Ancient Mode

Abstract

The Ancient Mode is a composing technique that is based on a synthetic scale named the "ancient scale," which has been used in my compositions since 2002. As I analyzed my own works over time, the Ancient Mode emerged as a technique and gradually developed into a complex system. The purpose of this white-paper is to reveal and explain the mechanics of the Ancient Mode, which has been de facto used systematically in all my works composed after 2014.

Introduction

Preamble/Statement

The Ancient Mode is a composition technique in which musical forces operate according to a clear and predefined tone-matrix; it is a self-sustained sphere of music mechanics. Unlike the major or minor scales, or the renaissance or Messiaen's modes, the Ancient Mode is not just a scale nor a mode, but it is a mode-of-operation. It involves a complex interplay of voice-leading, harmony, harmonic progressions, counterpoint, and even tone color.

My aim here is to present and explain crucial elements of my composition system, but on the other hand, it is not a tutorial on how to compose, and it is not necessary to comprehend the system before listening to my music. Rather, it is a theoretical work designed to bring my music and its mechanics closer to anyone interested in the field of music theory and composing techniques.

Inspired by Messiaen, who defines his theory of modal system, harmony, and rhythm that follows specific rules or constrains in his famous theoretical work "The Technique of My Musical Language", here I wish to present, in the same spirit, a precise and limited scheme that expands all principles of the tonal system (Ger. "tonsatz") as they are. This scheme may be compared to "Palestrina's strict counterpoint", and its main objective is to built a melodic and harmonic model, but may also include rhythm, instrumentation, tone color, and other principles of musical composition. The exact system of voice-leading and harmonic progressions is the essential fundament of the entire tonal system ("tonsatz") of the Ancient Mode.

Throughout my artistic journey, which is still ongoing and to me meaningful today, I have been influenced by various sources, including my own mental and spiritual endeavors as well as fortuitous circumstances. As a composer, I have always aimed to explore the realm of music where spiritual qualities are paramount, and where the principles of sound expression reign supreme. Thus, my journey towards discovering the Ancient Mode first as a musical language, and second as a mechanics, has been varied, joyful and blissful.

Acquiring knowledge of compositional techniques alone does not guarantee the ability to create exceptional works of musical art. It is questionable whether such a feat is even possible, as understanding of the work and compositional techniques requires knowledge, whereas creating something artistically profound by utilizing various compositional techniques requires genuine wisdom.

I hold the belief that this kind of wisdom exists in a meta-realm, where faith takes precedence over logic. When faith's warm glow suffuses all parts of one's being, and when it is a guiding light, the music creations become a reflection of an unbridled spirit, unafraid to explore the uncharted depths of the intangible and unexplained. However, faith is constrained by dogmas. Personally, my aim is to transpose the dogmas of my Christian faith into my musical dogmas. Following these dogmas means staying focused on a particular matter and attempting to move forward without distraction, move indefinitely, into the abyss of the unknown.

At this juncture, I shall eschew the imprecision of poetry and theology and instead rely on reason, for those lifting the eyebrows. Nonetheless, I must emphasize that reason alone cannot explicate the fundamental nature of my musical creation, but only the methodology employed in its construction. Therefore, in the coming text you will read "how" I have composed music, but not "what" I have composed. I will show how the system of Ancient Mode was created, starting from the ancient scale and demonstrate how to build melodic and harmonic structures using the scale. I will also compare this system with previous musical traditions, specifically the Byzantine music, which is the traditional spiritual music of the Orthodox Church located in the Byzantine Empire, as well as the strict vocal polyphonic style of the late Renaissance as exemplified in the music of Palestrina.

Limited Framework of Operation

In an effort to clarify my concept of a strict tonal structure (as in "tonsatz"), I posed the following question to myself in the year 2000: "What constitutes style?" I was contemplating both musical styles and the arts in general, and as a result, I arrived at the subsequent conclusion:

The style is: creation of endless possibilities within an extremely limited framework.

By imposing limitations, the arts are clarified and rendered more stylized. The more constraints are applied, the greater the resulting crystallization becomes.

The second important aspect of the arts is the verification of the plausible identity of the applied limitations mentioned above. This means that the identity must be verifyed through the acoustic properties of the music composition. By having its own tonal scheme, the music will attain its own plausible identity. It is suspicious to have an extremely complex compositional system in which errors cannot be detected or acoustically verified, as this can neither alter the identity of the work nor improve it. Therefore, in addition to the applied limitations in the form of the system by which the art is generated, the framework must also include the notion of error and its negative consequences for the final product of the artwork. This leads to the following, second important conclusion:

To create a plausible identity of a musical composition, the framework for music composition must include both A) the system of limitations that the music operates within and B) the definition of errors and their exclusion through acoustical verification. This limited framework ensures that errors are prevented, and that the work's identity is established.

Ancient Scale

Structure of the Ancient Scale

The Ancient Mode is founded on a synthetic scale, which I refer to as the "ancient scale," and I will clarify the reason behind its nomenclature later. In brief, the scale possesses a pleasant acoustic quality that I enjoyed when I first encountered it, and this enjoyment persists even today.

Ancient scale in C

The ancient scale is similar to Messiaen’s Second mode, which is an octatonic scale (OCT). The ancient scale is enneatonic, has one more pitch added into OCT₁₂ here creating ancient in C, and has a unique feature: the added pitch is considered as the central tone or "key", thus creating dense half steps around it. Unlike the tonic or the finalis, the central tone is not a specific, nor functional pitch in the scale. It is constructed in a particular way so that it creates symmetry. Therefore, the axis of symmetry is the central tone that creates the "key" for the scale. Here is the bracelet diagram, or MOD12, that shows the symmetry of the scale, and the Tonnetz diagram that helps to visualize common triads, the triangles, and circle-of-fifth relationships, the horizontal lines.

MOD12 of the ancient scale in C

Tonnetz diagram of the ancient scale in C

Properties of the Ancient Scale

The ancient scale has the following properties:

1. The cardinality is 9, it is an enneatonic scale.
2. The Pitch Class Set is [0,1,2,4,5,7,8,10,11].
3. The interval structure is [1, 1, 2, 1, 2, 1, 2, 1, 1].
4. The interval vector is {6,6,8,6,6,4}, and is not a deep scale (maximum hierarchization). e) The scale has symmetry with axis.
5. Forte Number is 9-10.
6. The scale is not in Prime Form (using the Starr/Rahn algorithm). The prime form is ancient scale in D.
7. There is none rotational symmetry, thus the scale has 12 transpositions.
8. It is a palindromic scale.
9. The scale has 6 hemitones (two tones separated by a semitone interval), and it has 3 cohemitones (an instance of two adjacent hemitones).
10. Proportional Saturation Vector is 0, 0, 1, 0, 0, 1, defined by M. Buchler (2001).
11. Heteromorphic Profile is (4, 84, 168), defined by N. Carey (2002).
12. It is not maximally even.
13. Coherence Quotient is 0.81.
14. Sameness Quotient is 0.417.
15. Naming: Ancient Scale (D. Zivkovic), Epolygic mode (by W. Zeitler), WAHian (dozenal system by J. Pecot).

Scales that are close to Ancient Scale in C are Octatonic in C (OCT₁₂), Messiaen Mode 7 Rotation 4, Moorish Phrygian (Phrygian/Double Harmonic Major Mixed), Chromatic Bebop, and Diminishing Nonamode.

Proto-use

The scale is used in my compositions since 2002, in works Two Sophisticated Preludes No.1 (2002), The White Angel (2006), Le Cimetière Marin (2008), I Shall Contemplate… (2011) and On the Guarding of the Heart (2011). Through the analysis of these works, particularly the last one, the Ancient Mode as a technique was slowly constructed, and works after 2014 are partly or fully composed in the Ancient Mode.

The first composition that features the ancient scale in key of G# was written in 2002, titled Sophisticated Preludes No.1. The scale was used in its chromatic genus, and without any deliberate attempt to create a system of any kind, be it symmetry, systematization of harmony, voice-leading, chord progressions, so I name that type of use as "free style".

PICTURE

It took approximately one decade to fully develop and synthesize the sound-aesthetic of the Ancient Mode, which reached its climax in the composition On the Guarding of the Heart in 2011. And after that it took a few years more to establish a system in which the scale would operate.

Other Qualities

The ancient scale has extremely diverse chordal possibilities. It includes a multitude of tonal associations and can create clusters, minor and major chords, pentatonic scale, diminished and augmented chords, and near-to complete the major and minor scale. Comparing to all modes that can be made using by combining 7 or 8 or 9 tones within the frame of octave (all their possible combinations), the ancient mode has the lowest difference-tone integrity. The low difference-tone integrity means that the ancient mode generates many difference-tones outside itself. We could also say that this is a phenomenological richness in reference. The highest difference-tone integrity has Messiaen’s third mode, which is the opposite attitude: it refers strongly to itself. Within 8 tone scales, the acoustic scale (Messiaen 2nd mode) also has low the difference-tone integrity. Investigating scale classes with 7 tones shows that major (and its related) has the highest difference-tone integrity, which is opposite to the ancient scale. Thus, the lowest difference-tone integrity of the ancient scale may be the reason of its vibrating sound, and even before that investigation I have named it the ancient, only due to its vibrant and colorful sound that reminds me of the past.

Here is an illustrative example of how triads are connected within the ancient scale in G#.

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Sculpting the Ancient Mode

Preliminary Analysis

The structure of the Ancient Mode (AM) was developed by analyzing pre-existing compositions, primarily I Shall Contemplate... (2011) and On the Guarding of the Heart (2011), in which is used the ancient scale in G#.

PICTURE

The reason for the key of G# is found in its construction which is very easy to remember and perform on the piano: all the black keys as the pentatonic scale and the C-major chord with add6. Therefore my first attempts to use more defined constrains were fundamentally grounded in the concept of symmetry in keyboard design. The scale in G# visually displays the axis and symmetry: starting from the middle G#, the keys are equally arranged as in mirror. The white keys can be practically arranged as two dyads (minor thirds) with the axis of G#: e-g-(G#)-a-c, and the black keys can be visually arranged as two dyads (minor thirds) including the axis of G#: d#-f#-G#-a#-c#.

PICTURE

The primary emphasis of the analysis was to investigate the piano texture of these two above mentioned compositions. While both utilize the ancient scale in the free style, they possess a unique sound compared to earlier pieces such as Two Sophisticated Preludes and The White Angel. Thus, my goal was to determine these unique parameters, and the mechanics of these textures were closely observed to identify the features that would make the foundation for AM. Now, take a look at the piano part from the beginning of On the Guarding of the Heart.

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The following features of the piano part in On the Guarding of the Heart are:

1. The scale in G# was used without notion of tonic (finalis);
2. The building unit of harmony (or harmonic blocks) are primarily dyads, mostly of the fourth, the fifth, and then the minor and major thirds;
3. When constructing harmonic blocks using the dyads, it is typically done on either two white keys or two black keys, because of the piano keyboard symmetry of the ancient scale in G#, there are many visual symmetries of dyads of intervals of third, fourth and fifth that can be easily utilized through improvisation on the piano:
   
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   However, the choice of using dyads on white or black keys does not have a significant impact on the mechanics of AM. Nonetheless, using only black or only white keys does result in more common thirds, with higher preferences for the minor thirds, which gives a particular "minor" or "introvert" sound.

   
   
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   It is important to note that all thirds were also utilized. If we pay close attention, we can see that the frequency of minor thirds is again slightly higher compared to the major thirds, with the vector ratio of 8:6.

   
   
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4. Harmonic units consist of two or more pitches. They are typically developed through either a) complementary or b) functional approach. Complementary harmony involves building the harmony by completing it with two (or more) consecutive intervals, so that the separated intervals that create one, single function Φ (Fig 12):
   
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   Functional harmony, on the other hand, involves creating new functions (Φ...), usually through leap or stepwise movement of two adjunct dyads:

   
   
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   Complementary harmonic units are constructed to affirm one function, according to the classical sense of tonality i.e. tonal harmony, using thirds, fourths, and their inversions to create a specific acoustic effect. On the other hand, functional harmonic blocks are designed to generate two or more new acoustic impressions of functions, while still considering the classical notion of tonality.

   The choice between using complementary or functional blocks is not fixed, and ultimately depends on the observer’s acoustic impression. As there is no defined concept of tonality in the AM, the notion of bitonality becomes questionable. Therefore, the second example, consisting of two functional blocks (Φ1 + Φ2), could also be interpreted as a single, yet more dissonant or bitonal, complementary block (Φ).

5. Applying the methods outlined in d) reveals a distinction in the way consonant and dissonant intervals are treated, according to the tonal or even acoustic interpretation of the intervals. This principle is particularly noticeable when harmonic changes take place within the same register range. Recognizing the concept of consonance and dissonance, as well as registers is the crucial aspect of the coming AM.

These principles served as the primary motivation behind my continued research into this scale and developing a structure that would generate this type of sound by pre-learned constrains.

Operations of the Ancient Mode

The Byzantine church music doesn't use scales in the same way it is used in the Western music, but instead utilizes so called tones, which are actually a combination of modes and patterns that determines how a particular tone operates. However, the characteristic of these tones is not in its scalar construction. The concept is primarily based on "melodic patterns", or micro- melodies, which are the building blocks of each individual tone. So, instead of having only an ascending scale consisting of seven pitches that could be freely used, the tone is "a library of patterns" which consists of numerous melodic snippets that are building that tone. There are eight tones, therefore the Greek name is octoechos, and all of them have their specific sounding, that reminds us of major or minor keys. There are a large number of snippets that are available, and all tones have their recognizable collection of melodic patterns. However, it is the text sung that determines which pattern can or cannot be used, depending on the number of syllables, phrasing of the text, accentuation, even the theme of the text, and so on.

The patterns that are a part of tonal system are not only found in the Byzantine music. Anyone who has studied the counterpoint, be it Renaissance or Baroque, finds that all kind of rules can be understood as a rule of "melodic patterns". The nota cambiata is a perfect example of it. It is a melodic figure, it has its proper function and can be used at specific points in musical texture. The Byzantine tones are however more constrained, since it is basically a single melody chant, highly controlled, sung over a semi-moveable tone called ison.

The First Mode of Operation

The First Mode of Operation in the AM consists of two rules:

1. the principle of complete utilization of the chromatic scale, and
2. the principle of filtering.

To compose within AM, all 12 pitches of the chromatic scale are utilized as the input {IN}, but by filtering through the ancient scale, only the pitches that belong to the ancient scale are selected as the output {OUT}, while others are eliminated or filtered using various techniques.

PICTURE

As it can be seen above, the ancient scale does not cover the entire chromatic scale. However, the use of all 12 tones as input is mandatory in the Ancient Mode. There are three types of solutions that create three genuses: chromatic, diatonic and melodic genus.

Chromatic genus

To create the chromatic genus, both the chromatic and the ancient scale must follow their own pitch order in both ascending and descending direction, and for that reason two rotors are used. Due to differences in the lengths of the scales, the rotors associated with each scale do not share the same size. The first rotor, located below, is representing MOD12 (rotor) of the chromatic scale, and the second rotor above is representing MOD9 (rotor) of the ancient scale in C. Both scales must have one single connection in order to operate, similarly to wheels in an analog clock. Their connection represents the transposing mechanism, and they turn each other as wheels. Transposition, or better to say "mapping" is done at the place they touch each other.

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As they must also have one default pitch from where the transposition starts, in our case it is the note C in the first octave or so called "middle C", MIDI number 60. This pivot note is arbitrarily chosen, but regardless of it, the system would work if the pivot note was another pitch as well. Having the central, pivot tone at pitch 60 is the most convenient for music operations.

It is also important to note that similarly to the rotors which move in the contrary motion as in analog wheels, so it is with our two rotors. Therefore, the rotor of the ancient scale above has its pitches in the reverse order, so that when the pitches go upward in the chromatic scale (0, 1, 2 or C, C#, D), the rotor of the ancient scale is moved also upward (0, 1, 2 or C, C#, D).

We should also keep in mind that the rotors are indefinitely going up and indefinitely going down, as integers. It means that the pivot note and the octaves of both rotors are only equal in MOD12 and MOD9 at note 60 (@MOD12 0=60 and @MOD9 0=60), it is the only note that is the same for both rotors. But as we go in the clockwise motion in MOD12 (turning the rotor to the left so that it is located on the top of the rotor), after pitch-class 11 (note 71) comes pitch-class 0 (note 72). The same principle is in reverse, counterclockwise motion. If we turn the rotor one pitch-class to the right in the MOD12 we will get 11 (but note 59), and turning the rotor one full circle to the right we get again @MOD12 PC0=note48, so to say one octave lower C. This also means that each one full circle clockwise and one full circle counterclockwise for both rotors means one octave below or one octave above. However, their rotors are not of the same size. Here (Fig 16) is how the transposition looks like after moving one full octave up of the chromatic scale (turning the rotor of MOD12 to the left, one full circle, from PC0 to PC0):

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The rotor of MOD9 looks now differently at the connection with MOD12 (Fig 16). The connecting tone for each, or the mapping, is now @MOD12 PC0=note72 and @MOD9 PC3=note76.

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The chromatic genus was sporadically used in my earlier compositions in which I utilized the ancient scale, such as "Sophisticated Prelude" No.1, "The White Angel" and "Le Cimetière Marin". To facilitate the process of transposition, various Max patches were created as the mapping (transposition) tools. It also means that the full piano keyboard could be used completely chromatically and freely. However, the registers were "narrowed" since the top and the bottom of the piano register was already out of the reach, since the MOD12 rotor spans more than one octave of the ancient scale’s rotor MOD9, more specifically: one octave and 3 pitches more. It means that after three chromatic octaves, one octave in ancient chromatic scale is lost, in both directions from note 60.

Let us now create music using the chromatic genus' rotors. Here is a fanfare for trumpet solo:

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Diatonic genus

In an attempt to solve the issue of octave shifting in the chromatic genus, I have utilized pitch repetition by tying the absent tones of the chromatic scale to the present ones in the ancient scale. This creates an opportunity to form MOD12 for the ancient scale as well. This principle creates the diatonic genus of the ancient scale (Fig 18), thus the same principle was used: the chromatic scale is used as the input and then filtering through the ancient scale in C, that included repeated pitches.

PICTURE

In the diatonic genus, the missing tones are replaced by repeating the previous pitches. This means that all 12 tones of the chromatic scale are used as input, but certain tones are repeated consecutively as they are filtered specifically. It is important to understand that the integers and the pitches are two separate subjects, and they can correspond or not. It means that pitch D can be either integer 2 or integer 3, and this depends on what integer was used as the input in the chromatic scale. We don’t know if tone D is the integer 2 or 3, we must see if the pitch was played as integer 2 (or PC2) in the chromatic scale or as the integer 3 (or PC3) as input {IN}.

Now we understand and can imagine that we have both for the chromatic and for the ancient scale the MOD rotor, of the same size, MOD12. Here is a melody built on this principle:

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The Second Mode of Operation

After conducting multiple tests on the diatonic genus, I have arrived at the conclusion that it has more flaws than merits when compared to the chromatic genus. The only positive aspect that I see is the principle of octavization. However, the system of repeated pitches and the absence of validation regarding the repeated tones (proof-of-work) present significant challenges. This is why the melodic genus was developed.

Melodic genus

The Second Mode of Operation means "melodization" of the ancient scale. The missing pitches are not replaced by repetition of the previous note but going back to the next to previous note. Because the term scale in Latin means to climb, we need to create a movement, not repetition. That gives us a scale that has 12 pitches in order to satisfy need for MOD12, and the pitches are "in move" in order to satisfy need for scalarity. There are numerous variants of melodization, but the following melodization of the ancient scale creates the most authentic sound which is similar to my compositions "I Shall Contemplate..." and "On the Guarding of the Heart", and it will be explained more later.

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Now, we must recall how the Byzantine tones operate, they are a kind of melodies. If we play now the chromatic scale by using only the semitones {IN}, very soon will various patterns establish its presence in the ancient scale's output. This technique has created a melodic pattern, the melodic genus. These characteristic intervals are, in the ascending direction, pitch of –1 and of +3 {OUT}, and both are repeated three times as a block [–1,+3] {OUT}.

It is now clear that this mode of operation can also use the rotor consisting of 12 pitches for both the input and the output. The difference from the previous diatonic genus is that now there is no presence of consequently repeating pitches, so when the rotor of the chromatic scale is turned for one step (positive or negative) we get always a new pitch, not the same pitch. Here are the MOD12 rotors, below is the chromatic scale as input, and above is the ancient scale in its melodic genus as the output:

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The Third Mode of Operation

As we have established the melodic genus of the ancient scale, now we must see how the scale operates on a micro level and what kind of motions are available. In general, there are two types of motion: the stepwise motion and the leap. The Third Mode of Operation declares that the scale uses the stepwise motion in the scalar order. It means that the stepwise motion is possible only by using +1 or –1 motion {IN}. As we have seen, not all motions of +1 {IN} will result in an increased semitone {OUT}. The Third Mode of Operation also declares that there is not possible to use a leap of 3, because it is equal to the motion of 1 {IN} between PCs 3-4, 6-7 and 8-9 {OUT}.

Using tonal harmony as an analogy, we can observe a differentiation of pitch classes that are positioned in a certain order. The dominant 7 in C major is G-B-D-F, and not randomly placed PCs 7-E-2-5. Therefore, we always use the ordered intervals, as we mentioned above, and the exact positive and negative distances, i.e. positive or negative integers. It means that if we go from PCE motion +1, we will get the exact pitch of PC"12", and not relative PC0. The same is if we go from PC0 motion –1 we arrive at 12–1 = PCE below, therefore every positive integer means higher pitch number {IN}, and every negative integer means lower pitch number {IN}, regardless of what we get as result by filtering the input through the melodic genus {OUT}. The importance of this factor is particularly evident in the motion of leap. Nonetheless, our subsequent investigation will demonstrate that this procedure is relatively simple and does not give rise to any uncertainty nor difficulty.

Creating Dual-identity

Now let us see if there is any possibility to create plausibility of the distinction between PC1 and PC3 in the ancient mode's melodic genus. Can we distinguish note G, and understand them as separate pitch-classes, as PC1 and as PC3?

If we use the Third Mode of Operation, thus allowing only the stepwise motion by 1, certainly we cannot move to any pitch freely. Let us start from the PC1 to investigate this:

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As we can see, the only possible movements from PC1 are half steps up or down in the chromatic scale {IN}. Now, we see that using MOD12 of the melodic genus, we still get the same pitches and PCs that are 2 and 0, as with IN. The question is what would happen if we start from PC3?

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If we now compare the same movements (1, –1) with the results of PC1 and PC3, we see that the stepwise motion from C# to E is possible only if we use PC3 and no other possibility. If we have output as C#-D, we understand it as two possibilities: either PC1+1 or PC3–1. Now, here is the question, how do we know if it is PC1 or PC3? We don't know as long as there is no presence of other pitches coming before or after. Let us see from what pitches we could come to note C#. It is not difficult to figure it out, these are the same pitches as we have now as the possible movements. It means that into the note C you could arrive:

1. PC1: 0 and 2
2. PC3: 2 and 4

We can stay forever between C#-D interval, and as quickly as we leave to other pitches, we understand that they are different classes and so the identity of each PC is created. The melodic pattern of preceding and next pitches gives us information of the PC's identity. It is also of utmost significance to mention that the subsequent Mode of Operation will categorically prohibit any kind of ambiguity, thus rendering the motion between Pitch Classes 3-4 feasible only in a stepwise fashion.

The Fourth Mode of Operation

To distinguish the stepwise motion from leap we must take in consideration that the notion of stepwise motion in the melodic genus also include the interval of minor third (3) in {OUT}. It means that we cannot create motion of leap by using 3. As I discussed above in the "Sculpting of the Ancient Mode", there are certain intervals that are more prominent than others in my analysis of the previous compositions. Here, with the melodic genus, we have motion of 1 and motion of 3. Now let us consider how we can get motions of the fourth (5) and motion of the fifth (7), or the motion of leap. These two intervals were the most prominent in my works from 2010 and later. Remember, if it is allowed any kind of leap, then there is no reason for creating the melodic genus, nor creating MOD12 rotor for the ancient scale that consists of different 9 pitches.

Therefore, the Fourth Mode of Operation instructs that there is only one type of leap: leap by fourth (+5 and – 5). It means now that we have stepwise motion by 1 and leap by 5. There are no other types of motions and these types of motion create a completely new spectrum of music mechanics. Remember, these types of movements are considered not as the {OUT} pitches but rather as the {IN} pitches of the chromatic scale. The input of stepwise motion in the chromatic scale by +1 or –1 and leap by +5 or –5 gives totally different results as output, than what we expect.

The very important aspect of the Fourth mode of Operation is therefore creating the MOD12^5 rotors that represent the leap motion of 5. The rotor below represents the chromatic scale's leaps of 5, or circle of the fourths as IN, and the rotor above represents the ancient scale melodic genus' leaps of 5, as {OUT}.

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Now let us create a melody using this operation and using the MOD12 rotors to get the correct pitches.

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The Matrix

Our objective is to simplify the MOD12^5 rotor's function and make it more practical, we will create a scheme, so called The Matrix of the Ancient Mode.

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From now, we can get familiarized with the Matrix, which will be one of the most important tools for the Ancient Mode. The Matrix consists of a) horizontal rows that represent the stepwise motion or MOD12>1, and b) measures or the columns that represent the leap of fourth or MOD12^5. The middle C, MIDI 60, is marked red. As we can see, motion from pitch to pitch can happen only vertically or horizontally, similarly to the rook figure in chess. The Matrix displays the output information {OUT}, it is what we get when the chromatic scale as input is filtered through the melodic genus of the ancient scale {IN}.

So, the Fourth Mode of Operation defines the vertical motions in absolute leaps, as discussed earlier and not relative pitch classes, while also including the horizontal, stepwise motions. It means also that we have two dimensional pairs of rotors as the mode of operation, the first pair for stepwise motion of 1 (MOD12>1) and the second pair for leap of 5 (MOD12^5). Additionally, we see that the intervals are fixed by pitch (as MIDI number) not by pitch-class, but still we need to keep both notions in our consideration.

We have already noticed that the melodic genus has specific intervals in the stepwise motions. Now looking at the Matrix, we see that every leap of 5 {IN}, as the interval of fourth, does not always give the exact leap of 5 {OUT}, but includes a limited number of various intervals that are fixed at very specific places. In that regard, the leap of 5 {IN} means that in the ancient mode of melodic genus we always get as the output intervals of 3, 5 and 7. These are exactly the same intervals I have analyzed in the compositions before the Ancient Mode was established!

It means that through the analysis of earlier works, I have tried to create a system and to get the same or similar acoustical result. My joy of these discoveries was great, and my satisfaction that the ideal of making music universe first and discovering the mechanics of it later was profound. After a musical style has been integrated into the automatic responses of a composer, it may be regarded as a multifaceted probability system. Out of an extremely limited scheme, I wanted to create a norm, or postulates in which the music mechanic operates - by default.

Questions

Can we create the melodic genus with any scale?

Indeed, the melodic genus can be created using any kind of melodic patterns, be it a cantus firmus, a melody, or a synthetic scale. It's important to note that the pattern should not simply consist of a stepwise motion upward, as is typical of regular scales.

What is difference between the stepwise motion and leap, can I make any kind?

The stepwise motion is an essential concept of the melodic genus that cannot be altered. It determines the micro-cells of the genus and is similar to the Byzantine music or the strict Renaissance style. Nevertheless, the leap of 5 can be substituted with other leaps, except for 1. Keep in mind that your goal is to develop a self-sufficient musical system that encompasses all its aspects. If your melodic genus has more than 12 tones, the leap of 5 {IN} will probably become third or even major second {OUT}.

Do I need to use MOD12 to create the melodic genus in it?

It is possible to use any MOD-length for this purpose. Creating a MOD14 or similar may result in interesting outcomes. The initial scale will be in that case longer than the chromatic scale, and it may have some benefits.

Do I need to create the melodic genus within span of one octave?

It is not a requirement, as said above, but I chose to do it to make the system more manageable for orchestration, transposition, and octave playing. However, if your scale extends beyond an octave, such as C(60)-C#(73), it may become more challenging to orchestrate when octaves are necessary. Nevertheless, octaves may not be essential, and you might be able to find a solution through your creativity!

What is future of the Ancient Mode?

I believe that this can unveil an entirely novel range of musical mechanics. It has the potential to generate music that is remarkably consistent, with an increased probability system that enables the formation of new kinds of matrices, characterized by high regularity. By adopting a constrained framework of the Ancient Mode, I endeavored to formulate a standard or a code of rules that govern the mechanics of music, not solely through numerical means but above all by means of the audible outcomes. Notably, Messiaen's treatise is concerned with his musical language, and here I would like to underscore the term "language". It is evident that Messiaen had first experienced his music as a language before documenting a theory on it.

Using the Ancient Mode

The first steps

It will be much easier to imagine and create music just by looking at the Matrix, without actually need to use transposition scheme or MOD12 rotors of the chromatic scale. The Matrix gives us instruction how to move in both directions stepwise (right and left) and in both directions by leap (up and down).

We can create also a Max patch use MIDI keyboard for direct input that would do the transposition for us, and we just need to play either stepwise {IN} motions by 1 or leap {IN} motions by 5 throughout the chromatic scale. Here is one:

PICTURE

(from below is not completed)

Chordal Functions

This explains that the functions are arranged vertically (by leaps) across the full spectrum.

Visual Blocks of Harmonization

This explains how the harmonization can be organized by "visualization" of the chords, making different patterns.

The rules of the Ancient Mode

Rule of Compound Leap

This rule covers compound motion of 5^2, or more.

Rule of Free Leap for Non-pivotal Notes

This rule covers the "movable" tones that are part of chord progressions. They are non-pivotal notes.

Rule of Free Leap Within Sequences

This rule covers free leap only in the case of sequential repetitions, or after the phrase closure.

- Sequences (Seq)

Explaining what is the sequence.

Rule of Modulation With Juxtaposed Scales

- Scale-filtering (Fil)

This is explanation of what is the scale filtering.

- Modulation (Mod)

This explains how the modulation rule works, on melodic and harmonic basis.

Rule of Moving Pivotal Note

This rule explains how in a phrase of harmonic progression one note can loose its pivot value and give it to some other voice.

Advanced techniques

Melodic Alteration (Alt)

This technique covers alteration of a phrase by keeping the same intervals, but not the same compound number of the leap.

Chord Alteration

This technique covers alteration of chords by using rotations around the pivot tone-

Modulation of the Registers

This technique explains how a particular register can be affected only by one scale filter, while another register by another scale filter.

Building Chords by Scale-filters

to cont.

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