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On the Occult Side - PaganSquare - PaganSquare - Join the conversation!

Pagan Studies

Learn how Classical Music harbors subliminal and not-so subliminal Pagan messages.

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On the Occult Side

Question: Does a twelve-tone matrix have any relationship with the 'Averse Table of Commutations' as found in Qabbalistic writings, and how does this speak to composer intent?
(In other words, did Arnold Schoenberg just copy from Medieval Manuscripts for his "unnerving" (to say the least) approach to music? And does that mean he's an Occultist?)

    A matrix is the most well-known form of compositional inspiration for serialist, 12-tone music. The serialist compositional technique was invented by Arnold Schoenberg in the early 1920's, and made a major impact on later 20th century composers.   The goal of the technique is to remove the predominance of key and replace it with equal emphasis on tone, and the means by which this is done is by randomizing said twelve tones into a matrix, which subsequently emphasises the importance of rhythm as primary thematic material rather than structural support.  The Averse Table of Commutations is a magical technique from the Middle Ages that randomized the 22 Hebrew letters for the purpose of extracting the names of spirits.  In reviewing the similarities between these two constructs, it is possible to determine that Schoenberg did not 'invent' the 12 tone matrix so much as transpose the principles of the table of commutations such that it could apply to music.

    The 'Averse Table of Commutations' is one of several tables used in Ceremonial Magick. The main tables in "Three Books of Occult Philosophy" are 'Right,' 'Averse,' 'Irrational Averse,' 'Table of Ziruph,' and 'Rational Table of Ziruph," making 5 tables (among others that can be constructed from the same system) from the 22 letters of the Hebrew alphabet, which are "...arranged in such a way that each letter appears just once in each row and each column" (p199, Clucas)1.  The underlying concepts of the Table are related to the Hebrew concepts of "... temurah (permutation) in connection with the operation of tseruf (combination)" (Reeds, p 22)2.  While these concepts relate more to alphabetical substitution in gematria, Reeds demonstrates that the prevalence of tabulation as an exercise was not limited to magical grimoires or qabbalistic writings, and furthermore, that the tables were derivative of Latin squares, or "magic" squares as we've come to know them today3.
   The purpose of the tables of commutations is to "...[draw] forth out of sacred writ..." the names of "...good and evil Spirits..." (Agrippa, "Three Books of Occult Philosophy" Book 3, Part 2, Chapter xxv)4.   The good and evil spirits mentioned are revealed to be the names of angels and demons, which can be discovered in verses of the Old Testament Bible and can also be developed from the names of God6.  Once the name is discovered through the process described, the spirit can be summoned to the magician and if said spirit is an Angel, can be asked to protect or otherwise benefit the magus. If the spirit is evil, can be controlled by the magus and forced to tell the magus how it can be overcome.

    The 12 tone matrix is constructed in the same way as the Table of Commutations, using

twelve pitches instead of twenty-two alphabet letters.  These twelve tones become labeled as "pitch-classes," for the reason that it is the name of the pitch, rather than its position on the staff, that is the most relevant factor. First, the twelve tones are arranged in a tone row (this can be determined by various methods), and then this tone row is extrapolated into a matrix such that every pitch-class is represented in each row and column only once.  (A modern example of this kind of structure is the Sudoku puzzle, which uses numbers instead of letters.)  At this point, tone rows can now be extracted for use in a composition, and these rows and columns can be used in four ways-prime (labeled 'P' on the diagram), retrograde ('R'), inversion ('I'), and retrograde inversion (RI). The twelve tones of the octave can also be divided into six-note 'hexachords' and used accordingly, as part of a system known as "hexachordal combinatoriality," where each note is only used once per series.   Put simply, " A twelve-tone row or twelve-tone series is a particular ordering of the twelve pitch classes," (161 Roig-Francoli), and the matrix is one way of creating that particular order. 

     The dodecaphonic matrix is created to ensure that no one pitch is favored above another, and the series of note-combinations produced from the matrix can be selected from in various ways to create music that exemplifies equal importance of pitch through an identifying tone row.  The Table of Commutations is used to determine the name and aspects of a spirit or spirits for the purpose of communicating with it, with the names of the spirits being equal in their value as modes of contact.   Therefore, both the table and the matrix can be used to extract variations upon existing material, and can be used to create new connections to an existing system-the Table to religion, the matrix to music.

        So, a constructional relationship is visible between dodecaphonic matrices and qabbalistic alphabet tables, as well as with the Sudoku puzzle and Roman Latin magic squares.  It is very clear that the Table of Commutations is not a new idea, and would not be considered such to those who were mathematically and musically inclined to high degrees, as was Schoenberg. Therefore, as an extension of the Table of Commutations, the matrix proves to be a product of occult religious practices.

  This begs the question: What was Schoenberg using as source material for his matrices, and what are the meanings to be found in the tone rows? In other words, what exactly was it that caused him to construct his atonal system as a table, or matrix? What was Schoenberg attempting to draw forth out of the 'sacred writ' of musical notes? Why not just continue with hexachordal combinatoriality alone?  We know that the construction of tables and matrices is extraordinarily similar, and we know that Schoenberg placed great spiritual importance upon his music.  Since the purpose of a table is to extract spiritual meaning from language, it is reasonable to start looking for clues to Schoenberg's musical approach through Schoenberg's spirituality, though that is another study entirely.

  According to Walter Boyce Bailey's "Programmatic Elements in Schoenberg's Music,"  Schoenberg had "... interest[s] in Balzac, Strindberg, and Swedenborg..."  Bailey furthermore provides Schoenberg's sketches for a symphony, of which 'Die Jakobsleiter,' was intended to be the last movement.  The sketches for the otherwise uncomposed symphony reveal Schoenberg's exposure to late 19th century spirituality through its textual inclusions.  "Gotterhochzeit (Marriage of the Gods)," "Aeonische Stunde (Aeonic Hour)," "Der Burgerliche Gott (The Bourgeois God)," "Unbefriedigt. Der burgerliche Gott genugt nicht (Unsatisfied. The Bourgeois God does not suffice," and "Gottheit des zertrummerten Tempels (Deity of the Ruined Temple)" are magnetic titles to one that is educated in Pagan and Occult spiritual practice.   The evidence shows that there is more going on with Schoenberg's spirituality than a side-interest in Swedenborg, and the possibility that Schoenberg borrowed the technique of the table of commutations for the matrix becomes more than a coincidence or a circumstance of time and place.  It becomes deliberate.

    Reasons for this are as follows: The implication of 'Gods' in the plural indicates polytheism, the reference to 'Aeon' indicates familiarity with the works of Aleister Crowley (possibly due to the OTO, which had its beginnings in and around Germany and Austria in 1910), 'The Bourgeois God' indicates class-related antagonism on the religious level (that 'God' in the Abrahamic sense was too good for mortals, and could not live up to the expectations of mortals), and 'Deity of the Ruined Temple' evokes a visual aesthetic not unlike a landscape painting of modern Rome.   In the book quoted above, Bailey is unclear whether the symphony had a name, and it is unclear whether it would have been the Seraphita symphony based on Balzac's novel of the same name. 

      Schoenberg contacted Richard Dehmel to supply poetry for the symphony's text, as it was intended as a twelve-tone oratorio.  Richard Dehmel, scholar, businessman, and poet, was born on the 18th of November in 1863*.  He mentored Thomas Mann and Herman Hesse, among other accomplishments. He was an important figure in the development of PAN Magazine (1895)*, a periodical that was "...regarded as one of the most important voices of Art Nouveau in Germany." * According to Project Gutenberg's German site,  in 1896 Dehmel was convicted for "..violation of religious and moral feelings" with the publication of his poem "Venus Consolatrix." *  Since Schoenberg contacted Dehmel to request poetry for the symphony's text, and included it in his sketches for the symphony, no doubt Schoenberg was well pleased with how Dehmel could help to communicate the musical idea of the symphony. 


1. Clucas, Stephen. John Dee: Interdisciplinary Studies in English Renaissance Thought. (c) 2006 Springer. International Archives of the History of Ideas.

2. Reeds, Jim. John Dee and the Magic Tables in the Book of Soyga.  accessed 6/28/2012. 

3. The Romans also used acrostics to create oracles for consulting the Sibylline Books. (Scheid, 122)

4. Agrippa, Heinrich Cornelius. Three Books of Occult Philosophy. Accessed 9/22/2012.

5. Further details of which can be found online at

6. "God" being the Abrahamic deity also known as Yahweh or Jehovah.


Bailey, Walter Boyce. Programmatic Elements in the Works of Schoenberg.  1984 UMI Research Press.

PAN Magazine. 
1.1895-96 (Heft I und II) Seite: 143

University of Heidelberg.
Project Gutenberg. Richard (Fedor Leopold) Dehmel.

Roig-Francoli, Miguel A. Understanding Post-Tonal Music. (c)2008 McGraw-Hill Higher Education. New York, New York.

Scheid, John; Janet Lloyd, Tr. An Introduction to Roman Religion. 2003 Indiana University Press. Bloomington & Indianapolis.

Swedenborg, Emmanuel. Arcana Coelestia.

Wikipedia.  Emmanuel Swedenborg.

Wikipedia.  Richard Dehmel.


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Amarfa has been studying the occult, wicca, and paganism for 17 years and counting.  She has been a musician since age 5, studying first guitar, then accordion for 10 years, placing 2nd in her division in the 1995 ATARI/ATAM New England Regional Competition,  and has been studying voice for 9. She has directed small early music ensembles, performed publicly, and starred in local theatre works, particularly the World Premiere of Nightsong, a musical theatre piece with direction and book by Jon Brennan and music by Kari Tieger and Kevin Campbell, as well as composing a musical of her own and writing music in her spare time.


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