R L Seven Degree Calculation Line for Mandolin, Tenor Banjo, and Violin   (or Perfect-Fifth reference line)     Fretboard Interval Calculator     Before reading this be forewarned that I use Commonsense String Numbers in all explanations. Mandolin specific drawing here. The Cipher System's translation tables of musical materials and formula are useful by themselves for the insights they provide.  To understand, at last, that a Major-13th interval spans 21 frets-worth of pitch is a major revelation for most of us. That's a good start, but it’s only the beginning. We still need to hear all of those musical materials, and we need to know how to locate them on the mandolin fretboard. The Seven Degree Calculation Line is a fretboard navigation tool that will help us do just that. The Seven Degree Calculation Line is the key component of the Cipher System for mandolin. Its a device that allows us to transfer and apply the Cipher System’s translated number formula to the mandolin fretboard.  But it is, and does, much more than that. The Seven Degree Calculation Line is also the key to the fretboard itself. Its a map-generator, a combination of movable schematic and counting-grid-overlay that reveals the fretboard's otherwise invisible anatomy with unequaled clarity and speed. It reveals the where, why, and how, of all fretboard patterns. Figure 1 shows the naturally occurring pattern of successive Perfect-Fifth intervals on the mandolin fretboard in standard tuning.  Each pair of adjacent dots (isolated from the full pattern at the far left) form and are Perfect-Fifth intervals spanning seven half-steps, seven frets, or seven degrees of pitch.     Figure 1       The pattern can be viewed two ways: in parts (as above) or as a whole, i.e. one continuous pattern, as follows. Given that Perfect-Fifth intervals encompass seven half-steps of pitch each, the pattern of P-5ths can be approached additively from its beginning to end (i.e. 7 + 7 = 14, 14 + 7 = 21.).  Numbered that way, the pattern can be used as a Seven Degree Calculation Line. See Figure 2.     Figure 2       As the pattern progresses (left to right, G to E string, first to fourth string [using Commonsense String Numbering Order]) each successive dot represents a seven half-step, seven fret, or seven degree raise in pitch (relative to the dot the precedes it). From the tone at the zero degree starting point, we can jump across the pattern in seven degree increments, continually widening the interval to a maximum of 21 half-steps — just under two octaves (two octaves = 24 degrees). The Seven Degree Calculation Line is only the baseline or reference-line of a larger device. Its ultimate function is to help us identify the number values (interval widths) of all points (neighboring tones) above and below the line, linking and servicing any area of frets. The Seven Degree Calculation Line (therefore) becomes the center or baseline of a counting-grid. See Figure 3.     Figure 3       The Seven Degree Calculation Line is more than a single thing: First, the Seven Degree Calculation Line is movable vertically. It can be positioned (visualized/overlain) at any fret-line. i.e. anywhere up and down the length of the fretboard. Second, the zero-point is movable horizontally across the fretboard. Zero-degrees (the tonic or root) can be moved and placed at any point along the path-line of the greater Seven Degree Calculation Line. i.e. on any string (one through 4). By moving the zero-point (horizontally), 3 or 4 variations (numerations) of the Calculation Line emerge. See Figure 4. [note; all variations shown in Figure 4 should be imagined superimposed upon each other — as if taking place within a single fret-line simultaneously]. Where-ever the zero-point is moved to, that tone becomes the new tonic/root (zero), (the count begins anew), and the pattern continues as before — following the same straight-line path, and (again) gaining seven degree raises in pitch with each jump to right. When the zero-point is moved horizontally, any strings and tones to the left of zero are (for that moment) “off the grid”/out of action. That is, until the zero-point is moved again to any tone residing on those (unused) strings.     Figure 4       Given that there are four variations of the Seven Degree Calculation Line — one for each of the four horizontal points (strings) that could be called zero degrees — there are also four variations of counting-grid. Each version of Seven Degree Calculation Line generates his own unique counting-grid — but on mandolin, all iterations are essentially the same, unlike the guitar. See Figure 5.     Figure 5        Everything you've seen here and all that follows is natural (innate) to the mandolin fretboard — including the Seven Degree Calculation Line (being, simply, the mandolin’s built-in pattern of successive perfect-fifths). The Seven Degree Calculation Line(s) and counting grid(s) simply make the mandolin’s natural patterns clearly visible to us, and because those patterns are rendered with counting numbers, they are clearly and immediately understood. The Seven Degree Calculation Line, “zeroed” (rooted and aligned) at a chosen tonic or root, functions as a reference line — the centerline of a counting-grid. The pitch and number-value of tones above and below the centerline are gauged and determined relative to the tone at zero-degrees and the other tones on the reference line. The numbers of any Cipher Formula are then plotted on the fretboard's natural grid of coordinates, vertical strings and horizontal frets, with the Seven Degree Calculation Line as the central calculation reference or plotting baseline. Plotting can be done directly on the fretboard (by visualizing the grid and either counting mentally or using your finger) or drawn on paper-grid facsimiles of the fretboard. [Sheets of blank mandolin fretboard grids (4 string grids) are available on the Free page in high quality PDF format.] Tone-plotting with the Cipher Formula and Seven Degree Calculation Line is straight forward and simple to do. Navigating the Grids (see Figure 5):     Vertical movement within any grid (i.e. up or down the neck on any string) changes the pitch and number-value of a given tone (or interval) one half-step (or one degree) per fret of movement in either direction. Horizontal movement across any grid (i.e. parallel with a fret-line and following the path of the Seven Degree Calculation Line) from one string to another changes the pitch of a given tone (or width of an interval) and it’s number value by a quantity of seven — seven half-steps, seven degrees, seven frets-worth of pitch change per jump i.e. per string or per horizontal move (in either direction). Having a movable calculation reference-line, with it’s floating zero-point, means that you can build or visualize a counting-friendly grid from (and around) any tone on the fretboard. By combining the Cipher Formula, the Seven Degree Calculation Line, and knowledge of the mandolin’s Pattern of Unisons and Octaves one can explore, manipulate, and understand the full range of fretboard patterns with ease and confidence. Please turn to the Mandolin Cipher Demonstrations Index of The Cipher for Mandolin (Tenor Banjo and Violin): 3 Minute Introduction for Mandolin Commonsense String Numbers for Mandolin Number formula translation tables: intervals, scales, and chords Seven Degree Calculation Line for Mandolin Cipher Demonstrations for Mandolin Pattern of Unisons and Octaves for Mandolin Triads on the Mandolin fretboard (two pages) Scales, Major and minor, in parallel, on the Mandolin fretboard Chord Progressions for Mandolin (Triads of Major) Notes of Mandolin fretboard spelled Blank 4 string fretboard grid paper in PDF         Up to Top of page