Page   1   2     Pattern of Unisons and Octaves for Stick (page 2)     The pattern in depth (continued) We'll begin with the Pattern of Unisons and Octaves for tone C.  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 On a 10 string Stick, here are 10 tones in any twelve-fret pattern, one tone on every string. Approximately half of those 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, 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 the pattern is shown rooted for tone C. Every tone in the pattern is a C note. Figure 4 (middle of) Unisons shows patterns within the greater pattern, encircled tones, where unison C 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 C note. [The groupings/routes shown here are not exhaustive. Numerous others could be shown, and none is more correct than another.] Pick up your Stick and play the groups of tones encircled within this illustration. You should be able to hear the difference between the unisons and octaves of this single tone C. The unisons are basically identical to each other, while the octaves sound higher or lower in pitch.     Figure 4       Figure 4b illuminates a special case specific to the Stick. That is, Unisons residing across logical tuning-halves [two versions: 10 string Standard and Matched Reciprocal tuning are included]. See Constellation of Unisons at far right. These patterns are in addition to the typical diagonal straight-line Unisons pattern common to all fretted string instruments including Stick.       Figure 4b     Tunings:   Standard   Matched Reciprocal       Figure 4c illuminates more special cases specific to the Stick. That is, one-octave intervals residing across logical tuning-halves [two versions: 10 string Standard and Matched Reciprocal tuning are included]. See Constellation of One-Octave Intervals at far right. Again, these patterns are in addition to the typical diagonal straight-line one-octave interval patterns common to all fretted string instruments, including Stick.       Figure 4c     Tunings:   Standard   Matched Reciprocal       Pattern parts or fragments Any complete Pattern of Unisons and Octaves as can be broken down into, or constructed from, many smaller elements or fragments of pattern. That is, every complete Pattern of Unisons and Octaves consists of (at least) 14 one-octave intervals of two tones each. 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 isolates the one-octave interval shapes and arranges them in a manner suited to examination and study. That is, in a straight line moving across the fretboard. The intervals are rendered using numbers rather than diamonds, with zero and twelve degrees marking each interval’s two relevant tones. To make sure that you see and understand that each (and all) of these intervals span twelve half-steps of pitch, a Five or Seven Degree Calculation Line is interposed within each interval. Figure 6 shows these same intervals again, but without numbers, to highlight another unique trait of the Stick's (verses the keyboard’s) scheme of available tones. That is, the existence of multiple identically-pitched octave intervals. Many of the one-octave interval shapes can be paired together with two or three of the others. The fingerings in each of these pairs of intervals produce the same sound, the same pitched one-octave interval. This redundancy doesn’t diminish the value and need of any of the one-octave interval fingerings. They're all equally important and should all be memorized. The fact that some of them can be paired off, because they create the same thing, should be taken as a bonus, a bonus pattern, that will help us later to conceptualize and link the parts of the whole fretboard together. These redundant octave intervals are a consequence of the Unison intervals present on the fretboard (but not on keyboard) 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 5           Figure 6       Once you know these one-octave interval fingerings you’ll be able to put your finger anywhere on the 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 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. Normally the Rooting-Center would be located on the lowest pitched bass string — which would be string-six on a 10 string Stick. After much consideration, I’ve decided to use the tone on string-one as my rooting center. It’s the point I can visualize best as the central reference tone with others radiating around it. The choice of which tone to use is up to you, but I’ll take you through my thought process just for the heck of it. As I said, normally the Rooting-Center would be located on the lowest pitched bass string — string-six on a 10 string Stick. The entire pattern would normally 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 given fretboard. All other tones within the pattern will be higher pitched octaves of it. In the end, I’ve decided that the one-octave-apart relationship between the tones on strings 1 and 7 are more important to me, more useful, easier to see and remember, they’re closer together, both in standard and matched reciprocal tunings. So in the end, I had to choose between the tone on either string 7 or string 1. Ultimately, my choice to use the tone on string 1 as my rooting center is because it’s on the first string of the melody half of the Stick, the half I’d be gravitating to most, being a guitarist. So I’d be piggy-backing off of things I already know best, the guitar’s (4ths tuned) Pattern of Unisons and Octaves, and then have that easy visual and physical link to the bass strings (5ths tuned) Octave Pattern radiating from a tone laying one fret and two strings over (in Standard tuning). From there I can visualize quite a bit of the bass strings Octave Pattern to get me started. See these radiations from the tone on String 7 in Figure 7. Both Standard and Matched Reciprocal tunings are shown.     Figure 7       Besides the fact of the close proximity and one-octave-apart relationship between the tones on strings 7 and 1, there’s another reason I decided against using the tone on string 6 as my Rooting Center.  In a nut shell, the tone on String 6 is only the “lowest pitched incarnation of a given tone” in half of all possible keys (tonics/roots). The other half of the time the tone on String 6 will be Unison with the tone on string 7. Meaning, half of the time the tone on Sting 6 will two octaves lower than the tone on String 1, and the other half of the time it will be only one octave lower in pitch than the tone on String 1 and in that latter case be Unison with the tone on String 7. Figure 8 illustrates this phenomenon with the tone on String 6 by aligning it in turn with each of the fretboard’s first 12 frets. Notice the alignments in the top row, the tones on strings 6 and 7 are marked Unison, because they are. First though, you might want to see the octave relationships among the tones in question (those on Strings 1, 7, and 6) shown in Figure 9. See the relationship between the two tones on Strings 6 and 7 marked Unison near the bottom of the drawing. It’s the instances where that relationship appears within certain alignments, certain keys, that led me to discard the tone on String 6 as the Rooting-Center tone. Its relationship to other tones on the fretboard, particularly it’s relationship to the melody strings, is not consistent enough to use as a primary referent.       Figure 8     Figure 9       In the end then, I chose not to use the tone on String-6 as my central reference (Rooting Center), and then had to choose between either the tone on String-7 or String-1. Again, I ultimately chose to use the tone on String-1. Side-note; In standard tuning, the note on String-1 is exactly midway between the two notes on String-6. That is, 6 frets above, or 6 frets below the tone on String-6. See Figure 9 again. Note the 2 black diamonds on String-6.  They are 12 frets apart from each other, or one octave. Then notice to black diamond on String-1. It lays exactly midway (6 frets) between the 2 black diamonds on String-6. Also note the octave relationships between the notes on Strings 1 and 6 (see Figure 10). The tone on String-6 that lies closer to the nut is two octaves lower than the tone on String-1 fret 6. With those preliminary discussions out of the way, we will return now to studying the Stick’s Pattern of Unisons and Octaves.       Figure 10       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 (however you choose to envision it) can be aligned/rooted on any the Stick’s first twelve frets. Using the tone on Sting-1 as our Rooting-Center, aligned to fret-1 = tone G, fret-3 = tone A. In the majority of cases, the pattern will occur broken or split somewhere between the nut and twelfth fret. That is, a greater or lesser part of a repeat-pattern will appear above or below the rooting-center. The rooting-center is simultaneously: the beginning, the end, and the centering-point of the pattern. Given that the pattern is repeating, above and below 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 on a Stick, 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 11. 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 of String-1) hence which tone the pattern is aligned for and representing. See the Rooting-Centers Alignment Key Figure 12. 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. Rooting Center is the note on String-1 (lowest pitched Melody string), but the 3 grayed tones in each isolation (3 lowest pitched tones) can be associated to each other. You'll find this useful in key of G , for example, where the Unison G on String-6  (of the G on Sting-7 at the nut which is not usable (is dampened) on the old Sticks) will be useful. *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 (or dampened) strings.     Figure 11           Figure 12       This illustrative device, 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 motivatednow 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 Five and Seven Degree Calculation Lines. [We have in fact been doing this all along already, every time we’ve used chromatic numbers in any of the preceeding drawings.] 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 10 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. Numbering  octave and unison tones In the preeceeding illustrations, we’ve already been assigning 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 renumbering 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, then thirty-six degrees — spanning a total of three octaves, the maximum range possible within either logical tuning-half of the Touch-Style fretboard. Note, when you cross logical tuning halves of the fretboard, adding up the total possible octaves of pitch range, you’ll find at least four octaves (48°) of available tones. 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°, 36°, or 48° 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.       Note; the Pattern of Unisons and Octaves for tapping fretboard instruments is somewhat abbreviated here compared to other iterations of it on this web site. There would be just too many drawings required to adequately cover 8, 10, and 12 string instruments, in two tunings each, plus the exponential increase in necessary pattern study due to the mixing of 4ths and 5ths tunings within a single instrument (in some tunings). Specifically, the special circumstances that arise when you cross over between logical tuning halves. [we saw some of this earlier in the Constellations of Unisons and One-Octave intervals across logical tuning-halves drawings.] But you’ll have more that enough material and information to get started, and plenty of blank fretboard grids to make as many of your own drawings as needs (for the instrument and tuning of your choice). You can use any other iteration of the Pattern of Unisons and Octaves (found elsewhere on this web site) as the basis and model for the kinds of patterns and relationships you might want to isolate and learn about. Remember, 5ths is like mandolin, 4ths is like guitar or bass. This concludes The Cipher for Stick and related instruments       Page   1   2           Index of The Cipher for Stick: 3 Minute Introduction for Stick Commonsense String Numbers for Stick Number formula translation tables: intervals, scales, and chords 5° and 7° Degree Calculation Line for Stick Cipher Demonstrations for Stick Pattern of Unisons and Octaves for Stick Notes of tapping fretboards spelled (and PDF) Blank tapping fretboard grid paper in PDF: 8, 10, 12     Up to Top of page