## The Music(al) Box

Over the last few weeks we’ve been looking deeply at the proportions used in the design of medieval furniture (and music, architecture, art, and several other evidently disparate fields). Kicking off this series was the layout of a vielle, a medieval musical instrument. Today we’re going to have a look at our boarded chest project from July and look not at the measurements in inches, but in proportion.

When I set about laying out the design for this piece, I did so with a basic proportion set in mind. The measurements in inches were plugged in after the fact to approximate some common whole number ratios.

Height to Width proportion is 2:1, inside the shoulders.

We’ll start looking at the end, as this is the basis of the entire proportional system. The width of the chest is one module. The height is 2M. The thickness of the faces and lid were not included in the proportional layout. In extant pieces, sometimes the thickness of a lid is counted in the layout, and sometimes it is not. Physically, since we ended up using dimensional lumber, one module (M) should translate to 11 1/4″. Since the overlap of the shoulders weren’t part of the original layout, 1M is something closer to 9 3/4″.

Next up, we go to the length of the chest. The circles identify the overall length as about  3 times the width (between shoulders), or 3M. According to Boethius, this proportion is a Triple, 3:1. The ratio of height to length, however, is about 3:2, a musical Perfect fifth. The face boards are also share the overlap of 1/5th M with the sides to create the shoulder.

The chest came out to 30″ in length, which is actually a little long of the proportional system. This is in part due to the inelegance of translating to inches and feet for simplicity, rather than staying with purely relative dimensioning. Given the actual width of dimensional 1×12, the proportional measurement for length at 3:1 should be 33 3/4″, including shoulders.  Saying 30″ was “close enough” of a simplification for the educational example, and is in proportion of the width between the face boards when looking at the side. If one were to change the actual cut length from our earlier design, the dimensions of the box will come out to slightly more pleasing.

Another length that might appear appropriate to the width of these boards might be 45″ for a long chest (double octave, 4:1), or a shorter chest that has a height equal to it’s length. Choosing instead to operate using perfect fifths (3:2) which is far more common in application of Boethean Proportioning, the chest body should be about 16 7/8″ in height, 11.25″ in width, and have a related length. The thickness of the lid would then bring the total dimension to something closer to 18″. But, this proportional set would have resulted in some very odd divisions of an inch for the cut list. Considering ease of production for the absolute pragmatic woodworker, the proportion set was moved to be 2:1, 3:1 for the major elements, with 3:2 becoming relative to the construction of the entire piece.

The location of the hinges on the back also are determined by the same proportional system. In this case, we approximated dividing the back into thirds, with the width of the hinges being split on either side of 1/3 of the length. Hinges seem to be typically placed here, or at 1/5th the length from each end, and sometimes having a third hinge somewhat centered along the back.

Even the locations for the nails are approximated on a Boethian Ratio for layout, usually 1:1 at a descending interval, or divisions of four.

There were a lot of short-cuts and simplifications taken with this design, as the purpose was to provide an easily constructed, period appropriate, boarded chest with a minimum of tools, expense, and effort without sacrificing on durability to form. Not expecting the majority of other re-creationists would take the time to layout with dividers; the translation to inches, and at most measurements in quarters of an inch, resulted in an approximation of the historically appropriate Boethian Modes that comes out a little “fat” of where they should.

As we move into more interesting applications of these proportions, the basics of design examined here are a good starting point.

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### 3 Responses to The Music(al) Box

1. imre sziebet says:

Hi,
I have greatly enjoyed the entire six board chest series and look forward to more like it. I do have questions about this article since the choice of where to apply the ratios seems arbitrary. Why not use the entire surface of one of the sides as the definition of one of the ratios? Second, the ratios you picked do not seem to represent what was actually done. For instance, the chest portion, i.e. the part that holds the goods that the chest is meant to protect is much smaller than the footprint allows and the photos of actual examples show that that was not generally done. The “legs” are much taller than usual. I would also appreciate a discussion on thickness of material particularly in areas where negative space is involved. Thanks for all your researches.

• You are very much correct, there are a good number of weirdnesses involved in this design. As explained in the article, some of these were due to the design needing to fit the requirement of being made from easily available lumber. In the U.S., this tends to mean the widest stock we can acquire is 11.25 inches (28.57 cm) wide. If the design were to have more storage space, it would have required edge joining additional boards to the front and back. While this would be more in line with extant examples, it is a slight leap from an absolute beginner project.
Were the whole chest shortened to have the storage body to “leg” height be proportionally more like most Medieval and Renaissance examples, the result would have been quite squat. Folks have a tendency to like sitting on these things, which suggests a certain height for comfort.
Figuring the proportion sets involved was worked from two directions. In most cases, I actually took a set of dividers to photographs and “walked out” the comparisons. The variations from the apparent ratios is assumed from added thicknesses of adjoining boards, lids, and in some cases decorations and finishes. I started down this path some years ago trying to find the Vitruvian proportions in Medieval Furniture. Discovering that Vitruvius’ set of dimensions were outre until the 16th Century, and that it was the Boethian Sets which had preeminence (with a handful of caveats for certain times and places) was something of a surprise to me.

• imre sziebet says:

Thanks for the help.