A Master Class by Elon S. Howe Reverse Graduation of the Violin’s Top Plate

The VMAAI and the MVA Journals is about Sharing

Figure 1: Was a try in making a better violin: (to view better Zoom 200%) The # 85 violin top wood, “For Reverse graduation”, Has to be light, has to have a high cross-wise grain stiffness, compared to the length-wise stiffness, as said by Edward Campbell at the 2004, Work-Shop, when ask about this “reversed graduation of the +/- 60% of the Antonio Stradivari violin top plates. (After 2003 I Started the long walk to try to learn “the Violin MORE”). (See Ref. 1) This wood was cut in the 1995 +/-, Engelmann Spruce in Idaho by Evan Smith. As here illustrated the center flat level 75mm or 3 inch wide, the thickness of 16mm, taper down to the edges @ 6mm. The tap tones, and mode testing fine length-wise stiffness E-5 @ 540 HZ, and the Cross-wise E-2 @ 715 HZ., that’s greater than most when compared to E-5 as in this perspective sized blank. The water test finds this wood has a .33% weight compared to water. This researching of this cut to size blank of wood will “or” may tell what this wood, is not, or has the right (high) rating for the violin top plate. Thus “knowing” the wood “More” before, you start making the violin top plate from it!! “Sorry” the Violin making, never was a “Guessing Game.”

Figure 2: Science of the Violin’s form Design begins with the 360° circle divided by 13 parts of “Fibonacci” numbers, as illustrated here. The Geometrical Measured Facts of This # 85 Violin’s Design is of Fibonacci numbers 0-1-1-2-3-5-8-13 (see the Fibonacci, 0-13 rule on the left side = 349.31mm, length of this geometrical rectangle, 1/13th = 26.87mm) that’s “Near” a completed Top Plate is the Geometrical (PHI- see the College Dictionary for PHI, and Φ) Proportion of the Golden Rectangle 8 0f 13 “Fibonacci” numbers, as to the 1721 Antonio Stradivari “Kruse” Violin “copy” of a one to one, PHI-Φ- intersect to intersect of all A- .618-C-Φ .382– B measurements. Note this plates corners are PHI- Φ “Geometrically” Positioned as to the under laying design Print, the same as did by Stradivari. At this stage in construction the plate wood arching between the upper F-holes is +/- 15.8mm – 16mm thick. And this plate is a near to the Exact craftsmanship of point-point to, The under lay “Design Print” of the “Fibonacci” 0-1-1-2-3- 5-8-13 Rectangle of Architectural Design of the Stradivari 1689 P-G violin Form was redrafted from my “design” of the Stradivari 1689 Violin’s P-G form in 2008, by an Architectural Engineer Lewis Fowler of Michigan, was also a Luthier. This “print and geometry” has been critiqued and confirmed by Mathematician, John F. Putz of Alma College in Michigan. (Ref. 2)

Figure 3: The thickness is 3.3mm in the f-hole area, and the tap tone is at E-5 (length-wise) @ 387 HZ. and the E-2 @ 184 HZ as illustrated is ready for the f- holes, and the Base-Bar placements. As illustrated, this node E-5 nodal pattern is near to PHI-Φ one half of the upper, lower Bouts, about as good as needed. Note the F-holes @ +/- 2mm hole was dilled, that was geometrical PHI-Φ positioned before graduation, on the flat inside projective plane of this plate. The arching at the plane stage was near 16mm, between the upper holes. “Note” Stradivari positioned the lower f- holes in a none vibration point of the free top plate.

Figure 4: This plate very near completed, edges need to be match to ribs, at this stage the outer side arching has been graduation has been lowered +/- .4mm down to a thickness of 2.4mm near the Bridge area, the sound post patch (hard Maple) is +/- .3mm thick, into the plate thickness at this point is at 2.4mm, thus be- comes a (more like) a reversed graduation Stradivari top plate. This E-5 nodal line is @ 370 HZ. for the length-wise stiffness. “Note” the bass side of this bass bar, is +/- PHI-Φ .618% of the upper, and the lower bouts cross-wise widest widths. Wt. 64 gm, less when edges are sized down to 2.5mm over the ribs.

Figure 5: This view, illustrates the Cross grain stiffness tap tone by the nodal pattern @171 HZ. Note the sound post patch simulate the old repaired Stradivari violin top plate. Also not shown on the outside of this plate Bridge feet cleats placed as were placed on most of my winning violins at the VMAAI Comp., are for reinforcement in that very thin area! (Note before the back plate is glued on this violin I Sign on the spruce wood and date this top plate as illustrated on the upper left bout, as shown here), note is history as the date on this photo .

Figure 6: This plate “was” as illustrated by PHI-Φ geometry, and is, as the same geometrical match to the top plate of the 1721 Stradivari “Kruse” Violin as published by the Strad Poster of 2006, and are the same as to the Geometric over lay, of the four Spheres, and the “Hexad” all of the order of 6/13, @ 161.2mm of 3/13, 6/13, and 9/13, in RED color, setting the Hexad’s center at 6/13, intersection 161.2 downward, near the center of the upper F-holes. In Greek this Hexad (hexagon) is called the “Structure-Function- Order”, as here position in the mechanical function area, between the C-Bouts corner blocks reinforcement perspective of this top plate. Also note this Order of 6 Diagonals lines confirm the U-B, and L-B of the Strad P-G form widths. “Also review View 2”. For more Zoom to 200%, or print a hard copy, and check it out all A-CΦ-B measures to the mm as here illustrated, note 9/13 center intersection mark-Φ, is the C Divine pin point of this A to B Diagonal, of the upper bout cross line, down to the saddle horizontal line of this 8 by 13 Golden Rectangle. Next note the Stradivari “Geometrical” “G” is to “Right” of the 9/13 intersection, and is right where Stradivari positioned it on His “G” F-hole Template rectangle sheet of paper, when this “G” F-hole template is over laid this top plate, with the paper upper edge positioned at the plate upper bout cross line. “Note” the PHI-Φ Bridge position was placed by the compass pin point at the center of the upper bout, the radius to 8-13 rectangle’s upper corners, by the 360° intersect the two Phi-Φ of 5/13th, downward on the Golden Rectangle, pin points the Bridge at 192mm below the plate upper edge.

Figure 7: The upper perspective projective illustration of the plate arching. The lower plate’s illustration of the center area between the Bouts. The last graduation is illustrated in “BLACK” on the top of this plate, lowering the thickness to 2.4mm, lowering the tap tones to E-5 @ 370 HZ, and E-2 @ 171 HZ. And “Perhaps” was the method that “May” have been used by Stradivari when he made violins. This perspective is when mass is removed on the plate outer arch side, is a flatten of the arch between the corners, and “the arch flatting” is lowering the plate the “E-5” tap tone node stiffness much faster than on the inside, as to the flatting of the plane of the plate arch stiffness in the “Mechanical function of the Bridge area”, adding more projection power of sound to this violin. This perspective is from the facts finding of top plate blank of the wood in View 1. That can point to the graduation method that can be used in the first steps in making a Violin’s top plate.

Figure 8: Feel free to Zoom – 300% to critique all, this violin will be at the full size, on a 18” by 12’’ window. This # 85 Violin is over laying it’s Geometrical Design and ready to be Varnish, after cleaned, scraped, and Horse-tailed, Ground Gypsum mixed with Liquin, will be brushed in to seal the wood, Horse-tailed, and one more coat of just Liquin brushed on, sanded before varnishing. “Only to my ear”, and Eyes”, as to now, this violin is one of my “BEST”.

Figure 9: The Beautiful Mother Nature’s Tangle With The Music of Proportion, is the “Falling Leaves” of the Science of Music, as old` as “TIME” being to END, of the 13 of 26 (A)-(B) length String! Thus today the violin string full length is one Italian “Braccio” one Human Arm length, Saddle end to Nut Stop, @ 483mm or the “Fibonacci” 144 Punti (one Punti = 3.358mm) x 8 = 26.87mm = 1/13th, of the violin 13, of the Stradivari 1689 P-G = (Proportional Geometry) of the Violin Form length @ 349.31mm, or 104 Punti, when Stradivari made that “Branded” P-G on this Form as positioned as placed on this form at PHI-Φ, of the lower rectangle of the 5 by 8 Golden Section of the 8 by 13 Golden Rectangle of it’s Design. All as the illustrations of Design for the top plate, and the setting of the Bridge position was determined geometrically to the PHI-Φ of the Golden 8 by 13 Rectangle as in Views 2, and 6. (Note when a violin is inter into the VMAAI Comp. the three lower fine tuners will be removed, to bring out “D” 146.83 HZ. tail piece Harmony to “D” 293.67 string, harmonizing with the A-1 air mode @ 466.16 HZ. x .63 = +/-293.58 HZ. the open D string, this is why the D is the only string that will hums, when blowing over the base side F-hole). Also note A @ 440 HZ. is in harmony with B-O & A- O @ C# @ 277.18 HZ., 440 x .63 = C# @ 277.2 HZ.(note.618 = PHI-Φ, The Golden Ratio, of 1.61803 number of the Divine Proportion, Know as the Music of the Spheres, without, it’s just “noise”.

Figure 10: This # 85 Violin in Garden of “DIVINE” Nature, of the 3+3+3 = 9/13 PHI-Φ = 241.56mm, or 72 Punti when Antonio Stradivari made Violins. Also = the 9/13th Φ of the “Pentagram” of 13 by Design: This violin was made to the Strad 1689 P-G form’s perspective of 13 = 349.31mm or 104 Punti when Stradivari made Violins. (one Punti = 3.3541666mm x 144 Fibonacci Order 12) = one Braccio = 483mm (Ref. 3) Thus “today” this violin’s String length from the Saddle to the nut stop, that = one human arm length elbow to longest finger end of +/- 483mm, thus becomes the design of “Divine Proportion” of 1-1-2-3-5-8-13 of 21 of 34 Fibonacci numbers of “MUSIC”: AS to all that played this violin, said it a very powerful, great sounding violin, was one that didn’t hang on the wall very long, Sorry It didn’t make the 2016 VMAAI Comp, Because this 2016 #85 “Miss Corrine” is gone it’s new Home.

Figure 11: The Art of the of Mother Nature, of the Red Maple wood, in Pine Woods of Michigan, and oil varnish drying in the August Sun.

Figure 12: The Beauty of the Divine Φ of Nature, and the Beauty of the Violin #85, ready to Sing Divine Music of the “Spheres”.

Figure 13: The Divine of Nature at the Wood ‘N Strings Violin Shop in the Pines, looking northward out of my dining room window into the Manistee National Forrest, of Michigan, just before Christmas 2016.

Ref.1, May 2003, CAS JOURNAL, “Reverse Graduation in Fine Cremonese Violins” by Jeffrey S. Loen. Page 27—39. Are the Cold Hart Facts of The Stradivari Graduations, of His top plates.

Ref. 2. Mathematician John F. Putz, of Alma College in Alma Michigan, “Music wrote to the Golden Ratio”, See this book, “The Golden Ratio, by Mario Livio, in 2000, see page 187-200.

Ref. 3. See this Book, The Violin Forms of Antonio Stradivari, by Stewart Pollens, 1992, see page 22. “WHY” THE VIOLIN is a “VIOLIN”. All as put, By Elon S. Howe: