The Davidic Cipher

In music, there is a particular type of interval that behaves in a very predictable manner within all of music. This interval of an augmented 4th is referred to as the tritone. As an example in the key of C, the tritone naturally occurs between the tones F and B. Very simplistically stated, the tritone is one of the inherent properties within music that helps create forward motion in a composition both harmonically and melodically. Like the opposing poles of a magnet attract and are drawn to each other, the natural tendency of the tritone pitches is to not remain static, but resolve (i.e., move and come to rest) to specific adjacent or neighboring tones.

Resolution of the tritone F and B (key of C Major)

     Using the tritone F and B above as our reference, we find that the F will naturally resolve ½ step downward to the E and the B will naturally resolve ½ step higher to the C. This motion also creates the basis for one of the strongest harmonic progressions in music (e.g., the Dominant to Tonic relationship), an authentic cadence (i.e., Major [V to I] and minor [V to i]). Relating this back to the quartertone scale previously introduced, we find that even though the quartertones between the F & E and between the B & C are theoretically possible, the inherent tendency of the tritone to resolve directly to specific tones might prohibit the use of these in-between quarter-tones in a practical compositional or performance situation.

modified ascending quartertone scale (twenty-two tones read left-to-right)
(omitted quartertones are shown with small x note heads)

     By eliminating the two quarter-tones that fall between the tones of the tritone and their notes of resolution, we now have twenty-two quartertones that can be mapped in some manner to the twenty-two letters of the Hebrew alephbet. But how? The solution presented itself in one of the oldest known ciphers found in the Bible, the atbash cipher.

Hebrew atbash cipher

     By definition, the atbash cipher is a simple substitution cipher used by early Hebrew writers of the Bible (see Jeremiah 25:26, 51:11, 51:41) to obscure or encrypt the original Hebrew word with a cipher. In the standard atbash cipher, the alephbet (i.e., the Hebrew equivalent of our alphabet) is applied in reverse to itself. In relation to the musical system of the Levites however, instead of the letters of the alephbet being applied in reverse, the tones associated with an ascending quartertone scale (left-to-right) were applied to the Hebrew alephbet (right-to-left). The application of this form of encryption (which will be referred to as the Davidic cipher in this book) is the fundamental interface that permits a mapping between the twenty-two letters of the Hebrew alephbet and the twenty-four tones of the quartertone musical scale enabling the music notation of the Psalm manuscripts (i.e., the te'amim) to be deciphered and transcribed into traditional music notation.

     In order to find a starting point for our applying the alephbet to the modified quartertone scale, we merely have to locate the mean or center of each relative component. In relation to our quartertone scale (shown in relation to the fundamental key of C major and its relative minor - A minor) we not only find that the center tone of our model is G# (enharmonic Ab), but also the center tone of the tritone (F and B). In relation to the Hebrew alephbet, the center letter is the lamed (i.e., the letter L). From this point, we can now work our way on either side of center, mapping the twenty-two letters of the Hebrew alephbet to the twenty-two tones of the modified quartertone scale.

The Davidic Cipher

     The completed cipher above shows the methodology in which the two systems are related in reverse to each other. The Hebrew alephbet applied as read (right-to-left) to the quartertone scale (read left-to-right) mapped in a descending manner from the initial aleph. The unique manner in which the Hebrew alephbet is applied to a musical scale and as we shall see, the music notation of the Hebrew texts themselves (i.e., the te'amim) is similar in many aspects to the ancient Greek system of music notation discussed by the 4th century C.E. music theorist, Alyphius [1]. The similarity between these two ancient systems of music notation may be an indication that both systems had common roots in antiquity.

     Relating this back to our original premise that David was literally able to play the name of God, let us see how this would be accomplished in relation to the Davidic cipher above. In order to do this, we first have to establish the Name of God David was referring to. In the following two scriptures we can see that David was referring to both the name Yah and the name Yahveh.

     We can further see the implication that the name of Yah and Yahveh were in fact able to be played in a very literal sense in three parallel accounts spanning over eight-hundred years from the time of Moses to the time of Isaiah:

     Relating this back to the Davidic cipher, we can see that the name of Yahveh is able to played melodically with the tones A - C - B - C and the name Yah with the tones A and C (which could be played both melodically and *harmonically).

     Another example of playing the Name of God is found in a phrase unique to the Psalm manuscripts, Halelu Yah (meaning praise Yah). When rendered in relation to the Davidic cipher we find that it not only makes musical sense melodically, but also harmonically as one of the strongest progressions in music, a perfect minor cadence (Am - E - Am [i - V - i]).

     One of the more profound relationships between the name of Yah, the Davidic cipher, and our present musical system is seen when applied to the cycle-of-5ths. Positioning the tritone F and B as the horizontal axis, we find the vertical axis is comprised of the tritone D and G#.

     These tones in relation to the Davidic cipher are in turn associated with the Hebrew letters aleph and lamed. When associated as a word, these two letters form the Hebrew word ël (meaning as a preposition, to and as a noun, God). We further find that the tones D and G# imply, as with all the opposite tones on the cycle-of-5ths, a tritone and an implied dominant 7th chord. In this instance, the D and G# are the 3rd and 7th tones of an E dominant 7th chord or E7 chord (i.e., E - G# - B - D). Tones that directly resolve to the tones A and C, Yah. In other words, the Hebrew word for God (ël) resolves to the name of God, (Yäh).

     In all of the above examples, we see that the tonality of Yah, Yahveh and Halelu Yah when rendered in relation to the Davidic cipher is A minor. This is the primary tonality of not only the Davidic cipher, the instruments of the Levites, but also the Psalm manuscripts themselves.
     As a final sidebar before we move on to the symbols of the te'amim and their relationship to the Davidic cipher, there are some very interesting relationships established when the Hebrew alephbet and numbering system are applied to the cycle-of-5ths. These two simple examples below (and there are many more) further demonstrate that there are often times many underlying and sometimes hidden relationships between seemly unrelated things: the alephbet, language, numbers, geometry, music and God.

     As with the our present system of musical notation, a secondary set of symbols and methodology was implemented within the Hebrew texts that would not visually conflict with the letters of the Hebrew alephbet. A system that would not only permit a composition or song to be written down, but would enable another musician or singer in another time to play and sing these important manuscripts.

Music Notation of the Psalm Manuscripts

1. Henderson, Isobel. "Ancient Greek Music" in Ancient and Oriental Music, edited by Egon Wellesz, (London, New York, Toronto: Oxford University Press, 1957), 358-363