Tzolkin in C Major
a Study for Full Orchestra
Full Orchestral Score
including title page with harmonic module graphic, instructions & instrumentation
Choose One, Press Play & Scroll Along Below
Theory Behind The Music
Tzolkin in C Major, Michael explains, “is an experimental and meditative orchestral performance of a mathematical composition based on an ancient sacred timing frequency; the mathematical ratio 13:20 or a matrix whereby 13 X 20 = 260 kin. A kin is a day, a person or a thing, a moment in time, or a number of any equivalence or conception. This timing system deals with radial and qualitative, as opposed to linear and quantitative, numerical expression. These concepts directly correlate to how the Maya understood the passage of time. Our modern conception is that time is a linear notion ruled by the clock, a division of space, but time is not a line and time is not space.”
The project encompasses several levels; primarily, it is a cycle of 260 consecutive musical harmonies that are performed by a full 90-piece orchestra n the span of around 20 minutes. Wiley states that “The project is also a cultural study in meditative unity whereby the energetic, conscious and collective participation of the audience is integral to the experiment. My orchestral meditation approach is unconventional in conception and form, yet musically classical in its instrumental arrangement. The purpose is to impart ancient knowledge on the nature of time in a meditative multi-media fashion while simultaneously creating public awareness for the discovery of the Law of Time.”
Michael holds that his composition was conceived and realized through the use of aesthetic and mathematical discoveries that have been made regarding the ancient Mayan Calendar, the Tzolkin. The work is a study in cohesive breath and is meant to be performed as a meditative exercise for orchestra and audience alike. The listener is therefore encouraged to meditate on the nature of time. It was the composer’s intention to create a Minimalistic effect, whereby the passage of all Harmonies, or kin, would remain almost all equal in length. This gives the work an air of spatial continuity where Melodic implications are quite subtle, leaving room for the listener to generate Melodies in their own minds. The work is laid out in Wavespells and has a Four Bar Intro. This serves to set the Tempo and Phrasing of the piece. Once again four Measures are used to close out the composition as well.
A somewhat brief description of the Tzolkin is in order. The calendar is not only a cycle of 260 days, but more so, it is a Universal Timing Frequency, known to the Maya, as a ratio and as a matrix (13:20), 13 Galactic Tones of Creation and 20 Solar Human Seals. The cycle of 13 Tones, the Wavespell, is musically represented by the first 13 pitches in an ascending Overtone Series in C: And likewise, the cycle of 20 Seals, or a Harmonic Run, is represented by two repeating and nested cycles: four ascending Perfect 5ths, the Harmonic, and five ascending Diatonic 4ths, the Chromatic, both pitched in the key of C Major.
It is important to understand that all three cycles begin on the Note C and end on the Note A, and that it is this very characteristic that holds the Tonal Structure of the music together. All three cycles progress in a nested fashion, sounding simultaneously. This generates an elegant and simple Harmonic Progression of 260 different consecutive Harmonies (260 kin). These three cycles are known as the three orders of the frequency of natural time, represented by the Tzolkin; the Wavespell, the Chromatic and the Harmonic. The track below is the harmonic skeleton of the work without any percussion or brass, which is a subdued listening experience of all 260 consecutive harmonies.
The four following graphs contain musical elements as well as Mayan information about the Tzolkin. The graphs are a series of cross reference and comparison charts between these two disciplines, music theory and Mayan math. As for musical information about musical notes, they are represented with their traditional spelling as well as through a series of twelve numbers called set theory. Where: C=1, C#=2, D=3, D#=4, E=5, F=6, F#=7, G=8, G#=9, A=10, a#=11 and B=12.
Other Tonal forces are at work in the music which gives it a more complex Harmonic Structure. These are implemented through the use of Pedal Points that code a certain given length of Measures. Each Harmonic Run, 13 in all, is coded by an upward Progression from C through the Circle of 5ths, and all 13 Pedal Points last 20 Measures in length. 52 Measures is a Castle, five in all, and they are all coded by the notes from the Chromatic. 65 Measures is a Season, four in all, and they are all coded by the notes from the Harmonic. The Seasons are however, offset from the rest of the composition for specific reasons, being linked to Wind Chime events which mark the appearance of a series of complex structural pivoting points called Polar kin. These three larger cycles are known as the three higher orders of time; the Harmonic Run, the Castle and the Season. For any given kin, from 1 to 260, six musical notes correspond to its location on the Tzolkin, creating two Triad Chords that together create a Hexa-chord Harmony for each.
Most 0f the percussive elements in the work are inherent in the Rhythmic structure of the Wavespell and Castle. Bells mark the 52 Portals or the 52 grey squares of the matrix, known as the Loom of the Maya. In the graph below, the musical harmonic language of the Tzolkin is shown. For any given Kin position, the harmony denoted is represented by the combination of three notes (i.e. the note inside each box and the notes directly to the far left and far right on the same row). These notes relate to the three orders of time, the wavespell, the chromatic and the harmonic. At the top of the graph are the harmonic run drone notes, and excluded are the two remaining drone notes that code the Castles and Seasons. The graph also shows where percussion elements happen like Wind Chimes (on every Spectral Polar Kin circle) and Tam Tams (on every Magnetic Gate square).
Math Behind The Music
Below in the graph The Overtone Series and the Vigesimal Count, the Mayan vigesimal system is correlated to the naturally occurring overtone series in music. This is the basis of the science behind the music. The fact that both the vigesimal system and the overtone series both have a total of 20 quantitative and qualitative numerical expressions.
The Overtone or Harmonic Series is a naturally occurring phenomenon in the nature of acoustics. A sound is invariably generated by the vibration of an elastic body, such as a stretched string, a tuning fork, or an enclosed column of air, such as in wind instruments. A simple vibration is characterized by it’s frequency (pitch) and amplitude (loudness). The acoustic effect produced by a vibration as described above (i.e., one determined by a given frequency) is called a pure sound.
All acoustic sound generating devices, however, produce a composite sound resulting from a simultaneous sounding of many pure sounds. The lowest of these is the so-called Fundamental (or First Partial), which is the one identified by the ear as the pitch of the musical tone. In addition to the Fundamental, there are the so-called Overtones or Upper Partials, which are not heard distinctly because their intensity (amplitude) is much less than that of the fundamental. Nevertheless, they are extremely important, since they account for the different tone colors produced when the same pitch is played on different instruments.
Since the intervallic relationships, or the distance between Overtones, are the same for any Fundamental, the question may well be raised as to how different tone colors can result from them. They result not from the Overtones as such, but from their signature of varying amplitudes in relation to one another (i.e. the varying degrees of their volume).
All acoustic sounds reside within the mathematical model of the Overtone Series. In theory, there are an infinite number of Upper Partials to any given Fundamental. But it is only after the 18th Partial that the intervals between adjacent ascending Overtones become increasingly smaller (micro tonal), than traditional chromatic half steps, which are tonal in nature (i.e., primarily chromatic, of or pertaining to the 12 chromatic steps in an Octave, and also diatonic, pertaining to the 8 scale degrees in and Octave). At this point, tonal forces fall back and micro tonal forces take over. Beginning with the 19th Partial, the ever shrinking micro tonal intervals between adjacent Partials begin to approach a limit or Zero Point. There are a total of 20 different tonal expressions within the span of an Overtone Series. These directly correlate to the Vigesimal Count, known in antiquity by the ancient Maya.
The Vigesimal Count is based on 20 (0-19) unlike the Decimal Count which is based on 10 (0-9). The Decimal Count is inferior to the Vigesimal Count. It seeks a quantitative accounting of number rather than a qualitative understanding of number, which is mathematically superior when dealing with fractal, exponential and aesthetic expression.
In the graphic, there are 7 columns of information for any given Partial. In order from left to right they are: 1) the quality of the interval in relation to the Fundamental, 2) the scale degree and chromatic position in the 13 tones of an Octave, 3) the graphic itself which shows a chain of linked ovals, in octave relationships, creating a series of ascending Partials which form a chord or harmony, 4) the numerical equivalent of the Partial, 5) the Mayan word for the number given, 6) the Mayan dot-bar notation for the number given, and 7) the qualitative expression of the given number and Partial in relation to the Fundamental (Tonic) or Tonal Center of any given Overtone Series. So, an explanation from bottom, up, of each individual Partial, as they accumulate, is as follows:
0 (Zakhal) - Silence (Zero Point) Potential (Conception of Tonal Center) This is the Universal Fire and the Enlightenment brought about by thought in the mind. It is the acoustical silence, the moment before the birth of a new Fundamental, struck somewhere in time.
1 (Hun) - Fundamental (Tonic) 1 (Establishment of Tonal Center) This is the purpose of a struck note which is “pitch” (i.e. the frequency of a tone). This is the unity, the magnet which attracts the resolution of all other Partials in its Series. It’s the core or seed vibration, the singular primal note or grounding father frequency in the Series.
2 (Ka) - 1st Octave (Tonic) 1 (Polarization of Tonal Center) This is the Octave in resonance, the dual nature of pitch. This is the breath of the core vibration. It is the twin center, the mother interval in music, the most perfect consonance in the Series.
3 (Ox) - 1st Perfect 5th (Dominant) 8 (Activation of Tonal Center) This is the sacred cut of the Octave (Phi(13)=8), the servant to the Tonic. It’s the bonding agent between Octaves, the progeny interval in music, the first hint of harmony in the Series.
4 (Kan) - 2nd Octave (Tonic) 1 (Definition of Tonal Center) This is the meaningful alignment of Octaves, the double Octave in resonance (i.e., three sounding Tonics). This is the solid foundation of the Tonal Center. It is the inherent harmonic order and establishment of form in the Series.
5 (Ho) - 1st Major Third (Mediant) 5 (Empowerment of Tonal Center) This is the sacred cut of the Perfect 5th (Phi(8)=5). This is the radiant tone in the Overtone Series harmony. This is the implied center of the first occurrence of a chord in the Series, the Major Triad, which is composed of 3 notes (i.e., the Tonic, Mediant and Dominant). It is the foundation of triadic harmony and utilization of form in the Series.
6 (Uac) - 2nd Perfect 5th (Dominant) 8 (Balance of Tonal Center) This is the sacred cut of the Octave (Phi(13)=8). This is the Dominant in Octave resonance. This is the extended Major Triad. It is the dynamic equilibrium inherent in the Series.
7 (Uuc) - 1st Minor Seventh (Subtonic) 11 (Attunement of Tonal Center) This is the sacred cut of the Perfect 4th (Phi(13-8)=3 where 3+8=11). This is a direct connection between Major and minor scales. This is the first occurrence of the Major Minor Seventh chord in the Series, only found in minor scales. It is the epitome of harmony in the Series.
8 (Uaxac) - 3rd Octave (Tonic) 1 (Harmonization of Tonal Center) This is the integrity of the Fundamental. It is the Tonic in triple Octave resonance (i.e., four sounding Tonics). The blue-plan of full harmonic resonance which models the order and construction of the Overtone Series.
9 (Bolon) - 1st Major 2nd (Supertonic) 3 (Pulsation of Tonal Center) This is the sacred cut of the Major 3rd (Phi(5)=3) This is the expansion of harmonic resonance. This is the first occurrence of the Major Minor Major Ninth Chord, the chord of mastery. It is the propensity of the Tonic to ascend in a diatonic fashion.
10 (Lahun) - 2nd Major 3rd (Mediant) 5 (Perfection of Tonal Center) This is the sacred cut of the Perfect 5th (Phi(8)=5). This is the Mediant in Octave resonance. This is the true identity, fully established, of the Tonic. It is the aligned manifestation of the Tonal Center.
11 (Buluc) - Augmented 4th / Diminished 5th (Tritone) 7 (Liberation of Tonal Center) This is the sacred cut of the Minor Third (Phi(8-5)=2 where 2+5=7). This is the inverse of the Tonal Center, the highly dissonant Partial. It is the dissolving of the Fundamental.
12 (Laka) - 3rd Perfect 5th (Dominant) 8 (Stability of Tonal Center) This is the sacred cut of the Octave (Phi(13)=8), the Dominant in double Octave resonance (i.e., 3 sounding Dominants) It is the universal bonding agent, the cooperative equilibrium in the Series. It represents the crystallization of harmony in the Series.
13 (Oxlahun) - Major 6th (Submediant) 10 (Transcendence of Tonal Center) This is the sacred cut of the Minor 3rd (Phi(11-8)=2 where 2+8=10). This is the presence of change and recirculation in the Overtone Series. It is the unseen movement and search for perfection within the octave, for the theoretical harmonic 6th.
14 (Kanlahun) - 2nd Minor 7th (Subtonic) 11 (Reception of Tonal Center) This is the sacred cut of the Perfect 4th (Phi(13-8)=3 where 3+8=11), the Subtonic in Octave resonance. It is the higher alignment to the diatonic language of minor.
15 (Holhun) - Major 7th (Leading Tone) 12 (Creation of Tonal Center) This is the sacred cut of the Major 2nd (Phi(13-11)=1 where 11+1=12). This is the visionary agent to the Tonal Center. It is the final movement before returning to the Tonic.
16 (Uaclahun) - 4th Octave (Tonic) 1 (Transmission of Tonal Center) This is the conduit of the Tonal Center. This is the Tonic in quadruple Octave resonance (i.e. five sounding Tonics). It is the higher communication of harmonic resonance.
17 (Uuclahun) - Minor 2nd (Chromatic Step) 2 (Evolution of Tonal Center) This is the sacred cut of the Major 2nd (Phi(3)=2), tonal fluidity. It is the synergy of the Tonic and its momentum to ascend and evolve chromatically (i.e. one semitone).
18 (Uaxaclahun) - 2nd Major 2nd (Supertonic) 3 (Realization of Tonal Center) This is the sacred cut of the Major 3rd (Phi(5)=3). This is the Supertonic in Octave resonance. It is the clarity and order of the Tonic to ascend in a diatonic fashion (i.e. one wholetone).
19 (Bolonlahun) - Micro Tonal (Approaching Limit) Infinite (Self-Generating Zero Point) This is the purification and transformation of the Fundamental. This is the beginning of an infinite and exponential decrease in the size of micro tonal intervals. It is the catalyst to the definition of silence, Zakhal, the limit, a cap stone, a new conception.