Back Mass/Stiffness Tests p.1

Overview

                  In this series of explorations, I am interested in mass and stiffness of the back. I am using an F style mandolin I built in 2007 which is made from the Sitka spruce,  hard maple back/sides/neck, ebony fretboard/bridge, a stamped tailpiece and Gotoh f-style tuners. It is a nice sounding instrument, not particularly loud, but with good tone and fits in the typical range of measurements of instruments I tend to like.  The D'Addario EJ74 strings are a couple weeks old and in the sweet spot as far as tone. I have cut the back off the instrument, installed some blocks in the kerfing and made the back replaceable with 16 #6 screws around the perimeter. I have also used it for experiments and have measured it extensively for the last year or so. This back alteration has not significantly changed the tone or volume of the instrument. So I am starting with a very familiar instrument with well documented initial conditions.

                  The aim of this investigation is to utilize the removeable maple back and run measurements with other backs that differ by being:

p.1) less massive and equal or more stiff

p.2) more massive and equal or less stiff

p.3) more massive and more stiff

                  The materials for these conditions will be 1) a carved spruce back plate with variations of spruce bracing, 2) the original maple back with mass added in a series of disconnected locations (steel washers and poster putty, 3) rims glued/clamped to a marble slab.

Setup

                  The spruce for this back is Colorado Blue Spruce which I have harvested locally, split, aged for 2 years, resawed, joined and carved. This particular piece is very wide grained, somewhat wavy and light. Colorado Blue Spruce has the character and feel of Englemann spruce, and works well as an instrument top. The density of this piece is .355 g/cc. This is on the lower end of the range of spruce according to a few resources (https://www.engineeringtoolbox.com/wood-density-d_40.html, https://www.agriculturejournals.cz/pdfs/jfs/2007/03/05.pdf) . I will apply three coats of shellac to the surface to account for any effect finish might have.

                  I will test this in 3 variations: first as a plain carved plate with no braces, next with a single long brace down the center, and third with 2 additional braces angling out from the neck toward the tailpiece.  Because I am trying to keep the mass low and stiffness high, I will make the braces tall (3/4" in the center tapering to 0)  and skinny (3/16") with a triangle cross-section. Tone bars are fit well enough to be attached with hot glue in the hottest setting for a secure connection that is easy to undo if necessary.

Results Discussion

Initial Conditions

No Braces: Mass change -45%, stiffness -30%

Tone generally got more lively, more treble but not harsh. Presence increase. Some loss of power on the e string, especially frets 5 and above. Lower notes feel less punchy, less power behind them, more tubby and kind of boomy. Defiitely knocked it out of balance toward the G strings, lower end. Overall this is not as big a change as I was expecting. Also, brand new wood on the back may not be "broken in" which will be a consideration for all variations in this trial.

One Brace: Mass change -40%, stiffness -15%

Marked increase in attack, punch and bottom end drive. Highs are clearer and more powerful too. Improvement from last one and even from original conditions. Chops have guts, bouncy. I really like it.

Three Braces: Mass change -32%, stiffness +12%

I had to replace 2 broken e strings, think it's fine. Not a ton of improvement from last one. Highs are a little more subdued. In the mids lost some sparkle and not as punchy. Lows still feel pretty strong, potentially even improved in punch and clarity. Nearly as nice as the last version but maybe one notch lower in the overall. I think the nature of the angled tone bars going across the cross dipole kills that frequency somewhat and I think is the source of the losses in the upper mids (600-100Hz).

                  I decided to check which modes were active using Chladni patterns. It was very difficult to get a clear Chladni pattern with the three braces, but much more active with the 1 brace and none. Interestingly the frequency is basically unchanged despite major change in stiffness and some mass added. Through sweeping the whole spectrum up to 2,000 Hz, the cross dipole was the only mode I could get the spruce back, in any variation, to show clearly (except in the three brace version which was not very clear).

Back cross dipole with no bracing: 622 Hz

Back cross dipole with 1 brace: 620 Hz

Back Cross dipole with 3 braces: 621?? not sure about this...

I have some good insights from this trial in context of the next two, so I will share the take-aways all at once after I’ve published all three trials.