Page   1   2    3   4     Mandolin Pattern of Unisons and Octaves (page 2)     The pattern in depth (continued) We'll begin with a conceptually ideal complete Pattern of Unisons and Octaves, one that is not split, divided, or fragmented.  Figure 3.     Figure 3       The Pattern of Unisons and Octaves requires a twelve fret area to express itself once and begin to repeat. Recall, the number twelve is the octave number. e.g. twelve chromatic scale steps, twelve frets, etc. Presence of both Unisons and Octaves There are four tones in any twelve-fret pattern, one tone on every string. Only two of those four tones are truly different in pitch, however. That is, they are different octaves of the given unnamed tone. The remaining tones are unison with them. That is, they are redundant duplicates, alternates that give his options. We'll address the specifics of which are octaves, which are unisons, and why, when we emerge the Seven Degree Calculation Line with the Pattern of Unisons and Octaves, in a few minutes. For now, I hope you'll be content with a quick demonstration of proof that the pattern does indeed contain both unisons and octaves of any given tone: In Figure 4 (far left) the pattern is shown rooted at the seventh fret = D. Every tone in the pattern is an D note. [four black diamonds (pattern points) will always occur within the first 12 frets no matter what key or root letter you’re using. For different keys the pattern is aligned at a different fret line. The grayed diamonds seen here are repeats or duplicates, each being one octave (12 frets) away from  a black diamond elsewhere on the same string. Any four consecutive diamonds (one on each string) make one complete pattern] Figure 4 (middle of) Unisons shows patterns within the greater pattern, encircled tones, where unison D notes can be found. Figure 4 (far right) Octaves show's other patterns within the greater pattern where, depending and direction of movement, one will find progressively higher or lower pitch octaves of a D note. [The groupings/routes shown here are not exhaustive. Numerous others could be shown, and none is more correct than another.] Pick up your mandolin and play the groups of tones encircled in this illustration. You should be able to hear the difference between the unisons and octaves of this single tone D. The unisons are basically identical to each other, while the octaves sound higher or lower in pitch compared to each other.     Figure 4       Five pattern parts or fragments Any complete mandolin Pattern of Unisons and Octaves as can be broken down into, or constructed from, five smaller elements or fragments of pattern. That is, every complete mandolin Pattern of Unisons and Octaves consists of five one-octave intervals of two tones each. See Figure 5. Each one-octave interval is a small pattern unto itself. In the end, while the complete Pattern of Unisons and Octaves is indispensable to one's understanding of the whole fretboard, i.e. the big picture, the smaller elements of pattern are more important to our everyday tool-set.     Figure 5       Figure 6 renders the five one-octave intervals using numbers.  Zero and twelve degrees mark each intervals two relevant tones (the two left-most grids contain two intervals each, see the two number 12’s). To make sure that you see and understand that each (and all) of these intervals span twelve half-steps of pitch, a Seven Degree Calculation Line is interposed within each fret-grid drawing. Notice another unique trait of the mandolin’s (verses the keyboard’s) scheme of available tones. That is, the existence of multiple identically-pitched octave intervals. Two of the five one-octave interval shapes can be paired together with two of the others. The fingerings in each of these pairs of intervals produce the same sound, the same pitched one-octave interval. You can see this in Figure 6 with the patterns rooted on strings one and two (the left-most two grids). There are two number 12’s, two options, in those two drawings. Those redundant octave intervals are a consequence of the Unison intervals present on the fretboard (but not on keyboard). The two 12’s are unison with each other (they’re the same pitched tone) These are the same Unison intervals referred to in the name of this greater pattern — The Pattern of Unisons and Octaves. We will focus more on Unisons as we go.       Figure 6             Once you know these seven fingerings you’ll be able to put your finger anywhere on the mandolin fretboard and instantly know the location(s) of similar tones one octave higher or lower in pitch. You could, for example, take any known chord voicing or fingering and create alternate fingerings and inversions of it. That is, by moving any desired tone(s) to a different octave (hence a different location). This is, in fact, how inverted chord voicings are created. Understanding and modifying chord voicings then, is dependent in large part upon your knowledge of these five one-octave interval fingerings. From this moment on, you’ll never truly be done with octave intervals, because you’ll be using them so frequently. For now, we’re going to return to the larger full-fretboard context and the complete (twelve fret) Pattern of Unisons and Octaves. The Rooting Center There is one point within the Pattern of Unisons and Octaves that functions as a beginning, an end-point, and a repeat point. It is called the Rooting-Center. It is located where a tone of the pattern falls on string-one. That  tone on string-one is the rooting-center. The entire pattern is said to be rooted, centered, or based on that tone because it is the lowest pitched octave (version or incarnation) of the given tone that can be found on the mandolin fretboard, standard tuning assumed. All other tones within the pattern will be either unison with it, (i.e. identical, same exact pitch/same octave), or higher pitched octaves of it — higher by one, two, or three (maximum) octaves. The Pattern of Unisons and Octaves, like all fretboard patterns, can be moved up or down the neck to serve any of twelve different tones. That is, the rooting-center can be aligned/rooted on any the mandolin’s first twelve frets. e.g. fret-one = tone G#/Ab, fret-two = tone A. Relative to the tones that are available solely within the first twelve frets, the pattern will present itself rooting-center through rooting-center (as per the black diamonds in Figure 3, in only a few  keys. For example, when rooted/aligned for tone/key G or G#. In the majority of cases, the pattern will occur split somewhere between the nut and twelfth fret. That is, a greater or lesser part of a repeat-pattern will appear above the rooting-center and the rest below. Most of the time then, part of the pattern will fall above the rooting-center and the rest below. The rooting-center is simultaneously: the beginning, the end, and the centering-point of the pattern. Given that the pattern is repeating, above the rooting-center, you never really loose any part of it — even when restricted to just the tones within the first twelve frets. It just splits in twelve slightly different places, depending upon which fret it is centered on, and of course, the pattern never actually stops at the twelfth fret. That boundary is given to make sure that you first understand the repeating nature of fretboard patterns. The pattern, in fact, continues well beyond the twelfth fret, and in many cases, far enough to complete another full pattern. The only real limiting factors are the number of frets your particular instrument has, and then how many of those frets are realistically usable/playable. So again, no matter where it is centered, you never loose any part of the pattern. To illustrate how the pattern splits and divides when aligned for different tones within the first twelve frets, a large repeating sample of the pattern can be used as an all-purpose or universal reference pattern. See Figure 8a. From the oversized reference pattern, at the center of the illustration, isolate or bracket-out any twelve-fret section of pattern* and imagine that it represents the first twelve frets of an actual fretboard, which it very well could. In each isolated section note the following things: where the rooting-center is, (i.e. on which fret) hence which tone the pattern is aligned for and representing. See the Rooting-Centers Alignment Key Figure 7. how and where the pattern splits. This, to begin to recognize pattern fragments. Confirm that all of the pattern is indeed there somewhere above or below the rooting-center (within those first twelve frets). and finally, note how the pattern would (and will) continue, on an actual fretboard, beyond and below the twelfth fret. Refer again to the central reference pattern. The (any) pattern will begin to duplicate (repeat) itself exactly as it fell (and began) from the nut down. That is, fret-thirteen = fret-one, fret-fourteen = fret-two, etc. *To alert or remind you of what is occurring in the open strings, i.e. at the nut or fret zero, like in actual fretboard, thirteen frets-worth of pattern, including the nut, is shown in each isolation. Note the white diamonds (pattern members/tones) present in the open strings.     Figure 7           Figure 8a       Figure 8b shows full fretboard maps of the mandolin’s Pattern of Unisons and Octaves rooted for the following keys, roots, or tonics: C, D, E, F, G and A.       Figure 8b       This illustrative device (Figures 8a and 8b), obtaining any and all specific patterns of unisons and octaves from a single repeating sample, helps us to conceptualize all patterns of unisons and octaves as being a single thing, THE pattern. We can think of the large repeating sample as the parent pattern. It, in turn, can generate twelve offspring sections of pattern. Each twelve-fret offspring-pattern contains all of the genes, (pattern parts) of the parent-pattern. That is, all twelve complete patterns are fundamentally the same. The only difference from one offspring to the next is the relative position of the rooting-center, and that determines how much of the pattern will occur above the rooting-center and how much of it will fall below We began by showing how multiple patterns of unisons and octaves, rooted at different places, are simultaneously superimposed upon the fretboard to create large chord-voicing maps. We used the “C” Major triad as our example. Looking at that illustration again we should be able to understand more clearly what was going on. There can be no doubt that the Pattern of Unisons and Octaves is universal. It is everywhere at all times. Knowing that, you should be motivated to learn everything you can about it. We still have to learn the details about the pattern. And for that, we'll need the Cipher System. We must now link and integrate two reference patterns: the Pattern of Unisons and Octaves and the Seven Degree Calculation Line. In combination, they reveal how all tones on the fretboard are laid out. That is, where everything occurs, and why. The reason for linking these two reference patterns is to allow us to construct and overlay counting-grids on top of and around the points of any complete Pattern of Unisons and Octaves. This will help us to understand the pattern: why it's points fall where they do, what the number-values of the points are, how the points relate to each other, which are octave tones and which are unisons. In the process of identifying the number-values of just the four points of any complete Pattern of Unisons and Octaves we will also and unavoidably obtain the number-values of all the in-between points. Hence, the locations and identities of all the raw material for any musical formula will also be made visible, available, and easy to understand. For the duration of this discovery session we will consider the member points of any Pattern of Unisons and Octaves to be tonics or root-tones, the first tones of any musical material or formula. Numbering  octave and unison tones Before we assign number-values to octave the unison tones on the fretboard, lets quickly review how the fretboard naturally employs and re-employes octave tones, and how the Cipher System handles the numbering and re-numbering of those tones accordingly. This, we will come to recognize, is one and the same thing. i.e. the Cipher System reflects how the fretboard truly and naturally works. In the Cipher System, the first tone, the tonic/root, of any musical material is always numbered “zero” degrees. The first higher octave of the tonic/root will always be found at (and numbered) “twelve” degrees. Additional higher octaves of the tonic/root occur at multiples of the number twelve. That is, at twenty-four degrees and then thirty-six degrees — spanning a total of three octaves, the maximum range possible on the mandolin fretboard. So the tonic/root, it's octaves and Unisons, all of which carry the same letter-name, will be found in any number-line or in any fretboard counting-grid at 0°, 12°, 24°, or 36° degrees. And all octaves of the tonic/root occur at and are numbered in multiples of the number twelve. [Recall, the octave designates of all octaves of zero (the tonic /root) are also encircled with a zero symbol to graphically distinguish them from all other tones and to reinforce and remind us of their shared relationship, function, and identity. They are all akin to zero.] Unison tones, being identical to each other (having the same letter-name and the same exact octave pitch) will, of course, share the same number designate. e.g. 0° and 0°, 12° and 12°, 24° and 24°, are pairs of unison tones. 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