 8 solid angles 6 faces Thus, 24:12 gives the Octave, 12:8 the Fifth, and 8:6 the Fourth. (Godwin HS 115, 269, 439) 9. The correspondences between the Strings, Elements, Humors and Qualities are given by Hunayn (c.803-873 CE),

The Four-String Lyre of Hermes 09-02-11 11:06 the Ikhwan al-Safa' (Brethren of Purity) and Isaac ben Haim (c.1467-after 1518). (Godwin HS 97, 113-4, 154) 10. The two interlocking Fifths correspond to the Opposed Elements: Fire/Water and Air/Earth. 11. According to Hunayn and Isaac ben Haim, some feelings and character traits associated with the Humors are: Feeling Yellow Bile courage Character Traits sovereignty, generosity, kindness Blood joy, pleasure justice, graciousness, love Phlegm fear righteousness, cowardice, vileness Black Bile sorrow, anguish foregiveness, impassiveness Notice how opposing Humors (Yellow Bile vs. Phlegm, Blood vs. Black Bile, corresponding to opposed Elements) are associated with opposing feelings and traits. 12. 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). 13. See The Elemental Tetrachord and The Ancient Greek Esoteric Doctrine of the Elements for additional Elemental correspondences to their explanation. 14. See The Elemental Tetrachord for the use and significance of the Plektrum (Pick). Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page

The Elemental Tetrachord 09-02-11 11:06 The Elemental Tetrachord Vowels Epsilon (ay) Alpha (ah) Primary pitches A B C D Secondary pitches a E F G Elements Earth Water Air Fire Qualities Dry Cool Moist Warm Seasons Autumn Winter Spring Summer Directions West North East South Deities Hera Demeter Eta (eh) Omega (aw) Persephone Zeus Hades Aphrodite Dionysos Hephaistos 1. See The Ancient Greek Esoteric Doctrine of the Elements for the Deities and additional Elemental correspondences. 2. 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. 3. Each Note of the tetrachord is called a Stoikheion (Element). (Wellesz 155) 4. 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. 5. 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. 6. 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). 7. 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 the Plektrum (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) 8. In ancient Greek practice, the Plektrum was stroked toward the body, which is toward the lower-pitched, but higherpositioned 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) 9. Some ancient sources suggest chanting the Vowels in your mind, rather than out loud (Wellesz 149). 10. 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.) 11. 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 the Deities. 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.

The Elemental Tetrachord 09-02-11 11:06 12. 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. 13. 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. 14. 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. 15. 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). Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page Last updated: Fri Aug 20 13:02:34 EDT 1999

Elemental Sequences 09-02-11 11:07 Elemental Sequences Progressive Sequences Primary Progression Female to Male Male to Female Lower to Upper Upper to Lower Secondary Progression Sequence Upper to Lower ABCD Lower to Upper BADC Upper to Lower CDAB Lower to Upper DCBA Male to Female DBCA Female to Male BDAC Male to Female CADB Female to Male ACBD Cyclic Sequences Primary Progression Female to Male to Female Male to Female to Male Upper to Lower to Upper Lower to Upper to Lower Secondary Progression Sequence Upper to Lower ACDB Lower to Upper BDCA Dry to Moist ADCB Moist to Dry BCDA Upper to Lower CABD Lower to Upper DBAC Dry to Moist DABC Moist to Dry CBAD Female to Male ABDC Male to Female CDBA Dry to Moist ADBC Moist to Dry CBDA Female to Male BACD Male to Female DCAB Dry to Moist DACB Moist to Dry BCAD 1. In the Progressive Sequences there is a movement from one Quality, Power or Dominion to its opposite, expressed in the Primary Progression. The Secondary Progression (or Internal Progression) takes place twice within the Primary Progression. Progressive Sequences can be used to move from one state to another. 2. In the Cyclic Sequences there is a departure from one Quality, Power or Dominion to its opposite and then a return; this is expressed in the Primary Progression. Superimposed on this cycle is the Secondary Progression from a Quality, Power or Dominion to its opposite. Cyclic Sequences can used to temporarily visit another state in order to make some change.

Elemental Sequences 09-02-11 11:07 3. See The Elemental Tetrachord for correspondences between the Notes and the Elements, Deities, Vowels, etc. 4. Lower refers to the Underworld (Hades and Tartaros), the chthonic dominion of Hades and Persephone. 5. Upper refers to the Heavens (Earth and Olympus), the celestial dominion of Zeus and Hera. 6. The Male Elements have the Warm (separating) Quality and the Female have the Cool (uniting). 7. Dry refers to the Quality of being strong, but also rigid. Moist refers to the Quality of being flexible, but also weak. The Moist and Dry powers correspond to the alchemical operations of Dissolution and Coagulation, referred to in the famous alchemical maxim Solve et Coagula. 8. For more on the Qualities or Powers (Warm/Cool, Dry/Moist), see The Ancient Greek Esoteric Doctrine of the Elements. 9. In choosing a Sequence, pay particular attention to the Element (Deity etc.) on which it ends. 10. A melodic step of a major third (e.g. A to C) represents a conjunction of opposing principles (e.g. Fire and Water) or the union of a God and Goddess (e.g. Hades and Persephone). 11. Melodic steps of a second (e.g. BC or DC) or a perfect fourth (e.g., AD) occur between principles that share some quality (e.g. gender or domain). 12. Notes within a Sequence may be repeated without altering the overall Sequence. Thus ADBBBC dwells in the Watery power of Persephone (B), before returning to the upper realms (C). 13. The Progressive Sequences occur in pairs, in which the notes are reversed in each pair of notes (e.g. ABCD vs. BADC). Such pair have opposing Secondary Progressions. 14. The Cyclic Sequences occur in pairs, which are reversals of each other (e.g. Dry to Moist and vice versa). It will also be observed that the Upper/Lower Sequences differ from corresponding Dry/Moist Sequences in having the middle two Notes reversed (look for yourself to see the pattern; it is easier to see it than to say it). 15. The Cyclic Sequences can be repeated to create double cycles. For example DCAB DCAB... cycles between Male (DC) and Female (AB) and between Upper (CA) and Lower (BD). 16. If we use the sequences in a cycle, then rotations make no difference; for example ADBC and BCAD both produce ...ADBCADBCADBCAD... If we eliminate the simple scales ABCD and DCBA, then there are only four distinct sequences: A D B C D C A B B A C D C B D A (Notice that the sequences form a Latin Square.) As it turns out, these are the same four Elemental Vowel Chants presented by R. J. Stewart (Music, Power, Harmony 126-7), although he uses different correspondences. Their meanings in the Greek Tradition may be determined by consulting the Table of Cyclic Sequences above. 17. There are twenty-four Sequences, corresponding to the twenty-four letters of the Classical Greek Alphabet. 18. DEFG can be used instead of ABCD, as can any other diatonic Phrygisti tetrachord (i.e., tone-semitone-tone). 19. If you know The Elemental Tetrachord and The Ancient Greek Esoteric Doctrine of the Elements. then you can throw away this chart, because you know everything you need to know to construct a Sequence corresponding to any desired progression of Qualities, Powers, Dominions, etc. Return to Greek Esoteric Music index

Elemental Sequences 09-02-11 11:07 Return to Biblioteca Arcana page Send comments about this page

Zodiacal Trigons 09-02-11 11:07 Zodiacal Trigons I Ares Trigons Leo Sagittarius II Taurus Virgo Capricorn III Gemini Libra Aquarius IV Cancer Scorpio Pisces Planets Sun Jupiter Venus Moon Mercury Saturn Mars (Moon, Venus) Pitches A B flat C D Eta (eh) Omega (aw) Alpha (ah) Vowels Epsilon (ay) 1. The Vowel and Pitch correspondences are given by Barker (II.481n131, 522nn174-5) based on Aristides Quintilianus and Bellermann's Anonymous manuscript. However, the usual Vowel-Tetrachord correspondence would be EpsilonAlpha-Eta-Omega (EAÊÔ); see the Greater and Lesser Perfect Systems. 2. It will be observed that the Elemental Correspondences (I=Earth, II=Air, III=Fire, IV=Water), which are based on the Vowels, do not agree with those of contemporary astrology. 3. See A Brief Guide to Ancient Greek Pronunciation for suggestions on pronouncing the vowels. Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page Last updated: Fri Aug 20 13:07:40 EDT 1999

The Five Tetrachords 09-02-11 11:07 The Five Tetrachords Greek Letter Tetrachord Tones Vowels * Element Sense Virtues Tau* Hyperbolaiôn e, f, g, aa AÊÔA Aithêr Sight Wisdom Omega Diezeugmenôn b, c, d, e AÊÔA Fire Hearing Courage * Air Smell Justice Eta Synêmenôn a, b flat, c, d E Ê Ô A Alpha Mesôn E, F, G, a AÊÔE Water Taste Moderation (enjoyment) Epsilon Hypatôn B, C, D, E AÊÔA Earth Touch Moderation (abstention) Proslambanomenos * A E 1. Suggested practice: Chant the vowels on their pitches in a Tetrachord in order to work with a corresponding Element, Sense or Virtue. 2. The note Proloslambanomenos does not belong to a Tetrachord; it was added to the bottom of the Greater and Lesser Perfect Systems as a foundation corresponding to the Moon and the Sublunar or Mundane Sphere. 3. The Tetrachords are listed from high to low pitch range, but their individual notes are listed from low to high (see The Greater and Lesser Perfect Systems). 4. Each Tetrachord has the form (from low to high): semitone-tone-tone. 5. See The Elemental Tetrachord for correspondences with the individual tones of the Tetrachord. 6. The Tones and Vowels are given in the Greater and Lesser Perfect Systems, as interpreted by Barker (II.481n131). We write A = Alpha, E = Epsilon, Ê = Eta, Ô = Omega. See A Brief Guide to Ancient Greek Pronunciation for suggestions on pronouncing the vowels. 7. Alpha begins each Tetrachord, except that each octave begins with Epsilon (= note A). 8. The vowels of the (anomolous) Tetrachord Synêmenôn are based on Barker's (highly informed) interpretation of Aristides Quintilianus and Bellermann's Anonymous manuscript (Barker II.481n131). However, Epsilon-Alpha-EtaOmega (EAÊÔ) is another possibility. 9. The letter Tau corresponds to the Fifth Element and the Plektrum of Apollo, as explained in the Elemental Tetrachord. 10. Five Tetrachords plus one added note make 21, which invites Tarot correspondences. (See the Planetary Heptachord.) This is also equivalent to five Rotations through the Elements plus the Added Note. Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page Last updated: Fri Aug 20 13:09:59 EDT 1999

The Planetary Heptachord 09-02-11 11:08 The Planetary Heptachord Tetrachord * Rom. Mod. Note Note Greek Note Sphere Astral Spheres * Hyperbolaiôn * P aa Nêtê Trigon IV O g Paranêtê Trigon III N f Tritê Trigon II M e Nêtê Trigon I Planetary Spheres Office Sect Day Vowel L d Paranêtê Saturn Male. Sun Sat. Ô K c Tritê Jupiter Bene. Sun Thur. U * I b Paramesê Mars Male. Moon Tues. O * H a Mesê Sun Imp. Sun Sun. I G G Likhanos Venus Bene. Moon Fri. Ê F F Parhypatê Mercury E E Hypatê Moon Diezeugmenôn Mesôn * Imp. Sun & Wed. Moon E Moon Mon. A Elemental Spheres D D Likhanos Fire C C Parhypatê Air * B B Hypatê Water * A A ProslambaEarth nomenos Hypatôn 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 EFGABb CD 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).

The Planetary Heptachord 09-02-11 11:08 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.

The Planetary Heptachord 09-02-11 11:08 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). Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page

The Planetary Heptagram 09-02-11 11:08 The Planetary Heptagram Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page

The Seven Harmoniai 09-02-11 11:08 The Seven Harmoniai Harmonia C-Maj. Rel. Planet Degree Deg. Day Parallel Guardian Mixolydisti (Mixolydian) B VII Mercury Wednesday Cancer Lydisti (Lydian) C I Venus Friday Leo Gemini Zeus Apollo Phrygisti (Phrygian) D II Sun Sunday Virgo Taurus Demeter Aphrodite Dôristi (Dorian) E III Mars Tuesday Libra Aries Hephaistos Athena Hypolydisti (Hypolydian) F IV Jupiter Thursday Scorpius Pisces Ares Poseidon Hypophrygisti (Hypophrygian) G V Saturn Saturday Sagittarius Artemis Aquarius Hera Hypodôristi (Hypodorian) a VI Moon Monday Capricorn Hermes Hestia 1. 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." 2. 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. 3. 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). 4. 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. 5. Relative Degree indicates where the Harmonia begins relative to any major scale. For example, Dôristi begins at E in C-major and at F# in D-major. 6. 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. 7. 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. 8. 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). 9. 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.)

The Seven Harmoniai 09-02-11 11:08 10. 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.) 11. 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). 12. 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. 13. The Dynamic Middle occupies the same position within the scale structure of each Harmonia: below the Tone of Disjunction between the Tetrachords Mes&ocircn 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. 14. 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. 15. 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. 16. The Elemental Sequences may also be used for constructing melodies. 17. 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. 18. 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). 19. 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.) 20. A particular Harmonia might be used for esoteric musical work when the Sun is in the corresponding Sign (thus, in Lydisti when the Sun is in Leo). 21. 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.) 22. 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. Return to Greek Esoteric Music index

The Seven Harmoniai 09-02-11 11:08 Return to Biblioteca Arcana page Send comments about this page

The Eight Modes 09-02-11 11:08 The Eight Modes Mode I Dorian II Hypodorian III Phrygian IV Hypophrygian V Lydian VI Hypolydian VII Mixolydian VIII Hypermixolydian Found. Note Element Humor Change Effect Planet Water Phlegmatic (Phlegm) more awake Sun D Phrygisti less asleep Moon A Hypodôristi Fire Choloric (Yellow Bile) more anger Mars E Dôristi less flattery Mercury B Mixolydisti Air Sanguine (Blood) more happy Jupiter F Hypolydisti less sad Venus C Lydisti Earth Melancholic (Black Bile) more melanch. Saturn G Hypophrygisti less beauty a Stars Harmonia 1. 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. 2. 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.) 3. 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 [see below] and others. The more familiar Eighth Mode is the Hypomixolydian, whose Foundation Note D is indeed a fourth lower than the Mixolydian's. 4. 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.) 5. 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.) 6. The correspondences between the Modes and the Changes in the Humors and the resulting Effects are given by Ramis de Pareja (1482). (Godwin HS, 171-3) 7. Modes I and II correspond to the Element Water and the Phlegmatic Humor. The Effects are of the Lamps of Day and Night: to awaken or to put to sleep. 8. Modes III and IV correspond to the Element Fire and the Choleric Humor. The Effects are Martial, for fighters wound with weapons, or Mercurial, for flatterers wound with words. 9. Modes V and VI correspond to the Element Air and the Sanguine Humor. The Effects are Jovial happiness or Erotic sadness. 10. Modes VII and VIII correspond to the Element Earth and the Melancholic Humor. The Effects are Saturnine melancholy or Celestial bliss.

The Eight Modes 09-02-11 11:08 Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page

Meanings of Greek Names of Notes and Tetrachords 09-02-11 11:09 Meanings of Greek Names of Notes and Tetrachords Note Names Hypatê: Highest, farthest. This refers to the position on the lyre, not to pitch (which the Greeks only rarely characterized as "high" or "low"). Likhanos: Licking (finger), i.e. forefinger. Mesê: Middle. Nêtê: Lowest, nearest. (See Hypatê above) Paramesê: Beside Mesê Paranêtê: Beside Nêtê Proslambanomenos: Taken in addition, i.e., the "added note." Tritê: Third (from top of Tetrachord). Tetrachord Names Diezeugmenôn: Disjoined. Hypatôn: Highest, farthest. (See Hypatê above) Hyperbolaiôn: Exceeding, going beyond, at zenith. Mesôn: Middle. Synnêmenôn: Conjoined. Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page

09-02-11 11:09 Sources 1. Anderson, Warren D. Music and Musicians in Ancient Greece. Cornell Univ. Press, 1994. 2. Barker, Andrew. Greek Musical Writings, 2 vols. Cambridge University Press, 1984 (v.I), 1989 (v.II). The principal writings of Ancient Greek musicology, translated into English with extensive notes. 3. Godwin, Joscelyn. Harmonies of Heaven and Earth: Mysticism in Music from Antiquity to the AvantGarde. Inner Traditions, 1995. 4. Godwin, Joscelyn. The Harmony of the Spheres: A Sourcebook of the Pythagorean Tradition in Music. Inner Traditions, 1993. 5. Godwin, Joscelyn. Music, Mysticism and Magic: A Sourcebook. Arkana, 1986. 6. Godwin, Joscelyn. The Mystery of the Seven Vowels. Phanes, 1991. 7. Nicomachus. The Manual of Harmonics of Nicomachus the Pythagorean, transl. & commentary by Flora R. Levin. Phanes, 1994. Also translated by Barker (vol. II, ch. 10). Nicomachus lived around the end of the first century CE. 8. Pole, William. The Philosophy of Music, 6th ed. Kegan Paul, Trench, Trubner & Co., 1924. 9. Wellesz, Egon. "Music in the Treatises of Greek Gnostics and Alchemists," pp. 145-58. 10. Werner, Eric. "The Origin of the Eight Modes of Music (Octoechos)," Hebrew Union College Annual, Vol. XXI (1948), pp. 211-55. 11. Winnington-Ingram, R. P. Mode in Ancient Greek Music. Adolf M. Hakkert, 1968. Return to Greek Esoteric Music index Return to Biblioteca Arcana page Send comments about this page